James B. Min

Glenn Research Center, Cleveland, Ohio

Kirsten P. Duffy

University of Toledo, Toledo, Ohio

Benjamin B. Choi and Andrew J. Provenza

Glenn Research Center, Cleveland, Ohio

Nicholas Kray

General Electric Aviation, Cincinnati, Ohio 

Piezoelectric Vibration Damping Study 

for Rotating Composite Fan Blades

NASA/TM—2012-217648

August 2012
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James B. Min

Glenn Research Center, Cleveland, Ohio

Kirsten P. Duffy

University of Toledo, Toledo, Ohio

Benjamin B. Choi and Andrew J. Provenza

Glenn Research Center, Cleveland, Ohio

Nicholas Kray

General Electric Aviation, Cincinnati, Ohio 

Piezoelectric Vibration Damping Study 

for Rotating Composite Fan Blades

NASA/TM—2012-217648

August 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

53rd Structures, Structural Dynamics, and Materials Conference

cosponsored by the AIAA, ASME, ASCE, AHS, and ASC

Honolulu, Hawaii, April 23–26, 2012
Acknowledgments

Authors express thanks to George Stefko and Milind Bakhle for valuable technical discussions; Carlos Morrison for a wireless 

inductive power transfer device development task during the course of the project; Karen Bartos helped for blade mesh modification; 

George Carlson for Ansys Multiphysics discussions; Greg Gemeinhardt for blade composite properties and ply-layup information; 

Ian Prentice for the original GE blade mesh; Karen Taminger, Ajay Misra, Leslie Greenbauer-Seng for the project support with 

the Subsonic Fixed Wing Project of the NASA Fundamental Aeronautics Program. This work was a collaborative effort between 

NASA GRC and GE Aviation through NASA Space Act Agreement SAA3-260, task order 31.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

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Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identification 

only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217648 1 

Piezoelectric Vibration Damping Study for 

Rotating Composite Fan Blades

James B. Min

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135 

Kirsten P. Duffy

University of Toledo

Toledo, Ohio 43606 

Benjamin B. Choi and Andrew J. Provenza 

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135 

Nicholas Kray

General Electric Aviation

Cincinnati, Ohio 45069 

Abstract

Resonant vibrations of aircraft engine blades cause blade fatigue problems in engines, which can lead 

to thicker and aerodynamically lower performing blade designs, increasing engine weight, fuel burn, and 

maintenance costs. In order to mitigate undesirable blade vibration levels, active piezoelectric vibration 

control has been investigated, potentially enabling thinner blade designs for higher performing blades and 

minimizing blade fatigue problems. While the piezoelectric damping idea has been investigated by other 

researchers over the years, very little study has been done including rotational effects. The present study 

attempts to fill this void. The particular objectives of this study were: (a) to develop and analyze a 

multiphysics piezoelectric finite element composite blade model for harmonic forced vibration response 

analysis coupled with a tuned RLC circuit for rotating engine blade conditions, (b) to validate a numerical 

model with experimental test data, and (c) to achieve a cost-effective numerical modeling capability 

which enables simulation of rotating blades within the NASA Glenn Research Center (GRC) Dynamic 

Spin Rig Facility. A numerical and experimental study for rotating piezoelectric composite subscale fan 

blades was performed. It was also proved that the proposed numerical method is feasible and effective 

when applied to the rotating blade base excitation model. The experimental test and multiphysics finite 

element modeling technique described in this paper show that piezoelectric vibration damping can 

significantly reduce vibrations of aircraft engine composite fan blades.

1.0 Introduction

The requirements for advanced aircraft engine components lead to designs which are more 

lightweight and efficient, yet more susceptible to excessive vibration, complex dynamic behavior, and 

uncertain durability and reliability. This complex nature of the dynamic behavior also leads to thicker 

blade designs, hence increased fuel burn, increased noise, potentially reduced engine life, and increased 

maintenance costs. As part of the NASA Fundamental Aeronautics Program (FAP) Subsonic Fixed Wing 

Project, NASA Glenn Research Center (GRC) is investigating potential technologies that support the 

FAP’s goals for lighter, quieter, and more efficient aircraft.
NASA/TM—2012-217648 2 

One of challenge areas in the development of highly efficient and lighter aircraft engines is that high 

performance rotating blades are subject to high cycle fatigue (HCF) limitations as a result of high 

vibratory stresses. HCF accounts for fifty-six percent of major aircraft engine failures and ultimately 

limits the service life of most critical rotating components. An estimated $400M is expended annually for 

HCF related inspection and maintenance of military aircraft alone (Ref. 1). 

Excessive vibration of turbomachinery blades requires damping treatments to mitigate excessive 

vibration levels which cause HCF problems. Designing damping treatments for rotating blades in an 

extreme engine environment is a difficult task with various factors such as high temperatures and 

centrifugal accelerations. Several damping methods have been investigated by NASA researchers for use

in aircraft engine blades, including viscoelastic damping of scaled composite fan blades (Ref. 2), tuned 

impact damping (Ref. 3), plasma sprayed damping coatings (Ref. 4), and high-damping high-temperature 

shape memory alloy materials (Ref. 5). 

Piezoelectric damping has also been explored as a solution for damping treatment. When a 

piezoelectric material experiences a strain, a portion of that energy becomes dielectric energy and is 

stored in the material. In this sense, piezoelectric materials behave electrically as a capacitor. A 

manufactured material with a high electromechanical coupling factor is lead zirconate titanate (PZT) that

is used in many piezoelectric actuators and sensors (Ref. 6). Many researchers have investigated 

piezoelectric materials in parallel with electric circuits that absorb the vibration energy of components. A 

survey of smart structures state-of-the-art has been reviewed (Ref. 7). A method to determine the effective 

damping of a shunted piezoelectric material has been detailed (Ref. 8). Lesieutre (Ref. 6) has also 

described the different types of shunt circuits and how they affect damping behavior. 

For application of piezoelectric dampers to turbomachinery blades, previous work was done with nonrotational applications. Hilbert et al. (Ref. 9) acquired a patent for shunted piezoelectric damping of blades, 

where piezoelectric patches were placed below the blade platform. Livet (Ref. 10) examined negative 

capacitance shunted piezoelectric materials on beams for turbomachinery blade application. Cross and 

Fleeter (Ref. 11) investigated the application of shunted piezoelectric elements to provide passive damping 

to control flow-induced vibrations of chordwise bending mode in a low-aspect-ratio stator vanes. 

