June 2013 

NASA/CR–2013-218005 

Large Civil Tiltrotor (LCTR2) Interior Noise 

Predictions Due to Turbulent Boundary Layer 

Excitation 

Ferdinand W. Grosveld 

Northrop Grumman, Langley Research Center, Hampton, Virginia 
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June 2013 

NASA/CR–2013-218005 

Large Civil Tiltrotor (LCTR2) Interior Noise 

Predictions Due to Turbulent Boundary Layer 

Excitation 

Ferdinand W. Grosveld 

Northrop Grumman, Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
1 

TABLE OF CONTENTS 

INTRODUCTION ......................................................................................................................... 4

VEHICLE DESCRIPTION ........................................................................................................... 4

CABIN DESIGN ........................................................................................................................... 4

PREDICTION SCHEME .............................................................................................................. 5

CABIN SIMULATION MODELS ............................................................................................... 6

Low Frequency Hybrid FE/SEA Models .................................................................................... 6

Structural Finite Element Models ........................................................................................... 6

Poro-Elastic Finite Element Method (PEM) Models .............................................................. 7

Acoustic Finite Element Models ............................................................................................. 9

High Frequency SEA Models ..................................................................................................... 9

Structural SEA Model ............................................................................................................. 9

Acoustic SEA Model .............................................................................................................. 9

EXCITATION MECHANISMS ................................................................................................. 10

Turbulent Boundary Layer Excitation ...................................................................................... 10

Cockburn and Robertson ...................................................................................................... 10

Efimtsov ................................................................................................................................ 11

Turbulent Boundary Layer Excitation Comparison with Measured Data ............................ 12

ANALYSES ................................................................................................................................. 12

Low Frequency Hybrid FE/SEA Analysis ................................................................................ 12

Structural Modal Response ................................................................................................... 12

Acoustic Modal Response .................................................................................................... 13

Poro-Elastic Modal Impedance Matrix ................................................................................. 13

Cabin Interior Noise Predictions ........................................................................................... 13

High Frequency SEA Analysis ................................................................................................. 14

LCTR2 Analysis Results for the Consolidated Frequency Range ............................................ 15

Bombardier Q400 Predictions Compared with Measurements ................................................ 16

SUMMARY .................................................................................................................................. 17

ACKNOWLEDGEMENTS .......................................................................................................... 17

REFERENCES ............................................................................................................................. 17

TABLES ....................................................................................................................................... 19

LIST OF TABLES 

Table 1. Design parameters for the LCTR2. ................................................................................. 19

Table 2. Section properties of the longitudinal stringers, ring frames and floor support beams. . 19

Table 3. Mechanical material properties of the skin, ring frames and longitudinal stringers. ...... 19
2 

Table 4. Dimensions of the cells in the honeycomb core of the floor panels. The geometric 

parameters a, b, t, d and φ are defined in Figure 6. ....................................................................... 20

Table 5. Three-dimensional orthotropic material properties of the floor honeycomb core. ......... 20

Table 6. Two-dimensional orthotropic material properties of the floor fiberglass face sheets. ... 20

Table 7. Mechanical material properties of the floor surface panels, the trim panels and the 

overhead bins. ............................................................................................................................... 20

Table 8. Biot properties of the floor porous material layer, the fuselage trim melamine acoustic 

foam and the foam in the seats. ..................................................................................................... 20

Table 9. LCTR2 cruise flight conditions. ..................................................................................... 21

Table 10. Attached turbulent boundary layer thickness as function of distance from the LCTR2 

nose. .............................................................................................................................................. 21

Table 11. Empirical constants used in the Efimtsov turbulent boundary layer model. ................ 21

Table 12. Boeing 737 flight test conditions. ................................................................................. 22

Table 13. Number of acoustic and structural modes in the one-third octave bands 5–160 Hz. ... 22

Table 14. Frequencies of acoustic and structural modes below 20 Hz. ........................................ 23

Table 15. Bombardier Q400 cruise flight conditions.................................................................... 23

LIST OF FIGURES 

Figure 1. Isometric and three-view of the Large Civil Tiltrotor (LCTR2) design. ....................... 24

Figure 2. Artist’s rendering of the LCTR2 concept vehicle in forward flight. ............................. 24

Figure 3. Sketch of a hypothetical LCTR2 90-passenger seating layout. ..................................... 25

Figure 4. LCTR2 cabin cross-section showing four-abreast seating and overhead bins. ............. 25

Figure 5. Basic finite element model of the fuselage skin, ring frames, longitudinal stringers, 

floor, and floor support beams. ..................................................................................................... 26

Figure 6. Rectangular unit cell of the honeycomb material. ......................................................... 26

Figure 7. Rudimentary Porous Elastic Finite Element Method (PEM) models for the seats, 

overhead bins, floor covering and interior trim. ........................................................................... 27

Figure 8. Cross-sectional view of the PEM models for the seats, overhead bins, floor covering 

and interior trim. ........................................................................................................................... 27

Figure 9. Diffuse field absorption coefficient of 0.08 m thick melamine acoustic foam with a 

rigid wall boundary condition. ...................................................................................................... 28

Figure 10. Shortest wavelengths as function of one-third octave band frequency for three poroelastic materials with the Biot material properties listed in Table 8. ............................................ 28

Figure 11. The forward and aft acoustic cavities above the floor relative to the tiltrotor plane. .. 29

Figure 12. Fifty seven 1.16 m wide structural subsystems (shrunken for clarity), including the 

floor panels and the curved ribbed skin sections above and below the floor. .............................. 29
3 

Figure 13. Thirty-eight acoustic cavity sections relative to the tiltrotor plane. ............................ 30

Figure 14. Typical measured average commercial airplane cabin absorption coefficient [15]. ... 30

Figure 15. Cockburn/Robertson and Efimtsov predictions compared with flight test 

measurements of turbulent boundary layer pressure fluctuations on a Boeing 737 aircraft [20]. 31

Figure 16. Isometric view of the first structural mode of the fuselage at 9.07 Hz. ...................... 31

Figure 17. Cross-sectional view of the 9.07 Hz structural fuselage mode. .................................. 31

Figure 18. Isometric view of the first acoustic (axial) mode at 5.7 Hz. ........................................ 32

Figure 19. View of the first cross-sectional acoustic mode at 73.8 Hz. ....................................... 32

Figure 20. Cabin average of the mean narrowband (1 Hz) LCTR2 cabin sound pressure levels 

forward and aft of the tiltrotor plane for the Efimtsov boundary layer excitation predicted with 

the low frequency hybrid FE analysis. .......................................................................................... 32

Figure 21. Second-order axial acoustic resonance at 11.6 Hz. ..................................................... 33

Figure 22. First-order axial structural resonance at 11.3 Hz......................................................... 33

Figure 23. First-order axial structural resonance at 11.5 Hz......................................................... 33

Figure 24. Cabin interior sound pressure level distribution in the 12 Hz band. ........................... 33

Figure 25. Third-order axial acoustic resonance at 17.6 Hz. ........................................................ 33

Figure 26. Second-order axial structural resonance at 17.3 Hz. ................................................... 33

Figure 27. Second-order axial structural resonance at 18.7 Hz. ................................................... 34

Figure 28. Cabin interior sound pressure level distribution in the 17 Hz band. ........................... 34

Figure 29. Acoustic resonance (89.2 Hz) with a vertical nodal line in the tiltrotor plane. ........... 34

Figure 30. Acoustic resonance (128.9 Hz) with a horizontal nodal line in the tiltrotor plane. ..... 34

Figure 31. Estimated modal density in the 100 Hz through 8000 Hz one-third octave bands. .... 34

Figure 32. SEA predicted one-third octave band LCTR2 subsystem sound pressure levels and 

their average for the Cockburn/Robertson turbulent boundary layer excitation. .......................... 35

Figure 33. SEA predicted one-third octave band LCTR2 subsystem sound pressure levels and 

their average for the Efimtsov turbulent boundary layer excitation. ............................................ 35

Figure 34. Averaged one-third octave band LCTR2 sound pressure levels predicted with the 

hybrid FE analysis (20-125 Hz) for the Efimtsov boundary layer excitation, and with SEA (125-

8000 Hz) for both the Efimtsov and Cockburn Robinson models. ............................................... 36

Figure 35. SEA predicted cabin interior sound pressure levels in the 125 Hz one-third octave 

band due to Efimstov turbulent boundary layer excitation. .......................................................... 36

Figure 36. FE predicted cabin interior sound pressure levels in the 125 Hz one-third octave band 

due to Efimstov turbulent boundary layer excitation. ................................................................... 36

Figure 37. Averaged predicted LCTR2 one-third octave band sound pressure levels compared to 

measurements in the Bombardier Q400 aircraft. .......................................................................... 37

 
4 

INTRODUCTION 

The Large Civil Tiltrotor (LCTR) is a conceptual vehicle that was developed under the 

NASA Heavy Lift Systems Investigation1

 as an economically competitive alternative to medium 

range regional airliners that could significantly relieve runway and terminal area congestion. The 

tiltrotor design combines the speed, altitude and range of a turboprop airplane with the vertical 

lift capability of a helicopter thereby freeing up existing runways for use by larger and longerrange aircraft. A second-generation configuration of this vehicle, designated LCTR2 (Figure 1), 

has a design goal to transport ninety passengers over a distance of 1800 km at a speed of 

556 km/hr. The LCTR2 was used as a representative vehicle design and mission under the 

NASA Fundamental Aeronautics Program (FAP) Subsonic Rotary Wing (SRW) project.2,3

Several high risk areas have been identified for the LCTR2 configuration, such as the need for a 

high torque, low weight drive system and a high performance, structurally efficient rotor/wing 

system. Interior noise is expected to be distinctive due to the very low blade passage frequency 

of the four-bladed rotor (as low as 6.75 Hz during cruise conditions), the presence of a mid-wing 

gearbox and the turbulent boundary layer excitation during cruise flight conditions. When 

combined with the anticipated use of lightweight composite and sandwich materials in the 

fuselage sidewall, achieving acceptable interior noise levels in the LCTR2 will be challenging. 

