March 2007 

NASA/TM-2007-214857 

Flutter Analysis of the Shuttle Tile Overlay 

Repair Concept 

Kim S. Bey, Robert C. Scott, and Robert E. Bartels 

Langley Research Center, Hampton, Virginia 

William A. Waters and Roger Chen 

Lockheed Martin Space Operations, Hampton, Virginia 
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March 2007 

NASA/TM-2007-214857 

Flutter Analysis of the Shuttle Tile Overlay 

Repair Concept 

Kim S. Bey, Robert C. Scott, and Robert E. Bartels 

Langley Research Center, Hampton, Virginia 

William A. Waters and Roger Chen 

Lockheed Martin Space Operations, Hampton, Virginia 
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National Aeronautics and Space Administration. 
Abstract 

The Space Shuttle tile overlay repair concept, developed at the NASA Johnson Space Center, is 

designed for on-orbit installation over an area of damaged tile to permit safe re-entry. The thin 

flexible plate is placed over the damaged area and secured to tile at discreet points around its 

perimeter. A series of flutter analyses were performed to determine if the onset of flutter met the 

required safety margins. Normal vibration modes of the panel, obtained from a simplified 

structural analysis of the installed concept, were combined with a series of aerodynamic analyses 

of increasing levels of fidelity in terms of modeling the flow physics to determine the onset of 

flutter. Results from these analyses indicate that it is unlikely that the overlay installed at body 

point 1800 will flutter during re-entry. 

Introduction 

The Shuttle tile overlay repair concept, developed at the NASA Johnson Space Center, is 

designed for on-orbit installation in the event of damage to the thermal protection system tiles to 

enable safe re-entry. It consists of a thin flexible C/SiC plate backed with a layer of fibrous 

insulation that covers the area of damaged tile. The plate and underlying gasket are secured to 

the tile with auger-like fasteners through holes at discreet locations around the perimeter of the 

plate. The tile overlay repair concept installed on an array of tiles is shown in Figure 1. As part 

of the development effort, a series of panel flutter analyses were performed to determine whether 

the concept met the required safety margins for the onset of flutter. 

Figure 1 - Tile overlay repair concept installed on a tile array. 

Panel flutter is a self-excited, dynamic-aeroelastic instability of thin plate or shell-like 

components of a vehicle occurring frequently, though not exclusively, in supersonic flow. 

Flutter is caused and maintained by interaction among the aerodynamic, inertial, and elastic 

forces of the system. [1] During panel flutter, the amplitude of the oscillatory out-of-plane 

motion increases exponentially with time, but is usually limited by the effects of in-plane stresses 
2 

and structural nonlinearities. At subsonic speeds, the instability is usually in the form of static 

divergence or aeroelastic buckling. [2] The onset of flutter is characterized by the dynamic 

pressure at which the amplitude of oscillatory motion grows with time. The accuracy of the 

prediction of the flutter dynamic pressure is determined by the accuracy of both the aerodynamic 

and structural analyses used to predict the aerodynamic forces on and structural response of the 

oscillating plate, respectively. To avoid flutter, a panel should be designed so that the flutter 

dynamic pressure is greater than the local dynamic pressure experienced in flight. The 

requirement for the Shuttle includes a 1.5 factor of safety on the flight dynamic pressure of 375 

psf, thus requiring that the flutter dynamic pressure of the overlay panel be greater than 563 psf. 

A number of vibration and flutter analyses of the overlay panel were performed to determine the 

onset of flutter and to quantify uncertainties in the analyses. The series of analyses are described 

and numerical results are presented in this paper. 

Structural Model and Modal Analyses 

The overlay plate is constructed of a C/SiC composite material and is 15 inches wide by 25 

inches long with a thickness of 0.04 inches. A series of holes are placed along the perimeter of 

the plate, as shown in Figure 1, to accept the auger and washer fasteners that attach the overlay 

repair to Shuttle tile. For the structural analysis, material corresponding to the holes was not 

removed from the finite element model. The material properties used for the C/SiC material 

were taken from experimental data obtained for a 0.13-inch thick plate of similar construction 

[4]. C/SiC is a nonlinear material in the sense that the stress-strain curves for the material are 

linear only for small strain. Additionally, the stress-strain behavior is different for compressive 

and tensile loading. The linear structural analysis for vibration modes assumed an orthotropic 

material with a modulus that is the average of the modulus obtained from compression and 

tension tests at 20000F given in Reference 4. 

A free vibration analysis of the plate was performed to validate the finite element model by 

comparison with experimental data. Then a modal analysis of the plate in an installed 

configuration was performed by constraining the model at the auger locations. The mode shapes 

from the modal analysis of the constrained plate were used in the flutter analysis. 