Piezoelectric networks have also been studied for reduction of mistuned blade vibration levels through blade 

coupling (Ref. 12). Researchers at GRC also carried out the design and implementation of an experimental 

system that utilized stator vane mounted piezoelectric actuators to control fan-stator interaction noise in a 

simulated turbo-fan engine (Ref. 13). More recently, a resonant damping study using shunted piezoelectric 

patches on plate specimens was conducted (Refs. 14 to 16), wherein the shunted piezoelectric circuit 

damping finite element (FE) models were developed using Ansys Multiphysics software for the resistive 

and inductive circuit piezoelectric simulations. A frequency-switching concept for avoiding resonant 

response in blades was also introduced and a significant amplitude reduction was reported (Ref. 17). These 

efforts reported significant reduction in resonant response utilizing various techniques; however their 

investigations were only non-spinning demonstrations.

While various research has been performed on the use of a shunted piezoelectric material connected 

to electric circuits for controlling vibration damping in a stationery frame, very little study has been done 

to assess rotational effects. The present study attempts to fill this void by demonstrating the feasibility of 

piezoelectric damping on rotating fan blades through design, build, and testing of piezoelectric subscale 

fan blade specimens subjected to high rotational speeds. Specifically, the objectives of this study were: 

(a) to develop multiphysics finite element modeling techniques for harmonic forced vibration response 

analysis coupled with shunted piezoelectric circuits under rotation, (b) to demonstrate the shunted 

piezoelectric blade damping control techniques by utilizing experimental spin rig test, and (c) to validate 

numerical modeling techniques by a comparison with experimental spin test results and vice versa. 

The resistive inductive (RL) shunted circuit technique is generally accepted for passive vibration 

damping control of a single mode or multi-modes (Ref. 18). However, a major problem with this 

approach is the large inductor size and mass for low frequency-tuned resonant circuit. Consequently, 

many researchers proposed the use of synthetic inductors (Refs. 10 and 11) to reduce the weight and 

volume of the circuits. It required a constant power supply, and its size was still considerably large. 
NASA/TM—2012-217648 3 

Nevertheless, the RL shunt or synthetic inductor is suitable for stationary frame applications. For 

turbomachinery applications, however, an implementation issue can arise when applied to the limited 

space in which the blades reside in the engine. Further, there is the risk of rotor imbalance with operation 

at high centrifugal loads. Therefore, our effort at GRC has been to investigate the effectiveness of a 

digital code shunt circuit technique (Ref. 19) using the subscale rotor blade specimens in the GRC 

Dynamic Spin Rig Facility (Ref. 20). 

The current study was focused on a resonant damping control using surface-mounted piezoelectric 

patches on graphite-epoxy composite subscale fan blade specimens. Tests were performed for both nonspinning and spinning conditions. Ansys Multiphysics software was utilized to incorporate our specific 

modeling techniques in the modeling effort and utilized along with experimental tests to validate the

numerical simulation model and vice versa. Some earlier test and analysis work conducted at GRC with 

piezoelectric beam specimens is described (Ref. 16). Our expanded research using plate specimens under 

centrifugal loading conditions at room temperature showed that shunted piezoelectric damping techniques 

have great potential to reduce plate vibrations under a centrifugal load (Refs. 14 and 15). The validated 

numerical models and the experimental test results obtained from these earlier studies allowed us to extend 

our effort for design and optimization of more complex actual turbomachinery rotor blade systems.

To complete the study, a careful combination of experimental test and analysis was performed with 

the intent of achieving the objectives described earlier. The target blade specimen for the present study 

was a General Electric Aviation (GE) GEnx engine subscale composite fan blade. The experimental test 

was performed by spinning the rotor in a vacuum tank with excitation provided active magnetic bearings. 

This rig allows for the measurement of structural damping by itself since the aerodynamic forces are not 

present in the test. Also, the use of commercially available measurement tools and realistic blade

hardware was intended to make the study as accurate as possible in applying the results of our feasibility 

study to real problems encountered in the design of advanced turbomachinery aircraft engines. 

The numerical component of this study was performed not only to develop an accurate analytical tool 

of predictions to compare with the spin rig test results, but also to guide the selection and location of the 

actuator and sensor for the experimental test. The large mass method finite element technique was 

developed for the forced vibration response analyses of blades subjected to blade base acceleration, which 

is generated by the active magnetic bearings directly from the rotor to the blade structure in the form of 

acceleration loads. This numerical technique was incorporated into Ansys Multiphysics program to solve 

the problem.

Experimental blade spin test and multiphysics finite element modeling techniques described in this 

paper show that piezoelectric damping can significantly reduce vibrations of composite fan blades. Our 

study results should serve to enhance the research to further investigate piezoelectric blade vibration 

control in real engine environments.

2.0 Materials and Approaches

Based on the technical challenges and requirements learned from our previous turbomachinery rotor 

blade research, our study was focused on the first bending (1B) mode resonant damping control using 

piezoelectric patches on graphite-epoxy composite blade specimens. Test articles were provided by GE 

Aviation (Ref. 21), and testing and finite element analysis were performed at GRC. While the 

piezoelectric elements can be embedded within the composite blades the subscale blades are very thin, so 

the piezoelectric patches were surface mounted.

Figure 1(a) and (b) show the subscale composite piezoelectric fan blade specimen studied with a 

combination of numerical predictions and experimental spin tests. Table I describes the materials used in 

the blades.

Since a goal of this study was to develop and analyze the forced vibration response model of an actual 

fan blade configuration, a realistic simulation was also wanted in concert to characterize the behavior of 

an actual blade subjected to the proper blade excitation and structural conditions seen during operation of 

the blade spin test. 
NASA/TM—2012-217648 4 

Figure 1.—(a) Piezoelectric fan blade test specimens. (b) Geometric illustration of composite fan blade with 

sensor and actuator locations.

TABLE I.—BLADE AND PIEZOELECTRIC MATERIALS

Blade material Type Description

Polymer matrix composite blades HexPly 8551-7 with IM 7 carbon 

fibers

Epoxy resin with unidirectional carbon fibers, 

ply stack-up

Piezoelectric materials Type Description

Flexible, macro-fiber composite,

d31-type, 300 μm (0.012 in.) thick

Smart-Material Corp.