Previous efforts4

 to predict the interior noise environment focused on the transmission loss 

characteristics of a notional LCTR2 sidewall structure. The materials and lay-up of this 

hypothetical sidewall were chosen to be similar to a Bombardier Dash-8 Q400 fuselage section5

for which limited interior noise measurement data are available in the literature.6 The objective 

of the present study is to perform a preliminary assessment of the interior noise environment in 

the LCTR2 with this notional sidewall due to turbulent boundary layer excitation during cruise 

conditions. The analysis frequency of interest extends from 6 Hz through 8000 Hz. Interior noise 

due to thickness and loading noise from the rotating blades and mechanical noise radiated by the 

mid-wing gearbox will be the subjects of a future investigation. 

VEHICLE DESCRIPTION 

Isometric, top, front and side views of the ninety passenger second-generation LCTR2 design 

are presented in Figure 1, while an artist’s rendering of the LCTR2 concept vehicle in forward 

flight is shown in Figure 2. Cruise operating altitude of the vehicle is 8,534 m. Each of the two 

tiltrotors has four blades with tip speeds of 107 m/s and helical tip Mach numbers of 0.61 during 

cruise. The rotational speed of approximately 102 rotations per minute (rpm) yields a blade 

passage frequency of 6.75 Hz. The design parameters for the LCTR2 are listed in Table 1. 

CABIN DESIGN 

The LCTR2 is a conceptual design and no details of the fuselage sidewall, materials, cabin 

arrangement, overhead bins or interior trim have yet been established. To enable preliminary 

assessment of the interior noise for this study, the notional fuselage construction and geometry, 

including the skin, the ring frames, longitudinal stringers, bulkheads, floor, floor support beams, 

sidewall trim panels and noise control/thermal protection treatment were chosen with dimensions 

and material properties typical for an aircraft of that size and range, such as a proposed stretched 
5 

90-passenger seating variant of the Bombardier Dash-8 Q400.7 A hypothetical layout of the 

LCTR2 fuselage including seats, seat pitch, lavatory, galley, and baggage areas is sketched in 

Figure 3. The passenger cabin is 2.68 m in diameter and is assumed to start at the door to the 

flight deck, 3.66 m from the nose of the vehicle, and end at the aft bulkhead for a total length of 

22.04 m. A notional cross-section of the LCTR2 passenger cabin is presented in Figure 4 

showing four-abreast seating and two overhead bins. The maximum height in the cabin is 

1.95 m. The nominal seat pitch is 0.79 m and the aisle was designed to be 0.40 m wide. 

PREDICTION SCHEME 

A prediction scheme was established to compute sound pressure levels in the interior of a 

simplified cabin model of the LCTR2, while being excited by a turbulent boundary layer flow 

over the fuselage. Structural and acoustic finite element models were created in MSC Patran 

2012 64-bit8

 and the finite element geometries were imported into the VA One9 vibro-acoustic 

analysis program. The fuselage structure, the cabin acoustic space and the cabin interior poroelastic components were modeled in VA One as energy transmitting, storing and receiving vibroacoustic systems. The external turbulent boundary excitation was represented as a fluctuating 

pressure spectrum consistent with semi-empirical turbulent boundary layer excitation 

predictions. The properties of the turbulent boundary layer were specified at nineteen axial 

sections of the fuselage structure to capture the evolution of the excitation in the flow direction 

as the boundary layer thickness changes. The sound pressure levels in the cabin were predicted 

employing different approaches for the low frequencies, 6-141 Hz with a 1 Hz analysis 

bandwidth, and the high frequency 125-8000 Hz one-third octave bands. The 141 Hz is the 

limiting frequency in the 125 Hz one-third octave band allowing comparison between the low 

and high frequency analyses in the overlapping 125 Hz one-third octave band. 

At low frequencies, where acoustic and structural wavelengths are long compared to the 

dimensions of the sidewall structure and interior cabin, the vibro-acoustic response is 

deterministic and can be described by modal interactions between the structure and the interior 

acoustic space. Representative finite element models require a minimum of 4-6 elements per 

wavelength to produce accurate results and, consequently, their mesh densities define the upper 

frequency limit for the low frequency analysis. A modal analysis of the fuselage structure was 

performed in MSC Nastran10 and the modal parameters and the mode shape deflection 

information were imported into the VA One program. Rigid-boundary acoustic modes were 

computed in VA One and were coupled with the in-vacuo modes of the structure by velocity 

continuity boundary conditions at their interfaces. Although the structural components and the 

acoustic space are modeled using finite elements, it is computationally efficient to use a 

stochastic representation for the sound radiated outward from the fuselage into the surrounding 

fluid. This is accomplished within VA One by using a hybrid method,9

 which combines Finite 

Elements (FE) with Statistical Energy Analysis (SEA) subsystems. Specifically, a stochastic 

semi-infinite fluid (SIF) is attached to the externally radiating face of the FE structural model as 

a radiation impedance to capture energy transfer propagating away from the fuselage structure. 

At the high frequencies, where wavelengths are short compared to the dimensions of the 

structure and acoustic space, it is more efficient and desirable to represent the structural and 

acoustic modes statistically. The VA One SEA method9

 is used to obtain the space averaged 

vibro-acoustic response. The modal density, or the number of modes per unit frequency, and the 

modal overlap, the average number of modes within a typical half-power bandwidth, determine 
6 

the validity of the statistical assumptions in SEA and the accuracy of the computations, which, in 

turn, determines the lowest frequency band of the analysis. 

CABIN SIMULATION MODELS 

This section describes the simulation models created for the low frequency hybrid FE/SEA 

analysis and the high frequency SEA predictions. 

Low Frequency Hybrid FE/SEA Models 

Fuselage cabin simulation models for the low frequency vibro-acoustic analyses include 

structural FE models, Poro-Elastic Finite Element Method (PEM) subsystems, FE acoustic 

cavities, and a semi-infinite fluid (SIF). The PEM subsystems are included to represent the 

impedance of components designed to absorb or reflect sound energy when applied to FE 

surfaces, such as noise control treatments. It was assumed that pressurization affects primarily 

the radiation response of the fuselage skin panels between the frames and longitudinal stringers 

and was not modeled for the low frequency range where global modes of the structure dominate.

Structural Finite Element Models 

The cabin structural models include the skin, longitudinal stringers, ring frames, floor, floor 

supporting beams, and bulkheads. For these predictions, the notional sidewall configuration was 

defined using geometry and material information of the Bombardier Dash-8 Q400 fuselage 

section described in Reference 5. The fuselage was modeled in MSC Patran8

 as a floor-equipped, 

stiffened cylinder. The fuselage is stiffened by thirty-nine evenly spaced ring frames and sixtyeight evenly spaced longitudinal stringers (longerons) framing a total of 2584 fuselage sidewall 

bays. The frame spacing is 0.58 m while the distance between stringers along the circumference 

is 0.124 m. The skin in each bay area between the ring frames and the longerons is represented 

by a matrix of two Quad4 elements in the circumferential direction and four Quad4 elements 

along the length of the cylinder. The floor is supported by thirty-nine horizontal floor beams with 

the same 0.58 m spacing as the ring frames and modeled with sixteen Quad4 elements along its 

width and four Quad4 elements between the beam supports. All beams are represented by Beam2 

elements. An isometric view of the basic finite element model is shown in Figure 5. 

The ring frames have a “U”-shaped cross-section while the longitudinal stringers have a “Z”-

shaped cross-section.5

 The floor support beams also have a “U”-shaped cross section. The 

perimeter and area of the cross sections were computed, along with the cross-sectional property 

parameters such as the moments of inertia, the polar moment, torsional constant, distance from 

shear center to centroid and the shear stiffness factors. The resulting section properties for the 

ring frames, longitudinal stiffeners and the floor beams are listed in Table 2. 

The skin of the fuselage consists of 1.6 mm-thick aluminum with a surface density of 

4.35 kg/m2

. The mechanical material properties of the aluminum skin are shown in Table 3. The 

ring frames and the longitudinal stringers for the baseline configuration are also made of 

aluminum. 

A honeycomb sandwich structure is used for the floor panels in the finite element model. 