Free Vibration of the Overlay Plate 

A free vibration analysis of the plate was performed to validate the finite element model by 

comparison with experimental data. The free vibration analysis of the plate was performed using 

MSC.NASTRAN SOL 103 with the finite element mesh shown in Figure 2. All degrees of 

freedom for a single node corresponding to a corner auger hole were constrained to eliminate 

rigid body motion, as indicated in Figure 2. Structural damping of the plate was neglected. The 

natural frequencies of the first four modes obtained from the analysis are compared to those 

obtained from a free vibration experiment [5] in Table 1. The correlation between the analysis 

and experiment suggests that the finite element mesh and material properties used in the model 

are adequate. 
3 

Figure 2 - Coarse finite element mesh used for free vibration analysis. 

Table 1 - Comparison of free vibration frequencies obtained with analysis and experiment 

Frequency (Hz) 

Mode Analysis Experiment 

1 19.4 16.4 

2 20.9 20.5 

3 47.4 40.6 

4 51.6 46.7 

Modal Analysis of the Installed Overlay Plate 

A modal analysis of the installed overlay plate was performed for use in the flutter analysis. A 

simplified structural model which neglects structural damping of the plate, damping associated 

with the underlying gasket and tile, and plate curvature and resulting stress due to compression 

of the gasket during installation was used. These factors tend to reduce the susceptibility of the 

panel to flutter, therefore, neglecting them results in a conservative analysis. 

For an actual installation of the overlay plate, it is likely that some of the auger holes will lie over 

inter-tile gaps or near tile edges. Augers will not be installed into such holes as illustrated in 

Figure 1. Since the location of uninstalled augers is installation location specific, it was assumed 

that all augers are installed for the modal analysis. In the finite element mesh, nodes are placed 

at locations corresponding to the center of the auger holes. The auger attachment to the tile is 

modeled as a rigid point constraint, meaning all degrees of freedom are constrained for the nodes 

corresponding to hole centers. The constrained nodes corresponding to the auger locations are 

denoted by ellipses on the coarse finite element mesh shown in Figure 3. 
4 

The modal analysis of the constrained plate was performed using MSC.NASTRAN SOL 103 [3] 

to determine the normal mode shapes to be used in the nonlinear flutter analysis. A mesh 

convergence study was performed to determine the sensitivity of the first natural frequency of 

the constrained plate to mesh size. The mesh convergence study consisted of a sequence of 

modal analyses performed with increasingly refined finite element meshes, starting with the 

mesh shown in Figure 3. The results of the mesh convergence study in Figure 4 show that the 

first mode frequency decreases as the number of nodes in the mesh increases, and that 

convergence isn’t reached with a mesh containing 26,539 nodes. A decrease in the predicted 

frequency of 4% is obtained when elements in the 26,539-node mesh are subdivided to obtain a 

105,557-node mesh. To achieve a balance between analysis complexity and accuracy, the 

vibration modes obtained with the 26,539-node mesh are used in the nonlinear flutter analysis 

described below. The first 25 modes having frequencies between 64 and 670 Hz are used. The 

first four mode shapes obtained with the 26,539-node mesh are shown in Figure 5. 

Figure 3 – Coarse finite element mesh with constrained nodes used for modal analysis of installed overlay 

plate. 

Figure 4 - Convergence of the first natural frequency of the constrained plate with mesh refinement. 
5 

Figure 5 - First four mode shapes for the constrained plate obtained with a 26,539-node mesh. 

Flutter Analysis using Linear Aerodynamic Theory 

The procedure used for a preliminary flutter assessment combines a linear flutter analysis 

performed at flow conditions of Mach 2 with correlations from classical design criteria [2] for 

extending the results to flow conditions of Mach 1. 

A linear flutter analysis was performed for Mach 2 flow aligned with the long axis of the panel, 

the flow direction for which the panel is most susceptible to flutter. NASTRAN Version 2005 

SOL 145 [3] was used for the flutter analysis. It uses a (linear) quasi-steady two-dimensional 

aerodynamic theory to predict the aerodynamic forces on an oscillating plate. In particular, firstorder piston theory was used and is believed to be reasonably accurate for Mach 2 flow. 