Sensor: M-0714-P2 

Quantity:1

14.0- by 7.0-mm (0.55- by 0.28-in.) 

6.5 nF nominal capacitance

–600×10–6 free strain

–85 N (–19 lbf) blocking force

Smart-Material Corp.

Actuators: M-2814-P2 

Quantity: 2

14.0- by 28.0-mm (0.55- by 1.10-in.) 

25.7 nF nominal capacitance

–700×10–6 free strain

–85 N (–19 lbf) blocking force

2.1 Spin Rig Blade Experimental Test

In the absence of the blade aerodynamic excitation, it was necessary to utilize an alternative technique

that would allow the blades to be excited in vacuum, such as a shaker system and impact hammers. 

Without the air surrounding the blades the aerodynamic damping is zero, allowing for only the structural 

and material damping on the blade response. The spin test configuration and results are described in 

Duffy et al. (Ref. 22). GRC Dynamic Spin Rig Facility (DSRF) was utilized for the rotating subscale fan 

blade tests (Ref. 20). The spin rig itself is comprised of a large vacuum tank (Figure 2(a)), with a cover 

fabricated to house a rotating axle. Beams, plates or blades can be clamped to the axle (Figure 2(b)) and 

excitation is provided by active magnetic bearings. With a vacuum, any additional damping caused by air 

resistance is negligible, allowing for a more controlled environment in which to test the damping 

effectiveness of implemented systems.

A digitally shunted active control approach that replaces equivalent passive shunt analog circuits with 

a digital code has been used for the current study (Ref. 19) as an alternative approach to the passive RL

shunt with its relatively large size and mass. More than any specific control law the location of the active 

patches is the most important factor affecting the performance of the control system. The active patches 

are placed where their authority over the vibration modes intended to be controlled is the largest. The 

search for candidate locations where active patches can be placed was greatly assisted by the examination 

of the map of the vibration strain energy in the blade structures, which was performed using finite element 

modeling techniques (Refs. 14 and 16). 

To prove the feasibility of this actively shunted digital code control and guide the full-scale 

experiments, several bench studies were also performed. These studies allowed for carefully monitored 

control of the technique and the opportunity to quantify the signal to noise ratio of the piezoelectric 

actuation method. The control components used for the bench tests are exactly the same as in the rotating 
NASA/TM—2012-217648 5 

experiments and more detail is described in (Refs. 19 and 22). A photograph of the entire test system used 

for our bench-top experimental test is shown in Figure 3. 

Many researchers tested their novel ideas by imposing stress in the airfoil to simulate rotational speed 

(Ref. 10), but it is very difficult to obtain a reliable and repeatable measurement due to all of the 

uncertainties associated with applying a distributed force. The only accurate way to perform vibration 

response experiments on the rotating blades is to use a spin test facility that places the blade in a realistic 

rotating environment.

To determine if the piezoelectric component actuates the rotating blades in the proper manner, it is

important to evaluate the experimental test resonance frequency as a function of rotor speed in 

conjunction with the finite element analysis. The analytical approaches described in the following section 

were used for the modeling objective.

Figure 2.—(a) Vacuum tank with cover. (b) Subscale GEnx piezoelectric composite fan blades 

in GRC spin rig facility. 

Figure 3.—Experimental bench-top test assembly.
NASA/TM—2012-217648 6 

2.2 Multiphysics Piezoelectric Finite Element Modeling Technique

The finite element prediction was used to provide a comprehensive study of a variety of structural 

characteristics of a rotating composite fan blade. The first task was to examine the steady stresses due to 

the centrifugal loading. The second task was to perform a free vibration analysis, allowing for the 

classification of every resonance mode within the frequency range of interest. This computation also 

provides information about areas of high stress and how the relative magnitude of these stresses varies 

with frequency. The third task was to accurately model the structural response of the piezoelectric rotating 

blade. Accordingly, a finite element method coupled with the piezoelectric sensor/actuator and electrical 

circuits for predicting forced vibration blade response as a function of the blade rotation has been

developed, and incorporated into the Ansys Multiphysics code. This procedure was for a rotating blade 

model which can predict the strain and stress in harmonically varying blade excitation. While the details

of the formulations to solve the rotating blades modal analysis and harmonic forced vibration analysis 

modeling were described in our previous paper (Ref. 14), its framework components are briefly described 

in the following subsections. 

2.2.1 Geometric Nonlinearity and Spin Softening for Rotating Blade 

To model the state of rotating composite fan blade, it was modeled using a prestressed modal analysis 

method prior to conducting the harmonic forced rotating blade vibration analysis. A blade spin rig 

experimental test was performed at speeds from zero rpm (revolution per minute) to 5000 rpm even 

though the GRC Dynamic Spin Rig Facility has the capability of spinning at up to 20,000 rpm. 

To capture the true blade behavior in this rotational condition, large strain (or finite strain) method 

was needed to take into account the blade shape and stiffness changes under high centrifugal rotation. 

Rigid-body effects (e.g., large rotation) were also taken into account, which separates displacements due 

to rigid-body motion and those associated with the small strains. 

Spin softening (or stress stiffening) of the rotating blade structure due to the stress state was also 

taken into account, which may also be known as geometric stiffness matrix or initial stress stiffness 

matrix. 

The governing equation of motion for rotation including inertia forces and moments can be expressed 

in matrix form as:

[ ] [ ] M U CU K S F   + ++ = { } ( )     { } U             (1) 

where

[ ] M global mass matrix = 

1

e n e M

e

=

∑

=

e   M  element mass matrix = [ ] [ ] T

V

N N dV ρ ∫

[ ] N shape function matrix

 ρ element density 

[ ] C global damping matrix = 

1

e n

Ce e

=

∑

=

n number of elements 

  K  global stiffness of piezoelectric plate including spin softening stiffness due to centrifugal 

force
NASA/TM—2012-217648 7 

  S  stress stiffening contribution matrix due to large strain and large rotation

[ ] [ ][ ] T

V

  S G G dv = τ   ∫

[ ] G matrix shape function derivatives

[ ] τ matrix of current Cauchy (true) stresses in global coordinate

  F  global load vector due to rotating body force, vibration shaker excitation force, and 

piezoelectric voltage and charge

The Block Lanzos Method was used to obtain the resonance frequencies by solving the eigenvalue 

problem. This method uses a combination of the automated shift strategy and the Sturm Sequence Check 

strategy. The two strategies aim to reduce the number of iterations in solving the eigenvalue problem yet 

maintain good accuracy. After obtaining the frequencies and mode shapes of prestressed piezoelectric 

blades under rotational conditions, the following steps were applied to build the coupled piezoelectric 

harmonic forced vibration analysis model to obtain the piezoelectric blade forced vibration responses 

under rotation.