Typically, product data sheets for honeycomb core materials11 provide geometric and mechanical 
7 

properties such as cell size, density, compressive stabilized modulus and plate shear moduli in 

the ribbon direction and along the direction perpendicular to the ribbon. Although these are the 

most important mechanical properties, the remaining core elasticity moduli are needed as input 

properties for the finite element analysis. Nast12 developed theoretical formulae to compute these 

core parameters. Experimental results in his research compared well with theoretical predictions. 

The formulae are valid for honeycomb cores with hexagonal type cells. A unit hexagonal cell can 

be defined by a rectangle containing three parts of the structure, one of which is double the foil 

thickness illustrated in Figure 6. The elasticity modulus of the core material Ef can be found by 

multiplying the transverse elasticity of the honeycomb E3 with the ratio of the area of the unit 

cell Aunit and the actual cross section of the core material Aactual

3

unit

f

actual

A E E

A  (1)

The elasticity moduli E1 and E2 and the shear modulus G12 are shown to be dependent on the 

core material elasticity modulus Ef, the core Poisson’s ratio νf, the foil thickness t, the cell size d, 

the cell wall length a, and the core angle φ.

12 These core cell dimensions are shown in Figure 6. 

 

 

3

1

32 2

1 sin

cos 1 cos 12 cos 1

3 8

f

f

t E

E

a



   

  	 
   
    

(2)

  

3

2 32 2

cos

sin 1 sin 1

f

f

t E

E

a



     (3)

 

  

3

12 3 2

1 sin

cos 6.25 6sin 1

f

f

t E

G

a



 

    (4)

The dimensions of the honeycomb cells for the floor panels are listed in Table 4 and were 

used, in combination with the available manufacturer material data, to compute the threedimensional orthotropic mechanical material properties for the floor aramid honeycomb core 

listed in Table 5. Unidirectional, 0.71 mm thick S-2 glass reinforced epoxy facings were selected 

as face sheets and bonded to the aramid honeycomb core in a construction similar to other typical 

aircraft flooring panels.13 The two-dimensional orthotropic material properties of the S-2 glass 

face sheets are listed in Table 6. The mechanical material properties of the face sheets and the 

8.92 mm thick honeycomb core, along with thickness and orientation values, were entered as 

laminated composites in the MSC Patran modeler. The total thickness of the stacking sequence is 

10.34 mm with a total density of 377 kg/m3

. 

Poro-Elastic Finite Element Method (PEM) Models 

PEM models were developed for the fuselage trim, the floor coverings, the seats, and the 

overhead bins to more accurately represent their poro-elastic properties. The PEM solver in VA 

One is based on a finite element implementation of the poro-elastic, elastic and acoustic 

equations of motion and is used to generate the modal impedance matrix coupled to the structural 

and acoustic FE subsystems. A PEM subsystem may encompass foam material, fiber material, 
8 

elastic solid structures, limp structures or acoustic fluids. Adjacent PEM subsystems must share 

the same nodes at their interface. 

The interior trim and the floor poro-elastic layer were modeled using solid Hex8 elements in 

the MSC Patran finite model of the LCTR2 fuselage. A maximum length of 0.145 m was 

conveniently selected for the element size as it equates to four elements between ring frames 

(bay length is 0.58 m). The volumes above and below the floor were subsequently meshed with 

Hex8 elements as well. Instead of accurately modeling the seats and overhead bins they were, in 

an initial approach, “carved out” of the FE volume above the floor. The resulting FE models of 

the seats and overhead bins were saved in binary files, imported in VA One and converted to 

PEM subsystems. An isometric view of the rudimentary PEM models for the seats and the 

overhead bins is presented in Figure 7. A cross-sectional view is shown in Figure 8. 

The trim arrangement consisted of a thin airgap, a porous absorption material and a trim 

panel. The honeycomb polymer trim panels, typical for a Q400 aircraft,14 were installed at a 

distance of 81 mm from the fuselage skin. The trim panels were 3 mm thick with a surface 

density of 0.765 kg/m2

 and an estimated loss factor of 0.02. The mechanical material properties 

of the trim panels are listed in Table 7. The trim absorption material consisted of 80 mm thick 

melamine foam layer with a loss factor of 0.17. The Biot properties of the melamine foam are 

tabulated in Table 8, while the diffuse field absorption coefficients are shown in Figure 9. The 

thin airgap layer (1 mm) was included to account for the trim absorption material not being 

bonded to the fuselage skin. The thin airgap and the melamine foam were modeled with solid 

elements, while shell elements were used for the trim panel. An isometric view of the interior 

trim PEM model is shown in Figure 7 and a cross-sectional view in Figure 8. 

The Biot properties of foam typically used in seats are listed in Table 8. The diffuse field 

absorption coefficients of a 25.4 mm thick sample of the foam as a function of one-third octave 

band center frequency are included in the VA One materials data base and are shown in Figure 9 

for rigid wall boundary conditions. 

The floor covering consisted of a 48.8 mm thick, fiber poro-elastic material and a 3 mm thick 

floor surface with an estimated loss factor of 0.1. The mechanical properties of the floor surface 

panels are listed in Table 7, while the Biot properties of the poro-elastic layer (felt) are tabulated 

in Table 8. The PEM model of the floor covering is presented in Figure 7 and Figure 8. 

The overhead bins were assumed to be stowed and were modeled with equivalent isotropic 

solid material properties (Table 7). Figure 7 and Figure 8 show the overhead bins PEM models. 

To allow an accurate analysis the mesh density of the PEM model has to comply with the 

requirement of at least four linear elements per wavelength. The shortest wavelengths of the 

propagating waves in the material as a function of one-third octave band center frequency were 

computed in VA One and are shown in Figure 10. The propagating wavelengths in the seat foam 

are the shortest. At 100 Hz the wavelength is about 0.30 m. The maximum element size of 

0.145 m used in the finite element models accommodates only two elements for the shortest 

wavelength at 100 Hz. However, VA One provides an option to use quadratic elements for the 

PEM analysis, whereby mid-side nodes are automatically added to the mesh, essentially doubling 

the number of elements per wavelength. Exercising this option resulted in at least four elements 

per wavelength allowing accurate PEM analyses up to and including the 100 Hz one third octave 

band for the seat foam, and up to 200 Hz for the melamine foam and the floor poro-elastic layer. 
9 

Acoustic Finite Element Models 

The acoustic upper cavity in Figure 8 was created in MSC Patran by subtracting the “carved 

out” finite elements models of the seats, overhead bins, floor arrangement and trim arrangement 

from the total volume above the floor bounded by the fuselage skin and the end bulkheads. The 

acoustic upper cavity was assigned properties of air for the pressurized aircraft cabin (Table 9) 

and divided in two parts, the space forward of the tiltrotor plane and the acoustic volume aft of 

the tiltrotor plane. The forward and aft acoustic upper cavity models were saved in binary files 

and imported in VA One as acoustic FE subsystems. Figure 11 shows the forward and aft 

acoustic upper cavities relative to the tiltrotor plane. The Hex8 elements in the meshed volume 

below the floor were also assigned properties of air for the pressurized aircraft to constitute the 

acoustic lower cavity (Figure 8). 

High Frequency SEA Models 

Predictions in the low frequency region were based on the structural and acoustic modes of 

the different subsystems and the deterministic description needs detailed information of the local 

geometry, material properties and boundary conditions. At the higher frequencies the modal 

density and modal overlap increase significantly and the modes in the subsystems are described 

statistically. Less detail is required and only the average response of the subsystem is predicted. 

The porous noise control treatments are weakly coupled to the structure and mainly provide 

sound absorption. 

Structural SEA Model 

The fuselage is supported by thirty-nine evenly spaced ring frames bounding thirty-eight 

axial segments. Nineteen SEA subsystems of the floor, and nineteen subsystems of the curved 

fuselage sections above and below the floor, each two segments long, were created for a total of 

fifty-seven subsystems (the subsystems are shown in Figure 12 and were shrunk for clarity). This 

allows computation of the energy flow and structural response at nineteen subsystems along the 

fuselage of the cabin. The fuselage skin, the longitudinal stringers and the ring frames were 

represented by ribbed plate subsystems with as input the skin material and mechanical properties, 

the beam material properties, the moments of inertia, the torsional constants, the cross-sectional 

areas, the locations of the shear center relative to the neutral axis of the section, the centroid 

offsets and the beam spacing. The floor and the supporting floor beams were modeled in a 

similar manner. Pressurization, the difference between internal and external pressures, was used 

in VA One to define the in-plane tensions and resulting geometric stiffness of the bay skin panels 

between the ring frames and the longitudinal stringers. 

Acoustic SEA Model 

For the high frequency analysis the fuselage was divided into nineteen identically-sized 

sections above the floor and nineteen sections below the floor. The thirty-eight acoustic cavity 

sections are shown in relation to the tiltrotor plane in Figure 13. The frequency dependent 

effective absorption in the cabin was taken as the upper bound of the average of experimental 

acoustic absorption data available for high-speed propeller driven aircraft15,16 and includes the 

combined influence of the floor covering, the trim and the seats. The experimental average cabin 

absorption coefficient is plotted in Figure 14 as function of one-third octave band center 

frequency. 
10 

EXCITATION MECHANISMS 

Turbulent Boundary Layer Excitation 

LCTR2 broadband noise due to an attached turbulent boundary layer were predicted for 

cruise flight conditions at a vehicle speed of 556 km/hr, an altitude of 8534 m, rotational Mach 

number of 0.35 and a helical tip Mach number of 0.61. The design parameters are listed in 

Table 1. 