The finite element mesh shown in Figure 3 was used for the structural portion of the flutter 

analysis. To determine the sensitivity of the onset of flutter to the auger attachment constraints, 

several constraint conditions at the auger fastener locations were analyzed. The resulting flutter 

dynamic pressure predictions are summarized in Table 2. The fastener constraint conditions 

listed in the first column of Table 2 represent the set of constraints applied to the nodal degreesof-freedom (DOFs) for each fastener - three translational DOFs u, v, and w and three rotational 

DOFs θx, θy, θz about the x-, y-, and z-coordinate directions respectively. A value of 1 indicates 

that motion associated with the degree of freedom was constrained and a value of 0 indicates that 

it was free. Therefore, a constraint condition 001000 means that only out-of-plane displacements, 

those in the z-direction, were constrained at the fastener locations. The cases are listed in Table 

2 in order of increasingly constrained motion, and hence, in order of increasing flutter dynamic 

pressure. The case with all DOFs constrained is believed to most accurately represent the 

fastener-tile attachments. For all constraint cases, a considerable margin exists between the 
6 

predicted flutter dynamic pressure and the 563 psf requirement. 

 

Table 2 – Summary of results from a NASTRAN flutter analysis (SOL 145) of a simplified model of the 

installed overlay panel at Mach 2 flow conditions. 

Fastener Constraints 

uvwθxθyθz 

(1 = fixed, 0 = free) 

Flutter 

Frequency (Hz) 

Mach 2 

Flutter Dynamic Pressure (psf) 

001000 63 1050 

111000 66 1056 

111111 100 1352 

Correlations from Reference 2 are used to extend the flutter analysis results to Mach 1 flow 

conditions. The correlation provides a multiplicative “knockdown” factor that is applied to the 

flutter dynamic pressure obtained from the linear flutter analysis at Mach 2. The correlation is 

based upon experimental data obtained for a plate with an aspect ratio of 2 with completely 

clamped edges. The flutter dynamic pressure at Mach 1, obtained from the correlation, is listed 

in Table 3. The constraint case 111111 in the last row of Table 3 most closely represents the 

experiments upon which the correlation is based, but it is likely that the actual flutter dynamic 

pressure is less than the correlated values. Since the flutter dynamic pressure from the 

correlation is less than 563 psf (the flight dynamic pressure with the required safety factor of 1.5 

applied), panel flutter cannot be eliminated as a design concern for the overlay panel using this 

simplified analysis. 

Table 3 - Summary of flutter results for a simplified model of the installed tile overlay panel at Mach 1, based 

on emperical correlation2

 of Mach 2 predictions. 

Fastener Constraints 

uvwθxθyθz 

(1 = fixed, 0 = free) 

Correlated2 Mach 1 

Flutter Dynamic Pressure (psf) 

001000 291 

111000 293 

111111 375 

According to classical literature on flutter [1], three-dimensionality of the flow becomes 

important when 1 1 2 − <

w

M l , where l is the length of the panel in the direction of the flow and 

w is the width. For the overlay panel, this parameter suggests that three-dimensionality of the 
7 

flow may be important for M<1.2. Since the flutter analysis at Mach 2 is based on twodimensional flow, and the empirical correlation is based on boundary conditions that are “stiffer” 

than those of the installed overlay panel, a flutter analysis using computational fluid dynamics 

(CFD) is required to reduce uncertainties in the aerodynamic portion of the flutter analysis. 

Flutter Analysis using Nonlinear Aerodynamic Theory 

To incorporate more realistic physics into the flutter analysis, a nonlinear aerodynamic analysis, 

specifically CFD solutions of the Euler and Navier-Stokes equations, was coupled with the 

simplified linear structural model for Mach 1.1 and Mach 2 flow conditions. The Euler 

equations describe three-dimensional inviscid flow and capture the effects of an oscillating plate 

on the flow, including shocks and expansions. The Navier-Stokes equations describe threedimensional viscous flow which adds the effects of the boundary layer near the surface of the 

plate. 

The CFD code CFL3Dv6 [6] was used for the flutter analysis. The CFL3Dv6 code solves the 

time-dependent conservation law form of the Reynolds-averaged Navier-Stokes equations using 

a finite-volume approach. Upwind-biasing is used for the convective and pressure terms while 

central differencing is used for the shear stress and heat transfer terms. Implicit time 

advancement is used with the ability to solve steady or unsteady flows. Sub-iteration and multigrid capabilities are available for improved accuracy and convergence acceleration. 

The typical procedure for using CFL3D for flutter analysis is to obtain a static aeroelastic 

solution prior to running a solution to determine dynamic stability. This is done by using 

artificially large values of structural damping in the analysis where CFL3D is run until in it 

converges. This step is unnecessary for the inviscid analysis as the static aeroelastic solution has 

zero panel deflection and the flow field has free stream conditions throughout. For the viscous 

analyses, the pressure difference across the panel is not zero, and a static aeroelastic solution 

must be obtained for each dynamic pressure. 