2.2.2 Equation of Motion and Constitutive Relationship of Piezoelectric Materials

Piezoelectric FE equations can be written in terms of nodal displacement {U} and nodal electric 

potential {φ} for each node. The displacement and potential for each element can be expressed, 

respectively, as

{ } [ ] { }

{ } { }e

T

u e

T

UNU

Nφ

=

φ= φ    

(2) 

where

[ ]T Nu displacement shape function (transposed)

T

Nφ     electrical potential shape function (transposed) 

{ } Ue nodal displacement

{ } φe nodal electric potential

The equation of motion corresponding to the piezoelectric actuator and the blade structure can be 

assembled in a global system coordinate based on Equations (1) and (2), which includes the degrees of 

freedom of the piezoelectric actuator (voltages and displacements) and the degrees of freedom of the 

blade structure (displacements) as follows: 

{ }

{ }

{ }

{ }

[ ] { }

{ }

{ }

{ }

0 0

0 0 00

uu u uu uu

T

u

M U U C K K U F

Q K K

φ

φ φφ

                   ++ =          

φ φ      φ              

 

  (3) 

where
NASA/TM—2012-217648 8 

[ ] [ ] [ ] [ ]

e

T

K BB uu u u c dV

Ω

= ∫∫∫ [ ] [ ]

e

T

K BB u u φ φ e dV

Ω

   =    ∫∫∫

[ ]

e

T

K BB φφ φ φ dV

Ω

    = ε     ∫∫∫ [ ] [ ] [ ] e

T

M uu N N u u dV

Ω

= ρ∫∫∫

[ ] [ ] Cuu = β Kuu

{ } F structural loads 

{ } U nodal displacement 

Ωe finite element domain 

[ ] Kuu mechanical stiffness matrix 

Kuφ     piezoelectric coupling matrix 

Kφφ     dielectric stiffness matrix 

[ ] M uu mass matrix 

[ ] Cuu mechanical damping matrix 

{ } Q electrical loads

{ }φ nodal electric potential

ρ piezoelectric density

[ ] Bu , Bφ     derivatives of FEM shape functions

 [c] elastic coefficients

 [e] piezoelectric coefficients

[ε] dielectric coefficients

β damping coefficient 

The basic constitutive relationship of piezoelectric materials is also outlined below. A piezoelectric 

model requires permittivity (or dielectric constants), the piezoelectric matrix, and the elastic coefficient 

matrix to be specified as material properties.

{ } { } [ ]{ } E T C S eE = −     (4) 

{ } [ ] { } { } t S D eS E = +ε    (5) 

where

{T} stress vector (six components x, y, z, xy, yz, xz) 

{ }S strain vector (six components x, y, z, xy, yz, xz) 

{D} electric displacement vector (three components x, y, z) 
NASA/TM—2012-217648 9 

{ } E electric field vector (three components x, y, z) 

E   c  stiffness matrix evaluated at constant electric field, i.e., short circuit 

[ ] e piezoelectric matrix relating stress/electric field

[ ]t e piezoelectric matrix relating stress/electric field (transposed)

S   ε  dielectric matrix evaluated at constant strains, i.e., mechanically clamped

[ ] d piezoelectric matrix relating strain/electric field

[ ]t d piezoelectric matrix relating strain/electric field (transposed)

T   ε

  dielectric matrix evaluated at constant stress, i.e., mechanically free

2.2.3 Piezoelectric Circuit Elements

The piezoelectric circuit element, CIRCU94, simulates basic linear electric circuit components that 

can be directly connected to the piezoelectric finite element domain. It is suitable for the simulation of 

circuit-fed piezoelectric dampers for vibration control under the influence of harmonic (sinusoidally 

varying) forces, currents, displacements, and voltages. CIRCU94 elements were used to model resistor 

(R) and inductor (L) elements connected to each electrode of the piezoelectric patch. Any number of 

combinations of loadings is permitted and they need not be in phase, but they must be at the same 

frequency. The finite element equations for the resistor, inductor, capacitor and current source were 

derived using the nodal analysis method (Refs. 23 and 24). To be compatible with the system of 

piezoelectric finite element equations, the nodal analysis method was adopted to maintain the charge 

balance at each node.

2.2.4 Piezoelectric Vibration Response Analysis Under Harmonic Forced Excitation

The harmonic response analysis solves time-dependent equations of motion shown in Equation (1) for 

structures undergoing steady-state vibration. All points in the structure are moving at the same known 

frequency, however, not necessarily in phase. It is known that the presence of damping causes phase 

shifts. Therefore, the displacements {U(t)} and electrical potential {φ(t)} may be defined as:

{ } ( ) { } { } ( ) { } j t j t Ut Ue t e − ω +ψ − ω +ψ = φ =φ (6) 

where

ω driving frequency 

ψ phase shift

t time

Force and charge are expressed as

{ } ( ) { } { } ( ) { } j t j t Ft Fe Qt Qe − ω +ψ − ω +ψ = = (7) 

Note that the {Q(t)} is related to the current I by 

{ } ( ) { }( ) 1 j t Qt j Ie− ω +ψ = ω (8) 
NASA/TM—2012-217648 10

Substituting Equations (4) to (8) in Equation (3) yields

2 ˆ ˆ

1 ˆ

UU UU UU U

T

U

F K jC M K U

K K I

j

φ

φ φφ

    + ω −ω           =

      φ     ω

 (9) 

where the superscript “^” represents the complex matrices.

Note that peak harmonic response occurs at forcing frequencies that match the natural frequencies of 

the piezoelectric composite blade. These formulations described in this section and Equation (9) were 

utilized to solve for the piezoelectric shunt rotating composite fan blade response in the following section. 