The turbulent boundary layer noise was modeled as a fluctuating pressure spectrum in the 

acoustic prediction code VA One.9

 A different boundary layer excitation was applied at each of 

the nineteen fuselage sidewall sections to account for the increase in boundary layer thickness as 

a function of the distance from the nose of the vehicle. The turbulent boundary layer thickness δ

at distance x0 from the nose of the tiltrotor vehicle was computed from the relation 

0

0.2 0.37 x

Re

  (5)

where Re is the Reynolds number, which is defined by 

U x0 0 Re

  (6)

The free stream velocity U0, the kinematic viscosity υ and the properties of air at cruise 

altitude are listed in Table 9. The computed turbulent boundary layer thickness as function of 

distance from the LCTR2 nose is listed in Table 10. Both Cockburn/Robertson and Efimtsov 

turbulent boundary layer semi-empirical models are available in VA One, each having different, 

frequency dependent power spectral density levels. To achieve better parameter control, the 

Cockburn/Robertson and Efimtsov turbulent boundary layer models were computed outside the 

program after which the excitation power spectral densities were imported into VA One. 

Cockburn and Robertson 

The power spectral density of the attached turbulent boundary layer was obtained by 

Cockburn/Robertson using vibration response measurements of spacecraft shrouds to in-flight 

fluctuating pressures.17 The power spectral density ΦC, non-dimensionalized by the free stream 

velocity U0, the local boundary layer thickness δ and the dynamic pressure q͚͚͚

∞ is defined by 

 

2

0

2 2.0 0.9

0 2

0 0

( ) (0.006)

1 1 0.14

C f U

q f f M

U f

  

 

  	 
 	
  
 
    

      

(7)

where 2

0

1

2 q U    ; 0

0

U M

c  .and 0

0 0.346U f   . 

The narrowband spatial correlation function RC between two points ε and η along the flow 

direction z is given by9,17
11 

  , , exp exp  z w

C c

czcw

R ik z

d d 

  

       

(8)

where cz and cw are the spatial correlation decay coefficients in the flow and cross-flow 

directions, kc=ω/Uc is the convection wavenumber, and d is defined by 

1 2

8 1

3 c

c

d k

k 



  	 


     
      

(9)

The convection speed Uc was chosen to be 0.7 times the free stream velocity U0, and cz= 0.1 

and cw=0.72. 

Efimtsov 

The power spectral density ΦE of the turbulent boundary layer pressure fluctuations 

according to the empirical model by Efimtsov is given by18,19

     

3 2

3 2 1/3 10/3 2

1 8 E

t t

U

a S Re S Re !

! !

"#  $ 

"#

 

  (10)

where Uτ=U0(cf/2)0.5=(τ/ρ)0.5 is the friction velocity, St=ωδ/Uτ is the Strouhal number, 

α=0.01, β=[1+(3000/Reτ)

3

]

1/3 and Reτ=Uτδ/υ is the Reynolds number. The root-mean-square 

pressure equals (ΦE(f)Δf)-0.5 in which Δf is the bandwidth. 

The spatial correlation function RF for a free stream velocity at M<0.75 with convection 

velocity Uc is given by 

     

0.5 0.5 2 2 2 2

1 45 2

2 2 2 2

23 56

, , exp / / / /

t t

F

cl cl c t t

aS aS a a i R

UU UU U S aa S aa

  

  

% &    ' ' 	
 	


    ( )    
 
 ' '        * +

(11)

where the ratio of velocities is defined by 

 

 

0.1 2

0.2 9

8 4

10

1

1

c t

t

l t

U a S

a S

U a S

     

    

(12)

and the coefficients a1 through a6 and a8 through a10 are empirical constants which are listed 

in Table 11. The constant a7 is not used for Mach numbers lower than 0.75. 

The convection wavenumber k(f) in the direction of the flow is ω/Uc and equals zero in the 

direction perpendicular to the flow. For Mach numbers lower than 0.75 the Efimtsov boundary 

layer decay coefficients cx and cy are given by18,19 
12 

     

0.5 0.5 2 2 2

1,4 2,5

, 2 2 2 2 0.2

2,5 3,6 0

1 7.11

/ / 0.37

t

x y

cl c t e

aS a

c f UU U S aa X R









  	 
 	 


     
  
       

(13)

Turbulent Boundary Layer Excitation Comparison with Measured Data 

The Cockburn/Robertson and Efimtsov predicted pressure power spectral densities are 

compared with measurements by Bhat20 on a Boeing 737 aircraft in Figure 15. The flight test 

conditions for the Boeing 737 turbulent boundary layer measurements are summarized in Table 

12. The measurements at Mach number 0.78 at a distance of 8.81 m from the nose of the aircraft 

were believed by the author to represent the turbulent boundary layer noise, masking any noise 

associated with the engine inlet. In the report20 a smooth line was drawn through the raw data 

resulting in the dashed spectral density curve in Figure 15. The pressure power spectral density 

was constant up to about 500 Hz. The Efimtsov predictions for those frequencies are constant as 

well although they overpredict the measured data by a factor of 1.62 or about 2 dB. Above 

500 Hz the measured spectral density levels decrease rapidly with increasing frequency and is 

better represented by the Cockburn/Robertson predicted values. However, the decay rate in the 

Boeing 737 measurement curve was believed to be steeper than expected for a smooth (fuselage) 

surface and level flight,20 due to a higher than expected wall roughness and a 5 degree body 

angle of attack. Assuming the decay rate of the measured data is less steep then a good estimate 

above 500 Hz will be a curve bounded by the Efimtsov and the Cockburn/Robertson predictions. 

Therefore, in subsequent analyses with turbulent boundary layer excitation over the full length of 

the fuselage cabin the results from the Efimtsov model will be used over the entire frequency 

range of interest (6-8000 Hz), while the Cockburn/Robinson results will be considered in the 

high frequencies when lower than Efimtsov. 

ANALYSES 

The hybrid FE approach in VA One9

 was used to compute the low frequency acoustic 

response in the cabin due to the Efimtsov turbulent boundary layer excitation over the frequency 

range 6–141 Hz with a 1 Hz bandwidth (141 Hz is the limiting frequency in the 125 Hz one-third 

octave band and is needed for conversion from narrowband to one-third octave band). 

Subsequently, the SEA approach was used to predict the interior noise for the 125–8000 Hz 

one-third octave bands due to either the Cockburn/Robertson or the Efimtsov turbulent boundary 

layer excitation. The two analysis methods overlap in the 125 Hz band. 

Low Frequency Hybrid FE/SEA Analysis 

Structural Modal Response 

The in-vacuo structural modal response of the fuselage model, including the fuselage skin, 

ring frames, longitudinal stringers, the floor and the floor supports, was computed using MSC 

Nastran 2010.10 Simply supported boundary conditions were assumed at the aft bulkhead 

location and the forward flight deck entrance. Future analyses will include more realistic 

boundary conditions to reflect the fuselage being supported by the wings at the wing box 

interface. The structural modal analysis results were then imported into VA One. A default 1% 
13 

structural damping loss factor was assumed. The lowest structural mode of the fuselage occurred 

at 9.07 Hz. The mode is a first order axial mode as it has no nodal lines between the aft bulkhead 

and the front flight deck access. Figure 16 shows an isometric view of the first mode while a 

cross-sectional view of the circumferential modal pattern is displayed in Figure 17. The number 

of structural modes in the one-third octave bands with center frequencies 5–160 Hz is listed in 

Table 13. 

Acoustic Modal Response 

The acoustic modes in the cavities above and below the floor were computed by a modal 

analysis in VA One. The lowest acoustic mode, in the axial direction, was predicted to occur at 

5.7 Hz (Figure 18) and is a first-order axial mode having one nodal line with the highest interior 

sound pressure levels occurring at the bulkhead and the forward flight deck wall. The first crosssectional acoustic mode, which may efficiently couple to structural circumferential mode(s), 

occurred at 73.8 Hz and is shown in Figure 19. The number of acoustic modes computed in each 

one-third octave band is listed in Table 13. 

Poro-Elastic Modal Impedance Matrix 

The modal impedance matrix of the contiguous PEM groups of seats, overhead bins, floor 

arrangement and trim configuration subsystems, which are coupled to the modes of the FE 

fuselage system and the modes of the FE acoustic cavity systems, is computed as an intermediate 

result. 

Cabin Interior Noise Predictions 

VA One computes the cabin sound pressure levels in the low frequency region by coupling 

the in-vacuo structural modes, the rigid-boundary acoustic modal parameters and the PEM modal 

impedance matrix; applying the turbulent boundary layer excitation; and accounting for energy 

propagating away from the structure by including a radiation impedance. The sound pressure 

level predictions for the Efimtsov turbulent boundary layer excitation were performed for the 

LCTR2 cabin forward and aft of the tiltrotor plane in the 6–141 Hz frequency bands using a 1 Hz 

analysis bandwidth. The predicted mean narrowband interior sound pressure levels are shown in 

Figure 20 along with the averaged sound pressure levels for the entire cabin. 