Once the appropriate flow field and static aeroelastic solution has been established, the dynamic 

analysis is performed. The structural damping is set to a realistic value (zero in this case) and the 

generalized coordinates are given small initial velocities. The analysis is run until dynamic 

aeroelastic stability can be established: if the generalized coordinate values converge to a finite 

value then the system is stable, but if they grow with time, then the system is unstable. For each 

freestream flow condition of interest, flutter onset is determined by varying the dynamic pressure 

until the system becomes unstable. 

Inviscid Flutter Analysis Results and Discussion 

For the flow field grid, the overlay panel is modeled as a flexible section of a larger rigid flat 

plate. Only one grid point upstream of the flexible panel is required, resulting in the grid shown 

in Figure 6. Time histories of the modal amplitudes from the flutter analysis at Mach 2 with 

dynamic pressures of 800 psf and 900 psf, are shown in Figure 7. For a dynamic pressure of 800 

psf, the amplitudes decay with time, and are therefore stable. For a dynamic pressure of 900 psf, 

the amplitudes are growing with time, and therefore, are unstable. Note that the first and second 

modes are involved in producing flutter. The third mode contributes only after the onset of 

flutter, suggesting weak participation. Thus, the dynamic pressure associated with panel flutter 
8 

onset at Mach 2 is between 800 and 900 psf. The inviscid flutter analysis for Mach 1.1 flow 

conditions predicted the onset of flutter at a dynamic pressure of 275 psf, significantly lower than 

the required 563 psf. Therefore, panel flutter cannot be eliminated as a design concern for the 

overlay panel using an inviscid analysis. The assumption of inviscid flow results in velocities 

near the surface of the plate that are larger than for the actual flow which is viscous. Results 

from flutter analysis using viscous flow are presented in the next section. 

Figure 6 - Volume grid used in the inviscid panel flutter analysis. 

Figure 7 - Generalized coordinate time histories from the inviscid flutter analysis for Mach 2 flight with 

dynamic pressures of 800 psf (left) and 900 psf (right). 
9 

Viscous Flutter Analysis Results and Discussion 

For the viscous analysis, the flat plate surface must be extended upstream in an attempt to match 

the boundary layer predicted by an OVERFLOW analysis of the flow over the entire vehicle. 

Thus, Mach numbers and Reynolds number roughly correspond to OVERFLOW boundary layer 

profile data at body point 1800 specified by the Johnson Space Flight Center [7]. 

For the analysis at Mach 2 flow conditions, the grid was extended upstream a distance of 860 

inches. The surface grid is shown in Figure 8 with displacements corresponding to the first 

vibration mode applied to the panel to reveal its location in the grid. The resulting boundary 

profile at the patch panel leading edge for a viscous steady analysis is compared to the 

OVERFLOW full-vehicle boundary layer profile in Figure 9. Notice that for the Mach number 

approaches 1.8 in the z-direction. The CFL3D analysis was performed at a Mach number of 1.8 

to match the boundary layer obtained from the OVERFLOW calculation of the entire vehicle at a 

Mach 2 flight (freestream) conditions. The time histories of the modal amplitudes obtained with 

the viscous flutter analysis at Mach 2 with dynamic pressures of 800 and 900 psf are shown in 

Figure 10. The system is stable at 800 psf and unstable at 900 psf, indicating a flutter dynamic 

pressure of approximately 850 psf. This flutter dynamic pressure is comparable to the inviscid 

flutter analysis prediction with acceptable margin above the 563 psf requirement. 

 

Figure 8 - Surface grid for Mach 2 viscous flutter analysis with the panel deflected to the first mode shape for 

clarity. The flow is from right to left. 
10 

Figure 9 - Comparison of boundary layer profiles at the panel leading edge placed at body point 1800 on the 

vehicle for Mach 2 flow. Solid line indicates OVERFLOW solution obtained with a flow domain 

encompassing the entire vehicle. Dahed line indicates CFL3Dv6 solution obtained with a truncated flow 

domain in the vicinity of the panel. 

Figure 10 – Generalized coordinates time histories from viscous flutter analysis for Mach 2 flight with 

dynamic pressures of 800 psf and 900 psf. 