3.0 Piezoelectric Rotating Blade Prestressed Modal Analysis Model and 

Determination of Actuator Location

To assist the setup of the piezoelectric blade spin rig experimental test correctly, piezoelectric finite 

element blade models were developed for rotating piezoelectric composite fan blades. The blade 

geometry is derived by geometric scaling of the actual fan blade. The quasi-isotropic bulk material 

properties from HexPly epoxy resin system with IM7 graphite fiber were used for the fan blade model. 

A finite element model of the entire blade model, including the airfoil and “dovetail” attachment was 

created. It is composed of 3D structural solid element (SOLID95) with twenty nodes having three degrees 

of freedom per node: translations in the nodal x, y, and z directions. The entire model is made up of 

24,395 nodes and 18,960 elements. All displacement directions are constrained at the top surfaces of the 

dovetail attachment to simulate the disk mounting.

The steady stresses are very important, but the alternating (or vibratory) stresses are the driving factor

for a dynamic fatigue stress which can cause fatigue failures when combined with high steady stresses. To

get an understanding of the vibratory response, a free vibration modal analysis was needed (without a 

forcing function). This required calculating the natural frequencies and mode shapes of the blade as a 

function of the rotor speed. 

Both blade spin rig experimental test and finite element modal analysis modeling were performed for 

both non-spinning and spinning conditions. A finite element analysis modeling technique described in 

Section 2.2 was incorporated into the Ansys Multiphysics which can model piezoelectric coupled-field 

elements. 

A finite element composite blade mesh without piezoelectric patch was developed and analyzed first

to identify an optimal location for the piezoelectric patch placement. Free vibration modal analysis (i.e., 

with no time dependent loads applied) was then used for natural frequency and mode shape determination.

The 1B mode was the target mode in this study. Through finite element analysis, patch positioning, taking 

into account both modal strain (for best damping) and steady centrifugal strain (affecting material limits), 

was determined for optimal placement for a higher speed rotational test. 

This FE analysis provided a background for the experimental test plan including the optimal use of 

the piezoelectric actuators and sensors, and setting of the blade experimental test rig operation conditions. 

Figure 4 to Figure 6 show the blade mode shape and modal strain information at zero spin speed. 
NASA/TM—2012-217648 11

Figure 4.—Blade modal displacement contours. 

Figure 5.—Blade modal strain contours. 
NASA/TM—2012-217648 12

Figure 6.—1B mode—modal displacement and strain on blade pressure side.

Subsequently a piezoelectric finite element blade model with the surface mounted piezoelectric patch 

was generated. The piezoelectric patch was meshed with SOLID226 which has 20 nodes with four

degrees of freedom including the piezoelectric effect per node: translations in the nodal x, y, and z 

directions, and the electrical potential V. The piezoelectric properties of PZT-5 (Ref. 25) are given in 

Table II. The poling direction for the piezoelectric patch is vertical through the thickness, and the 

mechanical boundary condition of the structure is clamped. On each interface between piezoelectric and 

the blade, the electrical potential is forced to zero. The piezoelectric patch was placed at the 1B maximum 

modal strain location. Midé PZT-5A qp10w15 piezoelectric patches were bonded to one side of the blade. 

A perfect adhesive bonding between actuator and beam was assumed in this model. The patch dimension 

in effect was 1.0 in. long, 0.5 in. wide, and 0.01 in. thick. In addition, resistor (R) and inductor (L) 

elements were meshed with CIRCU94 to model the resistor and inductor connected to each electrode of 

the piezoelectric patch for the simulation of circuit-fed piezoelectric damper. The finite element mesh of 

the blade specimen model is shown in Figure 7. 

TABLE II.—PIEZOELECTRIC PROPERTIES (εO=8.85×10−12 F/m, 

ELECTRIC PERMITTIVITY OF AIR) USED FOR FE MODEL

PZT-5 Elastic 

properties

Piezoelectric 

coefficients,

(10–12 m/V)

Electric 

permittivity

E11 (GPa) 77 d31 –130 ε11/εo 1300

E22 (GPa) 77 d32 –130 ε22/εo 1300

E33 (GPa) 77 d33 330 ε33/εo 1300

G23 (GPa) 29.6 d24 327 Mass density 

G13 (GPa) 29.6 d15 327 ρ (kg/m3) 7700

G12 (GPa) 29.6

ν12 0.3

ν13 0.3

ν23 0.3
NASA/TM—2012-217648 13

Figure 7.—Piezoelectric FE blade model with surface mounted 

piezoelectric patch (electrical resistor and inductor circuit 

elements are not shown).

Figure 8.—Blade 1B open circuit resonance frequency. 

FE model versus spin rig test. 

In order to assist in the setup of the piezoelectric blade spin rig experimental test, prestressed rotating 

piezoelectric composite fan blade modal analysis was performed to calculate the frequencies and 

corresponding mode shapes as a function of the rotor speed. The piezoelectric blade model was 

numerically spun up to 5000 rpm. The same blade was also experimentally tested in the spin rig to 

determine its natural frequencies and mode shapes. The results of the blade spin rig test were used to 

calibrate a FE model to determine if the modeling assumptions made were acceptable for rotating blade 

modeling. Figure 8 shows the 1B resonance frequency as a function of rpm for open circuit condition in 

which the piezoelectric terminals are not connected. The FE simulation results seemed to indicate that the 

rotational stiffening is the more dominant force, allowing the frequencies to slightly increase with 

rotational speed. The resonant frequency predictions and measured values show close agreement at 

different speeds during the vacuum spin tests. 
NASA/TM—2012-217648 14

In addition, the 1B modal strain values were calculated to see the effects of the blade rotor speeds on 

maximum strain location. Note that the piezoelectric patch location was optimally determined from nonspinning conditions. It was apparent that optimal patch location has to be considered as a function of the 

rotor speed for maximum piezoelectric vibration control benefit. As shown in Figure 9, the patch was no 

longer at the optimum location with increasing the rotor speed. Higher strain area (shown in lighter color 

contours) optimally determined with zero rotation condition for the piezoelectric patch placement was 

changed. This observation in terms of the effects of blade rotations led to further study using the 

generalized electro-mechanical coupling concept (Ref. 8) as a function of the rotor speed, as described in 

the following section.