At low frequencies the interior cabin sound pressure level variations are determined by the 

coupled acoustic and structural modal responses. The number of structural and acoustic modes in 

each of the one-third octave bands with center frequencies 5-160 Hz is listed in Table 13. The 

modal frequencies of the structural and acoustic modes below 20 Hz are tabulated in Table 14. 

The first, second, and third axial acoustic modes occur at 5.75 Hz, 11.6 Hz and 17.6 Hz 

respectively, and these are the only three acoustic cabin modes below 20 Hz. The acoustic mode 

number indicates the number of nodal lines in the response. Eleven structural modes were 

identified below 20 Hz and their axial mode numbers are included in Table 14 as well. The 

structural mode number indicates the number of anti-nodes (maximum response between nodal 

lines), or the number of nodal lines plus one. 

The second order axial acoustic mode at 11.6 Hz (Figure 21) has two nodal lines and a 

maximum response in the center. The closest structural modes are first-order axial resonances at 

11.3 Hz (Figure 22) and 11.5 Hz (Figure 23). The acoustic mode and the two structural modes all 
14 

have a maximum response in the center and similar spatial characteristics. Since their modal 

resonance frequencies are also very close to one another the acoustic and structural modes will 

couple and exchange energy resulting in a maximum predicted sound pressure level at 12 Hz in 

Figure 20. The resulting variation of the predicted sound pressure levels in the cabin interior at 

12 Hz is shown in Figure 24, with the local maxima and minima at the locations of the maximum 

and zero acoustic modal responses, respectively. Peak interior sound pressure levels coincide 

with the maximum acoustic modal response in the center and near both ends of the cabin. Sound 

pressure level variations inside the cabin are as high as 18 dB. 

The third-order axial acoustic resonance at 17.6 Hz (Figure 25) couples well with the secondorder structural modes at 17.3 Hz (Figure 26) and 18.7 Hz (Figure 27) due to the spatial 

characteristics of the acoustic modal pressures and the structural modal displacements. Both the 

acoustic and the structural modes have a nodal line in the center and maximum responses on 

either side. The resulting distribution of the predicted sound pressure levels in the cabin at 17 Hz 

is shown in Figure 28 and is similar to the variations in the acoustic modal response. Peak 

interior sound pressure levels coincide with the maximum acoustic modal response at 

approximately one-third and two-third of the length of the cabin. Sound pressure level variations 

inside the cabin are as high as 16 dB. The predicted space averaged interior sound pressure levels 

show a peak at 17 Hz as shown in Figure 20. All the peaks up to 70 Hz in the sound pressure 

level predictions of Figure 20 are attributed to the coupling of axial acoustic modes with axial 

structural modes. As frequency increases, progressively higher-order axial modes join the overall 

modal response. The first cross-sectional acoustic mode was computed at 73.8 Hz (Figure 19) 

and is characterized by a vertical nodal line in the tiltrotor plane cross-section. Figure 29 shows 

another resonance response with a vertical nodal line at 89.2 Hz in the tiltrotor plane crosssection of the aft acoustic cavity. The 89.2 Hz frequency is in the 100 Hz one-third octave band 

which contains 93 structural and 25 acoustic resonant modes (Table 13). Several non-resonant 

modes participate in the modal response of the 100 Hz one-third octave band as well. Figure 30 

shows a cross-sectional mode with a horizontal nodal line at 128.9 Hz in the 125 Hz one-third 

octave band. The number of acoustic and structural resonances in the 125 Hz band equals 21 and 

129 respectively (Table 13), and the number of modes participating has grown so large that the 

individual cross-sectional modes such as in Figure 29 and Figure 30 only partially contribute to 

the global cabin noise. However, they still may cause local hotspots of sound, especially close to 

the fuselage sidewall where they may efficiently couple to circumferential structural modes. 

High Frequency SEA Analysis 

A high frequency SEA analysis was performed for the structural and acoustic subsystems, 

while being exposed to either the Cockburn/Robertson or the Efimtsov turbulent boundary layer 

excitation. The modal density in the acoustic space above the floor was estimated in VA One for 

the one-third octave frequency bands of 100–8000 Hz as shown in Figure 31. The modal density 

exceeds approximately one mode per Hz in the 125 Hz and higher bands, sufficient to justify the 

high frequency SEA analysis. A semi infinite fluid (SIF) representing an unbounded exterior 

acoustic space was connected to the nineteen curved structural subsystems of the upper as well 

as the lower fuselage sections to serve as an acoustic radiation impedance. The curved shell of 

the fuselage was exposed to a pressure differential between the external atmospheric pressure at 

the cruise altitude of 8534 m and the pressure of the effective equivalent cabin altitude of 2438 m 

(Table 9). The pressurization of 42.3 kPa was used in VA One to define the in-plane tensions and 

resulting geometric stiffness of the fuselage skin panels. 
15 

Cabin interior sound pressure levels due to the Cockburn/Robertson turbulent boundary layer 

excitation were predicted for the nineteen acoustic subsystems in the cabin above the floor for 

the 125 Hz and higher one-third octave frequency bands. The subsystem sound pressure levels 

along with their averaged values are plotted in Figure 32. The highest interior sound pressure 

levels are in the aft cabin subsystem at the farthest distance from the nose of the vehicle where 

the turbulent boundary layer thickness has its highest value. 

The sound pressure level predictions due to the Efimtsov turbulent boundary layer excitation 

for the nineteen cabin subsystems are shown in Figure 33 along with their space averaged levels 

for the entire cabin. Highest sound pressure levels are again in the back of the cabin. The spread 

between the subsystem levels is greater than for the Cockburn/Robertson model due to the 

greater spread in their excitation spectral densities. 

LCTR2 Analysis Results for the Consolidated Frequency Range 

The hybrid FE predicted cabin averages of the LCTR2 sound pressure levels forward and aft 

of the tiltrotor plane due to Efimtsov boundary layer excitation were presented in Figure 20 as 

narrowband data with a resolution of 1 Hz. To assess the levels in the human audible frequency 

range (above 20 Hz) the narrowband predictions were converted to one-third octave bands and 

data in the 20-125 Hz bands are plotted in Figure 34. The SEA predicted cabin averaged sound 

pressure levels due to the Efimtsov and the Cockburn/Robinson excitations are shown in the 

same Figure 34. The predictions for the hybrid FE and SEA methods for the Efimtsov model 

differ by less than 1 dB in the 125 Hz one-third octave band. However, this good agreement may 

be fortuitous as the interior sound pressure levels are averaged over the cabin, and several 

parameters like loss factors, acoustic absorption values, boundary conditions, trim treatment and 

others are modeled differently in the low and high frequency approaches. Also, pressurization 

was not modeled for the hybrid FE approach but was included in the SEA analysis. 

Contour plots for the two prediction methods in the 125 Hz band are plotted in Figure 35 for 

the SEA method and in Figure 36 for the hybrid FE method. The SEA predictions show the 

nineteen acoustic subsystems, each of which having a constant subsystem sound pressure level. 

The hybrid FE predictions in Figure 36 show that the interior sound pressure level distribution is 

governed by the axial and cross-sectional modal behavior in the cabin interior. From an overall 

perspective the sound pressure level distribution for both the SEA and hybrid FE predictions 

show comparable characteristics. The cabin sound pressure level variation is as high as 18 dB for 

the SEA predictions and 20 dB for the hybrid FE results. 

The space averaged cabin interior sound pressure levels predicted for the high frequency 

Cockburn/Robertson model are also plotted in Figure 34 as it was assumed previously that the 

prediction curve most likely would be in between the two high frequency analyses. The different 

representations of the turbulent boundary layer spectra for the Cockburn/Robertson and Efimtsov 

models lead to large differences in the high frequency cabin interior noise predictions (13 dB at 

2000 Hz in Figure 34). However, this may be of little concern for human response issues as both 

models predict relatively low interior noise levels with the higher Efimtsov excitation dropping 

below 50 dB for the 2000 Hz and higher frequencies. 
16 

Bombardier Q400 Predictions Compared with Measurements 

Although no tightly controlled experimental acoustic data are available to validate the 

LCTR2 predictions a comparison is made with a 2002 study conducted by the National Institute 

for Occupational Safety and Health (NIOSH)18 to evaluate noise exposure by flight attendants on 

selected Bombardier aircraft among which the Dash-8 Q400 turboprop. In this survey spectral 

noise measurements were made with a Larson-Davis Laboratory Model 2800 real-time analyzer 

and a Larson-Davis Laboratory Model 2559 half-inch diameter random incidence microphone. 

The microphone had a frequency response range (± 2 dB) from 4 to 21000 Hz and was 

connected to the analyzer with a 1.8 m cable. One-third octave bands consisting of center 

frequencies from 25 Hz to 20 kHz were integrated for 15 seconds and stored in the analyzer. 

Samples were acquired at cruise altitude during level flight. The Bombardier Q400 aircraft is 

equipped with a noise and vibration suppression (NVS) system that actively suppresses propeller 

tones before reaching the occupants in the cabin. The NVS system was operational during the 

noise measurements. 