 

In order to achieve the desired boundary layer profile for Mach 1.1 flow conditions, the grid was 

extended upstream of the overlay panel for a distance of 415 inches. The resulting surface grid is 

shown in Figure 11 with first mode displacement applied at the location of the panel. The 

OVERFLOW boundary layer profiles were rescaled to approach a Mach number of 1.1 to 

provide the target boundary layer profile for the CFL3D analysis. A comparison of the boundary 
11 

layer profiles at the panel leading edge is shown in Figure 11. Time histories of the modal 

amplitude show that the system is stable at a dynamic pressure of 1000 psf and unstable at a 

dynamic pressure of 1100 psf, indicating a flutter dynamic pressure of approximately 1050 psf - 

sufficient margin above the 563 psf requirement and significantly higher than the inviscid 

prediction of 275 psf. Based on this analysis, it is unlikely that the overlay panel will flutter if 

installed at body point 1800 on the Shuttle. 

Figure 11 - Surface grid for viscous flutter analysis at Mach 1.1 with panel deflected to the first mode shape. 

Flow is from right to left. 

Figure 12 - Comparison of boundary layer profiles at the leading edge of overlay panel for Mach 1.1 flow. 
12 

Summary and Concluding Remarks 

A comparison of the results from the flutter analyses with all degrees of freedom constrained at 

all auger locations is listed in Table 4. These analyses indicate that at Mach numbers of 2.0 and 

higher, adequate panel flutter margins exist within the shuttle flight envelope for the overlay 

panel installed at body point 1800. However, near Mach 1.0 empirical flutter analysis using the 

criteria described in Reference 2 yield inadequate flutter margins. To address this concern, 

flutter analyses were performed using CFL3D modeling both an inviscid (Euler) and viscous 

(Navier-Stokes) flow field. The inviscid analyses indicate that panel flutter onset would occur at 

lower dynamic pressures than had been predicted by the linear and empirical solutions; yet, the 

bottom line results are the same with sufficient flutter margin still remaining at Mach 2 and 

inadequate flutter margin near Mach 1.0. The viscous flutter analysis for Mach 2.0 was 

consistent with the inviscid solution. The viscous flutter analyses near Mach 1.0 indicate that the 

flutter onset dynamic pressure is, in fact, well outside the Shuttle flight envelope for body point 

1800. 

Table 4 - Flutter analysis results for increasing levels of fidelity flow physics 

Mach 2 Flutter Mach 1.1 Flutter 

Analysis Type Frequency 

(Hz) 

Dynamic Pressure 

(psf) 

Frequency 

(Hz) 

Dynamic Pressure 

(psf) 

Piston Theory 

+ Correlation 100 1352 -- 375 

Inviscid 

CFL3D 75 890 61 275 

Viscous 

CFL3D 69 850 47 1050 
13 

References 

1. Dowell, E. H.: Panel Flutter. NASA Space Vehicle Design Criteria (Structures) SP-8004, 1964, 

Revised 1972. 

2. Lemley, Clark E.: Design Criteria for the Prediction and Prevention of Panel Flutter, Volume I: 

Criteria Presentation. AFFDL-TR-67-140, Air Force Flight Dynamics Laboratory (FDDS), WrightPatterson Air Force Base, Ohio 45433, 1968, Figure 1, page 8. 

3. NASTRAN User’s Guide, MSC Software, 2005. 

4. Cuneo, Jacques: A-Basis Mechanical and Thermal Properties of GE 2D C/CSiC for RCC Plug 

Program. ITAR Test Report, Southern Research Institute, Huntsville, AL, SRI-ENG-06-15-11502.01, 

2006. 

5. Coa, Tim: Free-Free Vibration Test Report, NASA Johnson Space Center, 2006. 

6. Bartels, R. E.; Rumsey, C. L.; Biedron, R. T.: 2006 CFL3D Version 6.4 General Usage and 

Aeroelastic Analysis. NASA-TM 2006-214301, 2006. 

7. Greathouse, Jim: private communications, NASA Johnson Space Center, 2006. 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Flutter Analysis of the Shuttle Tile Overlay Repair Concept

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Bey, Kim S.; Scott, Robert C.; Bartels, Robert E.; Waters, William A.; and

Chen, Roger

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

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

Washington, DC 20546-0001

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14. ABSTRACT

The Space Shuttle tile overlay repair concept, developed at the NASA Johnson Space Center, is designed for on-orbit

installation over an area of damaged tile to permit safe re-entry. The thin flexible plate is placed over the damaged area and

secured to tile at discreet points around its perimeter. A series of flutter analyses were performed to determine if the onset of

flutter met the required safety margins. Normal vibration modes of the panel, obtained from a simplified structural analysis of

the installed concept, were combined with a series of aerodynamic analyses of increasing levels of fidelity in terms of

modeling the flow physics to determine the onset of flutter. Results from these analyses indicate that it is unlikely that the

overlay installed at body point 1800 will flutter during re-entry.

15. SUBJECT TERMS

Flutter; Repair; Shuttle; Tile

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