Figure 9.—Plot shows that optimum patch location for 0 rpm is no 

longer optimal with increasing rotor speed.
NASA/TM—2012-217648 15

4.0 Generalized Electromechanical Coupling Coefficient Method for 

Influence of Blade Rotation on Piezoelectric Vibration Damping

To further examine the piezoelectric vibration control benefit, the generalized electromechanical 

coupling coefficient, K, of the mode was considered. When the piezoelectric patch is loaded, the 

transverse (bending) mode can be described as: force in “1” (length) direction, field in “3” (thickness) 

direction in the common piezoelectric data. Hagood and Flotow (Ref. 8) described the energy dissipation 

properties of the shunted piezoelectric with the piezoelectric constant electromechanical coupling 

coefficient, k31 (lower case), which was defined as the ratio of the peak energy stored in the capacitor to 

the peak energy stored in the material strain with the piezoelectric electrodes open. Square of k31

represents the percentage of mechanical strain energy converted into electrical energy and vice versa.

Also, the generalized electromechanical coupling coefficient, K31 (upper case), was defined as a direct 

measurement of a shunted piezoelectric influence on the system by relating the frequency changes as the 

stiffness changes of the piezoelectric from the open circuit to short circuit value in the same reference. 

Hence, the generalized electromechanical coupling coefficient (added damping) for our piezoelectric 

patched engine fan blade was obtained from the frequency changes from open circuit to short circuit. 

The open-circuit condition is the baseline, where no circuit is attached to the piezoelectric actuator 

terminals. The short-circuit condition is when both of the actuators have a jumper wire attached across the 

terminals. K decreases with increasing rotor speed, indicating that the ability of our current actuator to 

control 1B mode also decreases with increasing rotor speed. More details of our spin rig experimental test 

on this subject are described in our complementary work (Ref. 26). 

The piezoelectric-patched finite element blade models were also built to simulate the open circuit and 

short circuit cases as a function of the rotor speed. Models were used to obtain the first bending 

frequencies as a function of the rotor speed for open circuit and short circuit, respectively. For our 

rotating piezoelectric finite element blade model simulations, electromechanical coupling coefficient, k31, 

was 0.34, resulting in the short circuit stiffness being 88.4 percent of the open circuit stiffness. The 

stiffness of Smart Material Corp.’s piezoelectric patch used in this study was 4.395×106

 psi and 

3.887×106 psi for open circuit and short circuit, respectively, along the fiber direction. From this finite 

element modeling approach, the generalized electromechanical coupling coefficients, K31, were obtained 

as a function of the rotor speed using Equation (10). 

2 2

2

31 2

oc sc

oc

f f K

f

− = , (10) 

where foc and fsc are the blade resonance frequencies with an open circuit and a short circuit across the 

patch, respectively, as a function of the rotor speed.

Figure 10 shows a rotational influence of piezoelectric vibration response measured experimentally 

and a harmonic forced vibration response simulated by finite element analysis, respectively. K31 (nominal 

vibration damping) decreased with increasing the rotor speed since the high modal strain area changes 

with the rotor speed. The finite element results correlated well with those of the blade spin rig

experimental test, and the piezoelectric finite element modeling approach for open circuit and short circuit 

simulations including the blade centrifugal rotational effects were well demonstrated and validated with 

the blade spin rig experimental tests. Based on this observation, it was again apparent that optimal patch 

location has to be considered as a function of the rotor speed for maximum piezoelectric vibration control 

benefit. 
NASA/TM—2012-217648 16

Figure 10.—Effect of rotation on electromechanical

coupling for piezoelectric blade damping (blade spin 

rig test versus finite element model prediction).

5.0 Numerical Model for Forced Vibration Blade Response and 

Piezoelectric Damping Analysis With Blade Spin Rig Test Specimens 

During our blade spin rig experimental testing, the structural response of the rotating blade was 

investigated with the representative blade aerodynamic excitation. The results of the magnetic bearingexcited blade spin rig experiments in vacuum provide crucial information to develop the numerical 

prediction model on the vibratory response and structural damping predictions in the absence of the blade 

aerodynamic forces. This representative experimental test of blade aerodynamic excitation could also 

provide a controlled structural response to guide the more realistic experiments with the blade 

aerodynamic excitations. The following points were taken into consideration in this modeling effort: 

(1) identify the change in forced vibration response with increasing rotational speed, and (2) evaluate the 

finite element predictions to the blade rotating experimental test data for validations. 

To accurately model the condition of the piezoelectric rotating blade spin rig experimental tests, finite 

element modeling techniques were coupled with the piezoelectric for predicting forced vibration blade 

response to blade rotations, and a method has been developed with a harmonically-varying blade base 

excitation by the GRC magnetic bearing blade spin rig while the blades rotate. 

5.1 Piezoelectric Composite Rotating Blade Harmonic Forced Vibration Response 

Analysis Model

A blade base (hub) excitation finite element model has been developed as alternative modeling 

approach to see the effects of the blade rotor speeds on the piezoelectric-patched blade vibration response 

described in Section 4.0. Both the frequency and amplitude of the forcing function are needed to solve 

forced response problems of a particular excitation. Once the physical nature of the forced vibration is 

understood, a prediction of the harmonically-excited rotating blade structural response can be obtained. 

The most important comparison for the purpose of a forced response analysis is to determine how 

well the code can predict the strains as a function of the rotor speeds. It is important to see the effect of 

the blade vibration on the excitation loading in order to understand the interaction between the blade 

structural system and a prescribed blade excitation. While the aerodynamic excitation methods such as 

wind tunnel test are the most realistic for the better-quality blade structural response of a rotating blade in 

operation, our numerical modeling technique was attempted in concert with the experimental test 

conditions used in our magnetic bearing excitation rotating blade rig system. 
NASA/TM—2012-217648 17

To analyze how different boundary conditions affect the vibration response, the boundary conditions 

described in the following subsections were tested to validate the boundary conditions for modeling. 

Since this would be a complicated stick and slip friction contact at the blade hub attachment, there are 

many ways that this constraint boundary condition can affect the response. The nonlinear friction contact 

was not modeled in this study. 