The Bombardier Q400 one-third octave band spectrum measured during cruise conditions in 

the front of the cabin is plotted in Figure 37 showing peak levels at the propeller blade passage 

frequency in the 80 Hz one-third octave band and harmonics in the 160 and 315 Hz bands. 

Superimposed on this plot are the predicted interior noise levels due to Efimtsov and 

Cockburn/Robertson turbulent boundary layer excitation averaged over the cabin space. The 

cruise conditions for the Q400, used in the predictions, are summarized in Table 15. The low 

frequency (< 125 Hz) Efimtsov model overpredicts the broadband components of the Q400 

spectrum by up to 9 dB at 25 Hz. However, inaccuracies in the low-frequency predictions are 

associated with assumptions made for material properties, structural and acoustic modal 

parameters and boundary conditions, structural damping and acoustic absorption. Also, the inflight measurements have several unknowns including detailed test conditions, the precise 

measurement location and the proximity of that location to the sidewall trim and seat surfaces. 

Finally, applying A-weighting to the predicted data (from -50.5 at 20 Hz to -16.1 at 125 Hz) to 

account for the fact that the human ear is not as sensitive to the lower frequencies reduces the 

levels in the 20-125 Hz bands to less than 53 dB, which are considered acceptable cabin noise 

levels. The cabin averaged high frequency predictions with both the Efimtsov and 

Cockburn/Robinson models show (much) lower levels than the one-third octave band sound 

pressure levels measured for the Q400. In addition to the argument of assumptions in the 

predictions and unknowns in the measurements, it has to be noted that other sources than the 

turbulent boundary layer excitation may have contributed to the measured noise at the high 

frequencies such as the pressurization and air conditioning systems, passengers, equipment, 

lavatories, etc. Since the highest noise levels due to turbulent boundary layer excitation occur in 

the aft cabin the Efimtsov predictions for that location are also plotted in Figure 37 for 

comparison with the measured levels in the front of the Q400 cabin. The averaged cabin noise 

levels in the LCTR2 during cruise conditions (Figure 34) are predicted to be lower than those for 

the Q400 aircraft in cruise (Figure 37), due to lower cruise speed (Mach 0.51 versus Mach 0.60 

for the Q400) and higher cruise altitude (8534 m versus 7620 m for the Q400). The cruise noise 

levels predicted for the LCTR2 cabin are thus comparable or lower than measured in the Q400 

cabin and thus will be acceptable to passengers and crew. It should be emphasized that only 

turbulent boundary layer noise is considered here and contributions due to thickness and loading 

noise from the tiltrotor blades and mechanical noise radiated by the mid-wing gearbox will be 

the subject of another study. 
17 

SUMMARY 

A prediction scheme was established to compute sound pressure levels in the cabin of the 

notional Large Civil Tiltrotor (LCTR2) due to turbulent boundary layer flow over the fuselage 

during cruise flight conditions. Structural and acoustic finite element models were created in 

MSC Patran and a modal analysis of the fuselage structure was performed in MSC Nastran. An 

acoustic modal analysis of the cabin space was completed in VA One. The finite element 

geometry along with the structural modal parameters and mode shape deflection information 

were subsequently imported into VA One to model the fuselage, the cabin acoustic space and the 

cabin interior components as energy transmitting, storing and receiving vibro-acoustic 

mechanisms. Poro-Elastic Finite Element Method (PEM) models were developed for the seats, 

the overhead bins, the fuselage trim, and the floor coverings to more accurately represent their 

poro-elastic and structural properties. Cockburn/Robertson and Efimtsov turbulent boundary 

layer excitation models were applied to nineteen segments of the fuselage to represent the 

variation of the excitation spectra with distance from the nose of the vehicle. Cabin interior 

sound pressure levels were predicted employing a narrowband (1 Hz) hybrid Finite Element (FE) 

analysis for the low frequencies (6-141 Hz) and a Statistical Energy Analysis (SEA) method for 

the high frequency one-third octave bands (125-8000 Hz). It is shown that the interior sound 

pressure level distribution in the low frequencies is governed by interactions between individual 

structural and acoustic modes. Only axial acoustic modes were computed below 73.8 Hz at 

which frequency the first cross-sectional mode was predicted. Peak sound pressure levels 

occurred at the same locations as the maxima in the acoustic modal response. Interior sound 

pressure level predictions for the low and high frequencies were combined and averaged over the 

entire cabin volume. The spatially averaged predicted interior sound pressure levels for the low 

frequency hybrid FE and the high frequency SEA analyses, due to the Efimtsov turbulent 

boundary layer excitation, were within 1 dB in the common 125 Hz one-third octave band. 

However, this good agreement may be fortuitous due to the assumptions in the modeling 

parameters and the averaging of the cabin sound pressure levels. The averaged interior noise 

levels for the notional LCTR2 cabin due to turbulent boundary layer excitation were predicted 

lower than the levels in a Bombardier Q400 aircraft cabin during cruise flight due to the higher 

altitude and lower cruise Mach number of the LCTR2 and will be acceptable to crew and 

passengers. 

ACKNOWLEDGEMENTS 

This work was performed under the Analytical Mechanics Associates, Inc. Contract Number 

NNL12AA09C. Dr. Randolph H. Cabell, Technical Direction Notice (TDN) owner. 

REFERENCES 

1. Johnson, W., Yamauchi, G.K., and Watts, M.E.: NASA Heavy Lift Rotorcraft Systems 

Investigation. NASA TP-2005-213467, September 2005. 

2. Acree, C.W., Yeo, H., and Sinsay, J.D.: Performance Optimization of the NASA Large 

Civil Tiltrotor. International Powered Lift Conference, London, UK, July 2008; also 

NASA TM-2008-215359, June 2008. 

3. Acree, C.W. Jr.: Integration of Rotor Aerodynamic Optimization with the Conceptual 

Design of a Large Civil Tiltrotor, NASA Ames, ARC-E-DAA-TN1176, January 2010. 
18 

4. Grosveld, Ferdinand W. and Cabell, Randolph, H.: Preliminary assessment of the interior 

noise environment in the Large Civil Tiltrotor (LCTR2). nc11_129, Proceedings of 

Noise-Con 2011, Portland, Oregon, USA, 25-27 July 2011. 

5. Gardonio, P. and Gonzalez Diaz, C.: Bombardier Dash-8 Q400 Fuselage Section with 

Five Decentralized Velocity Feedback Control Units. ISVR Technical Memorandum 983. 

Institute of Sound and Vibration Research, Southampton, UK, January 2009. 

6. Tubbs, Randy L.: NIOSH Health Hazard Evaluation Report HETA 2002-0354-2931. 

Horizon Air. Seattle, Washington. February 2004. 

7. Aviation International News: Bombardier considers stretch variant for Q400. Paris Air 

Show. Air Transport and Cargo Aircraft. June 2009. 

8. MSC Patran 2012. MSC Software Corporation, Santa Ana, California, 2012. 

9. VA One 2011 User’s Guide. ESI Group North America, December 2011.

10. MSC Nastran 2010.1.1. MSC Software Corporation, Santa Ana, California, 2012. 

11. HexWeb HRH-10 Aramid Fiber/Phenolic Honeycomb Product Data Sheet. Hexcel 

Corporation, Dublin, CA, 2012. (http://www.hexcel.com) 

12. Nast, E.: On Honeycomb-Type Core Moduli. AIAA -97-1178, Proceedings of the 28th

AIAA/ASME/ASCE/AHS/ASC SDM Conference, 1997. 

13. Gillfloor 4017T Light Weight Aircraft Flooring Panel. M.C. Gill Corporation, El Monte, 

CA, March 2001. 

14. Alujević, Neven: Smart double panel with decentralised active damping units for the 

control of sound transmission. Institute of Sound and Vibration Research, University of 

Southampton, England, August 2008. (http://eprints.soton.ac.uk) 

15. Wilby, J.F., Rennison, D.C. and Wilby, E.G.: Noise Control Predictions for High-Speed, 

Propeller-Driven Aircraft. AIAA-80-0999, June 1980. 

16. Rennison, D.C., Wilby, J.F., Marsh, A.H., and Wilby, E.G.: Interior Noise Control 

Prediction Study for High-Speed, Propeller-Driven Aircraft. NASA Contractor Report 

159200, NASA Langley Research Center, Hampton, Virginia, September 1979. 

17. Cockburn, J.A., Robertson J.E.: Vibration Response of Spacecraft Shrouds to In-flight 

Fluctuating Pressures. Journal of Sound and Vibration, 1974, 33(4), 399-425. 

18. Efimtsov, B.M.: Characteristics of the field of turbulent wall pressure fluctuations at 

large Reynolds numbers. Soviet Physics Acoustics, 1982, 28, pp. 289-292. 

19. Miller, T.S., Gallman, J.M., and Moeller, M.J.: Review of Turbulent Boundary-Layer 

Models for Acoustic Analysis. AIAA Journal of Aircraft, Vol. 49, No. 6, NovemberDecember 2012, pp. 1739-1754.DOI: 10.2514/1.C031405 

20. Bhat, V.W.: Flight test measurement of measurement of exterior turbulent boundary layer 

pressure fluctuations on Boeing Model 737 airplane. Journal of Sound and Vibration

1971, 14(4), pp. 439-457. 