5.1.1 Approach of Directly Applied Blade Vibration Excitation on Rotating Blade With Blade 

Base Clamped Boundary Condition

After verifying the accuracy of the prestressed modal analysis described in Section 3.0, a frequency 

response function analysis was conducted to predict the harmonic strain and stress in the blade. The 

harmonic sweep was conducted over the frequency range known from the prestressed modal analysis 

described in Section 3.0. A node on the FE model was chosen which corresponded with a piezoelectric 

sensor location on the blade. Its nodal strain value was sampled and compared with the experimentallymeasured value. 

First, a finite element modeling attempt was made by applying a blade vibration excitation load as an 

acceleration load on the rotating blade, which was applied to the entire blade structure as follows: 

The differential equation of motion of the rotating blade system was assumed as depicted in 

Figure 11. 

mx cx x f t   1 11 + += ( ) (11) 

where the blade hub is fixed, x1 is the displacement from the static equilibrium position, c is a damping 

constant, k is spring stiffness, and the blade mass (m) is subjected to the harmonic excitation force f (t) = a 

sin ωt, a is the harmonic blade excitation amplitude and ω is frequency of the harmonic motion. 

The blade model shown in Figure 7 was constructed for the testing conditions used in the 

experimental blade spin rig tests. To determine the excitation level in the spin rig, the acceleration 

amplitude at the blade fixture location was measured as a function of the voltage amplitude provided to 

the magnetic bearings (MBs) at 150 Hz, below the 1B resonance frequency.

The blade excitation, f (t), of 0.45-g (g = 9.81 m/sec2

), where g is the acceleration of gravity, was 

applied to the entire rotating blade system. All degrees of freedom at the blade hub (base) were fixed. 

Figure 11.—FE rotating blade model 

assumption with single-degree-offreedom system. 
NASA/TM—2012-217648 18

Figure 12.—Forced vibration blade structural response (blade spin rig test versus blade 

base fixed boundary conditioned FE model). 

The harmonic forced blade vibration response model was run as a function of the rotor speed. The 

analysis results were then correlated with those of the actual blades magnetically excited (0.45-g) in the 

blade spin rig shown in Figure 2. A correlation plot is shown in Figure 12. As shown in Figure 12, the 

blade fixed hub approach along with Equation (11) can cause significant errors in numerical simulation 

modeling for the harmonically-forced blade vibration response analysis under rotational conditions. It 

appears that a harmonically-forced blade excitation load was uniformly applied to the entire blade system, 

as opposed to only the blade base (blade hub). The method to apply excitation forces of uniform 

magnitude directly to the entire blade, including the blade hub (blade base), results in the lack of 

significant inertia and varying local stiffness, which would have resulted in non-uniform accelerations 

over the blade base area and caused significant errors in the harmonically-forced vibration response 

analysis under rotational conditions. 

5.1.2 Approach of Rotating Blade Vibration Excitation Through Large Mass Blade Base

Excitation Boundary Condition

A different method for predicting forced vibratory blade response to blade rotations was attempted

with a notion that the rotating blades excited through the base of blades attached to the magnetic bearing 

spin test rotor has a similarity to the ground motion problem in seismic structural engineering (Ref. 26). 

To verify a possible applicability of such a method employed in seismic structures subjected to arbitrary 

base excitations for our rotating piezoelectric blade modeling, a two-degrees-of-freedom system shown in 

Figure 13 as a simple illustration was considered for our numerical simulation of multiple degrees of 

freedom finite element rotating blade modeled in this study. 
NASA/TM—2012-217648 19

Figure 13.—FE rotating blade model 

assumption with two-degrees-of-freedom 

system. 

The differential equations of motion for the system become in the matrix form, 

( )

11 1

22 2

0 0

0

m cc kk xx x

M cc kk xx x F t

        − −       ++ =              − −  

 

  (12) 

where x1 and x2 are the displacements from the static equilibrium position, c is a damping constant, k is 

spring stiffness, blade mass (m), and largely massed blade hub (fictitious large mass, M) subjected to the 

harmonic excitation force F(t) = a sin ωt, a is the harmonic blade excitation amplitude and ω is frequency 

of the harmonic motion.

The blade base-excitation force vector, F(t) was defined as the base mass times the acceleration. In 

this approach, the actual physical base mass is unknown, so the actual applied forces to the blade base are 

physically immeasurable but rather measured as an enforced motion (acceleration, displacement, or

velocity). Hence it is assumed as a very large value multiplied by a factor of 105 or greater on the actual 

blade model mass taken from its modal analysis for all enforced degrees of freedom. This must be 

checked out for sufficient numerical accuracy in calculations by a trial and error approach. Basically, this 

large mass method (LMM) approach is a method of converting these blade base-excitation motions into 

equivalent forces to be utilized in the matrix equation of motion, Equation (12). This large base mass 

decouples the systems and keeps the blade base response from being amplified at the blade resonance. 

For the current analyses, this approach involved attaching a point mass of significantly greater mass 

than that of the blade itself (MASS21 element) to one of the nodes on the blade hub (blade base) and 

coupling all degrees of freedom for the remainder of the blade base nodes to this “master node.” This 

“master node” of the blade base area is now coupled to the large mass, M, where the blade forced 

excitation is applied. The enforced motions are specified as a base acceleration time history. The 

converted force becomes simply F(t) =M × a sin ω(t) at each enforced DOF. 
NASA/TM—2012-217648 20

[ ]

00000

0 0000

00 000

000 00

0000 0

00000

e x

y

z

A x

B y

C z

M

D

E

F

   

   

 

    = ⋅   θ 

  θ

      θ 

(13) 

where [Me] is the element mass matrix, and A, B, C, D, E, and F are real constants for mass and rotary 

inertia components. A mass element (MASS21) which has six degrees of freedom (three translations and 

three rotations in the x, y, and z directions) was attached to the “ground” (rotor part) to define a large 

mass element [M] with concentrated mass matrix components and rotary inertias as shown in 

Equation (13). 

The harmonic-forced excitation was then applied as a force of magnitude of the combined mass, m

and M, times the desired acceleration, a, on the master node. This method results in a uniform blade 

excitation acceleration being applied to the blade hub (blade base) only. 