21. Grosveld, Ferdinand W., Cabell, Randolph H., and Boyd Jr., Doug D.: Interior Noise 

Predictions in the Preliminary Design of the Large Civil Tiltrotor (LCTR2). Proceedings 

of the AHS International 69th Annual Forum and Technology Display, 21-23 May 2013. 

 
19 

TABLES 

Table 1. Design parameters for the LCTR2. 

Parameter LCTR2 

Passengers 90 

Range [km] 1800 

Maximum cruise speed [km/hr] 555.6 

Maximum operating altitude [m] 8534 

Fuselage diameter [m] 2.74 

Maximum cabin width [m] 2.56 

Cabin length [m] 21.84 

Number blades [-] 4 

Tip speed cruise [m/s] 107 

Rotational Mach number [-] 0.35 

Helical tip Mach number [-] 0.61 

BPF cruise [Hz] 6.75 

RPM cruise [rpm] 101 

Rotor radius [m] 9.906 

Engine power [kW] 10067 

Clearing rotor tip-fuselage [m] 0.457 

Table 2. Section properties of the longitudinal stringers, ring frames and floor support beams. 

Property Parameter Label Ring Frames Longitudinal Stringers Floor Beams 

Shape ‘U’ ‘Z’ ‘U’

Cross sectional area A [m2] 0.0002925 0.0001025 0.0002607 

Perimeter P [m] 0.2390 0.0870 0.2238 

Moments of inertia Ixx [m4] 2.299E-7 7.286E-9 1.532E-7 

Iyy [m4] 1.249E-8 1.848E-9 1.516E-8 

lxy [m4] 0.0 -2.652E-9 0.0 

Polar Moment J [m4] 2.424E-7 9.134E-9 1.684E-7 

Torsional constant Q [m4] 6.094E-10 2.070E-10 4.922E-10 

Distance shear center dhorizontal [m] 0.0 0.0 -0.01386 

to centroid dvertical [m] -0.01099 0.0 0.0 

Shear stiffness factors K1 0.60684 0.43902 0.53624 

K2 0.35043 0.43902 0.42030 

Table 3. Mechanical material properties of the skin, ring frames and longitudinal stringers. 

Density Young’s modulus Shear modulus Poisson’s ratio



[kg/m3

] 

E11

[GPa] 

G12

[GPa] 

12

[-] 

Aluminum 2720 71.0 26.7 0.33 

 
20 

Table 4. Dimensions of the cells in the honeycomb core of the floor panels. The geometric parameters a, 

b, t, d and φ are defined in Figure 6. 

a 

[mm] 

b 

[mm] 

t 

[mm] 

d 

[mm] 

࣐

[deg] 

Floor 1.83 1.83 0.076 3.175 30 

Table 5. Three-dimensional orthotropic material properties of the floor honeycomb core. 

Density Thickness Young’s moduli Shear moduli 



[kg/m3] 

t 

[mm] 

E11

[MPa] 

E22

[MPa] 

E33

[MPa] 

G12

[MPa] 

G31

[MPa] 

G23

[MPa] 

Aramid honeycomb floor 144 8.92 2.30 1.77 621 0.407 120.7 75.9 

Table 6. Two-dimensional orthotropic material properties of the floor fiberglass face sheets. 

Density Thickness Young’s moduli Shear modulus Poisson’s ratio 



[kg/m3

] 

t 

[mm] 

E11

[GPa] 

E22

[GPa] 

G12

[GPa] 

12

[-] 

S2-glass unidirectional face sheet 1840 0.712 56 18 7.5 0.27 

Table 7. Mechanical material properties of the floor surface panels, the trim panels and the overhead bins. 

Density Surface mass Thickness Young’s modulus Shear modulus Poisson’s ratio 



[kg/m3

] 

m 

[kg/m2

] 

t 

[mm] 

E11

[GPa] 

G12

[GPa] 

12

[-] 

Fuselage trim panel 255 0.765 3.0 15.0 5.77 0.30 

Floor surface panel 1100 3.3 3.0 2.3 0.772 0.49 

Overhead bins 100 0.03 0.0125 0.2 

Table 8. Biot properties of the floor porous material layer, the fuselage trim melamine acoustic foam and 

the foam in the seats. 

Density Surface 

mass 

Thickness Young’s 

modulus 

Poisson’s

ratio 

Flow 

resistivity Porosity Tortuosity Loss factor 

Material ρ m t E ν σ φ α∞ η

[kg/m3] [kg/m2] [mm] [Pa] [-] [Ns/m4] [-] [-] [-] 

Melamine foam 8.8 0.704 80 80000 0.4 10900 0.99 1.02 0.17 

Floor porous layer 50 2.44 48.8 45000 0.92 1.5 

Seat (foam) 40 95000 0.34 11500 0.95 1.9 0.1 
21 

Table 9. LCTR2 cruise flight conditions. 

Parameter Symbol Outside Cabin 

Operating altitude h [m] 8534 2438 

Temperature T [°C] -40.7 20.0 

Pressure P [Pa] 32934 75266 

Density ρ [kg/m3] 0.4931 0.897 

Speed of sound c [m/s] 305.8 343.3 

Kinematic viscosity υ [m2/s] 3.05 10-5 2.02 10-5

Heat capacity ratio γ [-] 1.401 1.401 

Prandtl number Pr [-] 0.722 0.715 

Free stream flow velocity U0 [m/s] 154.3 

Free stream Mach number Mc [-] 0.505 

Table 10. Attached turbulent boundary layer thickness as function of distance from the LCTR2 nose. 

Fuselage 

section 

Distance 

from

nose 

[m] 

Boundary 

layer 

thickness 

[m] 

1 4.24 0.0536 

2 5.40 0.0650 

3 6.56 0.0760 

4 7.72 0.0866 

5 8.88 0.0968 

6 10.04 0.1068 

7 11.20 0.1166 

8 12.36 0.1262 

9 13.52 0.1356 

10 14.68 0.1448 

11 15.84 0.1539 

12 17.00 0.1628 

13 18.16 0.1716 

14 19.32 0.1804 

15 20.48 0.1890 

16 21.64 0.1975 

17 22.80 0.2059 

18 23.96 0.2143 

19 25.12 0.2225 

Table 11. Empirical constants used in the Efimtsov turbulent boundary layer model. 

a1 a2 a3 a4 a5 a6 a8 a9 a10 

0.1 72.8 1.54 0.77 548 13.5 9.55 0.000638 0.00398 
22 

Table 12. Boeing 737 flight test conditions. 

Parameter Symbol Value 

Operating altitude h [m] 7620 

Temperature T [°C] -34.53 

Pressure P [Pa] 37600 

Density ρ [kg/m3] 0.5489 

Speed of sound c [m/s] 309.7 

Kinematic viscosity υ [m2/s] 2.8 10-5

Heat capacity ratio γ [-] 1.401 

Prandtl number Pr [-] 0.72 

Free stream flow velocity U0 [m/s] 241.5 

Free stream Mach number Mc [-] 0.78 

Distance from the nose d [m] 8.81 

Table 13. Number of acoustic and structural modes in the one-third octave bands 5–160 Hz. 

One-third octave band 

center frequency

[Hz] 

Acoustic 

modes 

# 

Structural 

modes 

# 

5 1 

6.3 

8 

10 2 

12.5 1 2 

16 1 4 

20 9 

25 1 17 

31.5 1 19 

40 2 29 

50 2 31 

63 3 42 

80 20 73 

100 25 93 

125 21 129 

160 60 183 

 
23 

Table 14. Frequencies of acoustic and structural modes below 20 Hz. 

Acoustic 

mode 

[Hz] 

Axial 

mode order 

Structural 

mode

[Hz] 

Axial 

mode order 

5.75 First 

9.07 First

9.20 First

11.6 Second 11.4 First

11.5 First 

14.3 Second 

14.8 Second 

15.3 First 

17.6 Third 17.3 Second 

18.5 First 

18.7 Second 

19.4 Third 

Table 15. Bombardier Q400 cruise flight conditions. 

Parameter Symbol Value 

Operating altitude h [m] 7620 

Temperature T [°C] -34.53 

Pressure P [Pa] 37600 

Density ρ [kg/m3] 0.5489 

Speed of sound c [m/s] 309.7 

Kinematic viscosity υ [m2/s] 2.8 10-5

Heat capacity ratio γ [-] 1.401 

Prandtl number Pr [-] 0.72 

Free stream flow velocity U0 [m/s] 185.3 

Free stream Mach number Mc [-] 0.60 
24 

FIGURES 

Figure 1. Isometric and three-view of the Large Civil Tiltrotor (LCTR2) design. 

Figure 2. Artist’s rendering of the LCTR2 concept vehicle in forward flight. 
25 

Figure 3. Sketch of a hypothetical LCTR2 90-passenger seating layout. 

Figure 4. LCTR2 cabin cross-section showing four-abreast seating and overhead bins. 

 
26 

Figure 5. Basic finite element model of the fuselage skin, ring frames, longitudinal stringers, floor, and 

floor support beams. 

Figure 6. Rectangular unit cell of the honeycomb material. 

d

b t

a 2t
27 

Figure 7. Rudimentary Porous Elastic Finite Element Method (PEM) models for the seats, overhead bins, 

floor covering and interior trim. 

Figure 8. Cross-sectional view of the PEM models for the seats, overhead bins, floor covering and interior 

trim. 

Interior trim 

Overhead bins 

Seats 

Floor covering 

Floor arrangement 

Seats 

Overhead bins 

Interior trim 

 arrangement Upper acoustic cavity 

Lower acoustic cavity 
28 

Figure 9. Diffuse field absorption coefficient of 0.08 m thick melamine acoustic foam with a rigid wall 

boundary condition. 

Figure 10. Shortest wavelengths as function of one-third octave band frequency for three poro-elastic 

materials with the Biot material properties listed in Table 8. 

 One-third Octave Band Center Frequency, Hz

Absorption Coefficient

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

6.3 12.5 25 50 100 200 400 800 1600 3150 6300

8.8 kg/m3 Trim Panel Foam - 0.08 m thick

40.0 kg/m3 Seat Foam - 0.0254 m thick

 One-third Octave Band Center Frequency, Hz

Propagating Wavelength, m

0.1

0.2

0.3

0.4

0.5

0.7

1

2

3

4

5

7

10

6.3 12.5 25 50 100 200

Melamine foam

Porous floor covering material

Typical seat foam
29 

Figure 11. The forward and aft acoustic cavities above the floor relative to the tiltrotor plane. 

Figure 12. Fifty seven 1.16 m wide structural subsystems (shrunken for clarity), including the floor panels 

and the curved ribbed skin sections above and below the floor. 

Tiltrotor plane 

Aft acoustic 

upper cavity 

 Forward acoustic 

upper cavity 
30 

Figure 13. Thirty-eight acoustic cavity sections relative to the tiltrotor plane. 

Figure 14. Typical measured average commercial airplane cabin absorption coefficient [15]. 

 

 One-third Octave Band Center Frequency, Hz

Absorption Coefficient

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

100 200 400 800 1600 3150 6300

Tiltrotor plane 
31 

Figure 15. Cockburn/Robertson and Efimtsov predictions compared with flight test measurements of 

turbulent boundary layer pressure fluctuations on a Boeing 737 aircraft [20]. 

Figure 16. Isometric view of the first structural mode of 

the fuselage at 9.07 Hz. 

Figure 17. Cross-sectional view of the 

9.07 Hz structural fuselage mode. 

 Frequency, Hz

Pressure Power Spectral Density, Pa2/Hz

5 6 78 10 20 30 50 70 100 200 300 500 1000 2000 5000 10000

0.1

0.2

0.3

0.4

0.5

0.7

1

2

3

4

5

7

10

Flight test data [Bhat, 1971]

Cockburn/Robertson prediction

Efimtsov prediction
32 

Figure 18. Isometric view of the first acoustic (axial) mode at 5.7 Hz. 

Figure 19. View of the first cross-sectional acoustic mode at 73.8 Hz. 

Figure 20. Cabin average of the mean narrowband (1 Hz) LCTR2 cabin sound pressure levels forward 

and aft of the tiltrotor plane for the Efimtsov boundary layer excitation predicted with the low frequency 

hybrid FE analysis. 

 Frequency, Hz

Sound Pressure Level, dB

5 6 7 8 9 10 20 30 40 50 60 70 80 100 140

40

45

50

55

60

65

70

75

80

aft of tiltrotor

plane

forward of

tiltrotor plane

12 Hz

17 Hz

Cabin average
33 

Figure 21. Second-order axial acoustic resonance at 

11.6 Hz.

Figure 22. First-order axial structural resonance at 

11.3 Hz.

Figure 23. First-order axial structural resonance at 

11.5 Hz. 

Figure 24. Cabin interior sound pressure level 

distribution in the 12 Hz band. 

78 dB 

38 dB

Figure 25. Third-order axial acoustic resonance at 

17.6 Hz.

Figure 26. Second-order axial structural resonance 

at 17.3 Hz.
34 

Figure 27. Second-order axial structural resonance 

at 18.7 Hz. 

Figure 28. Cabin interior sound pressure level 

distribution in the 17 Hz band. 

78 dB 

38 dB

Figure 29. Acoustic resonance (89.2 Hz) with a 

vertical nodal line in the tiltrotor plane.

Figure 30. Acoustic resonance (128.9 Hz) with a 

horizontal nodal line in the tiltrotor plane.

Figure 31. Estimated modal density in the 100 Hz through 8000 Hz one-third octave bands. 

 One-third Octave Band Center Frequency, Hz

Modal Density [modes/Hz]

0.5

0.7

1

2

3

5

7

10

20

30

50

70

100

200

300

500

700

1000

2000

3000

5000

100 200 400 800 1600 3150 6300

Tiltrotor plane 

cross-section 

Tiltrotor plane 

cross-section 
35 

Figure 32. SEA predicted one-third octave band LCTR2 subsystem sound pressure levels and their 

average for the Cockburn/Robertson turbulent boundary layer excitation. 

Figure 33. SEA predicted one-third octave band LCTR2 subsystem sound pressure levels and their 

average for the Efimtsov turbulent boundary layer excitation. 

 One-Third Octave Band Center Frequency, Hz

Sound Pressure Level, dB

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

100 200 400 800 1600 3150 6300

Aft cabin

Nineteen acoustic subsystems

Cabin average for Cockburn/Robertson boundary layer excitation

 One-Third Octave Band Center Frequency, Hz

Sound Pressure Level, dB

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

100 200 400 800 1600 3150 6300

Aft cabin

Nineteen acoustic subsystems

Cabin average for Efimtsov boundary layer excitation
36 

Figure 34. Averaged one-third octave band LCTR2 sound pressure levels predicted with the hybrid FE 

analysis (20-125 Hz) for the Efimtsov boundary layer excitation, and with SEA (125-8000 Hz) for both 

the Efimtsov and Cockburn Robinson models. 

 

Figure 35. SEA predicted cabin interior sound 

pressure levels in the 125 Hz one-third octave band 

due to Efimstov turbulent boundary layer 

excitation. 

80 dB 

40 dB 

Figure 36. FE predicted cabin interior sound 

pressure levels in the 125 Hz one-third octave band 

due to Efimstov turbulent boundary layer 

excitation. 

 One-Third Octave Band Center Frequency, Hz

Sound Pressure Level, dB

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

25 50 100 200 400 800 1600 3150 6300

Hybrid Finite

Element Analysis

Statistical

Energy Analysis

|

|

|

|

|

|

Cabin average for Efimtsov boundary layer excitation

Cabin average for Cockburn/Robertson boundary layer excitation
37 

Figure 37. Averaged predicted LCTR2 one-third octave band sound pressure levels compared to 

measurements in the Bombardier Q400 aircraft. 

 One-third Octave Band Center Frequency, Hz

Sound Pressure Level, dB

20

30

40

50

60

70

80

90

100

25 50 100 200 400 800 1600 3150 6300

Measured sound pressure level data [NIOSH, 2002]

Averaged cabin predictions (Efimtsov TBL excitation)

Averaged cabin predictions (Cockburn/Robertson)

Aft cabin prediction (Efimtsov)
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Large Civil Tiltrotor (LCTR2) Interior Noise Predictions Due to Turbulent 

Boundary Layer Excitation 

5a. CONTRACT NUMBER

 NNL12AA09C 

 6. AUTHOR(S)

Grosveld, Ferdinand W.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center 

Hampton, Virginia 23681

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

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 REPORT NUMBER

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

This report was prepared by Northrop Grumman under NASA contract NNL12AA09C with Analytical Mechanics Associates,

Inc., Hampton, VA

Langley Technical Monitor: Randolph H. Cabell

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

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Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

The Large Civil Tiltrotor (LCTR2) is a conceptual vehicle that has a design goal to transport 90 passengers over a distance of 1800 km at a speed of 556 km/hr. 

In this study noise predictions were made in the notional LCTR2 cabin due to Cockburn/Robertson and Efimtsov turbulent boundary layer (TBL) excitation 

models. A narrowband hybrid Finite Element (FE) analysis was performed for the low frequencies (6-141 Hz) and a Statistical Energy Analysis (SEA) was 

conducted for the high frequency one-third octave bands (125-8000 Hz). It is shown that the interior sound pressure level distribution in the low frequencies is 

governed by interactions between individual structural and acoustic modes. The spatially averaged predicted interior sound pressure levels for the low 

frequency hybrid FE and the high frequency SEA analyses, due to the Efimtsov turbulent boundary layer excitation, were within 1 dB in the common 125 Hz 

one-third octave band. The averaged interior noise levels for the LCTR2 cabin were predicted lower than the levels in a comparable Bombardier Q400 aircraft 

cabin during cruise flight due to the higher cruise altitude and lower Mach number of the LCTR2. LCTR2 cabin noise due to TBL excitation during cruise 

flight was found not unacceptable for crew or passengers when predictions were compared to an acoustic survey on a Q400 aircraft.

15. SUBJECT TERMS

Acoustics; Finite element; Interior noise; Noise prediction; Tiltrotor; Turbulent boundary layer

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