An objective of the finite element modeling was to predict frequency response function (FRF) for a 

comparison with experimental spin test response. The blade excitation, F(t), of 0.45-g (g=9.81 m/sec2

) 

amplitude was applied on the large mass M. The harmonic forced blade vibration response model was 

performed as a function of the rotor speed, described in Section 2.2. The analysis results were then 

correlated with those of the actual blades magnetically excited (0.45-g) in the blade spin rig shown in 

Figure 2. A correlation plot for the vibration responses is shown in Figure 14. Blade damping as a 

function of the rotor speed between modeling and experimental test is also shown in Figure 15. The 

results displayed a good correlation. Therefore, it has been proven that the proposed method is feasible 

and effective when applied to the rotating blade base excitation modeling. 

Figure 14.—Forced vibration rotating blade structural response (blade 

spin test versus large mass blade base method FE model). 
NASA/TM—2012-217648 21

Figure 15.—Correlation for rotating piezoelectric composite blade 

vibration damping. 

Figure 16.—Piezoelectric actuator voltage versus blade rotor speed.

5.2 Shunted Circuit Piezoelectric Finite Element Simulation for Digitally Shunted 

Active Control Rotating Blade Spin Rig Experimental Test 

A piezoelectric rotating blade was modeled as part of the open-loop and closed-loop vibration control 

systems implemented for our blade spin rig test (Ref. 22). For the lowest excitation level of 0.4V to the 

magnetic bearings (MB), each actuator was able to reduce the response by about 45-65×10-6 m/m at the 

highest level of 200 V to the patches. A voltage signal of the same frequency was sent to the actuator 

patch. Figure 16 shows the voltage applied to a piezoelectric actuator as a function of rotor speed.

As already mentioned in previous sections, our control system is based on a digitally-tuned RLC

circuit. A target frequency is chosen (set by choosing the inductor value L), along with a bandwidth over 
NASA/TM—2012-217648 22

which the damping functions (set by choosing the resistance R). The inductor value, Li, is chosen for the 

particular (target) frequency, ωi, using Equation (14). 

 1

i L Ci pi

ω = (14) 

where the value of Cpi is the capacitance of the piezoelectric patch in farads. The resistor value, R, is 

chosen to optimize the damping over a frequency bandwidth. In general, increasing the R value means 

good damping, but high control power consumption. Thus, the optimized R value must be selected by 

taking into account the test equipment specifications. 

In our spin rig test, R = 2500 Ω gives a bandwidth of approximately 4 Hz. Since the resonance 

frequency changes with rotor speed, the L value also changes using Equation (14); however, R remains 

the same in our blade spin rig test. These corresponding resistance and inductance values used in our spin 

rig experimental test were input into the rotating shunted-circuit-fed piezoelectric finite element model.

Figure 17 shows a comparison of the strain amplitudes from the numerical spin simulation and spin rig 

test at a piezoelectric sensor location, demonstrating very good correlation. This result clearly indicates 

that a multiphysics electrically-circuited piezoelectric finite element modeling technique developed in this 

study has been nicely validated through the harmonically forced vibration response analysis with actual 

aircraft engine subscale composite fan blade specimens.

As shown in Figure 17, when the control system was implemented in the blade spin test using a 

piezoelectric actuator, the blade forced vibration response amplitudes were significantly decreased over 

the baseline response amplitudes. 

The piezoelectric control vibration damping ratio changed with rotor speed, from about 1.0 percent

critical damping at 0 rpm to about 0.5 percent critical damping at 5000 rpm where the damping increased 

approximately 70 percent over the baseline damping. Our target damping value was 0.5 percent critical 

damping, and this was achieved over the entire test speed range at a low blade excitation level of 0.45-g 

(Figure 18).

Figure 17.—Correlation of actively-shunted piezoelectric blade 

spin rig test versus electrical circuit-fed shunted piezoelectric 

rotating blade forced vibration response model. 
NASA/TM—2012-217648 23

Figure 18.—Damping factor for baseline open circuit 

(no-controlled) and actively-controlled blades.

6.0 Summary

A numerical and experimental study using the electrical circuit-fed piezoelectric patched subscale 

composite fan blade specimens under rotation was performed to develop and demonstrate a shunted 

piezoelectric vibration damping technique to reduce vibrations in aircraft engine blades. No previous 

numerical or experimental studies have investigated the effects of the piezoelectric damping on the 

behavior of turbomachinery aircraft engine rotating composite fan blade structures. The present study 

used both analytical and an experimental study to evaluate the feasibility of piezoelectric blade damping 

approaches during rotation using real composite fan blade subscale specimens. 

In the blade spin rig experimental test, an active control approach, where the passive shunt circuits 

were replaced with equivalent digital code shunt circuits as an alternative approach, was implemented and 

demonstrated. 

A cost-effective numerical method was developed for the rotating blade forced vibration response 

analysis and piezoelectric vibration damping predictions. The multiphysics finite element analysis 

procedures associated with predicting the piezoelectric rotating blade vibrations was developed along 

with blade base (blade hub) excitation modeling approaches where efforts were directed towards 

improving numerical accuracy in forced response predictions. Large mass blade base method was found 

to be the most effective means of reducing the potential errors in the finite element model of a rotating 

blade with blade base excitation. The method was validated with the rotating fan blade specimen 

experiments using a unique magnetic bearing blade spin rig experimental test facility at GRC. The 

numerical methods developed from this study allows for the prediction of modal frequencies and mode 

shapes of the rotating piezoelectric composite blade structures, the harmonic forced vibration responses 

and damping, and the validation of experiment test results and vice versa. 

Spin rig experimental test and numerical modeling results of the subscale piezoelectric composite fan 

blade specimens indicate that active piezoelectric resonance control approach can substantially reduce 

vibrations of rotating composite fan blades. The piezoelectric blade vibration damping of 0.5 to 

1.0 percent was observed for the 1B mode of the subscale GE piezoelectric composite fan blade at speeds 

of 0 to 5000 rpm at a low blade excitation level of 0.45-g, where g is the acceleration of gravity. Even at a 

relatively higher blade rotational speed of 5000 rpm, the blade piezoelectric vibration damping increased 

by as much as 70 percent over the baseline damping. Our target damping value was 0.5 percent critical 

damping, and this was achieved over the entire test speed range at a low blade excitation level of 0.45-g.
NASA/TM—2012-217648 24

The results presented in this study have provided insight for future research by indicating that smart 

piezoelectric damping technology can alter the dynamic behavior of a structure intelligently. The 

technology can reduce unsafe vibration dynamic stresses, resulting in increased engine life as well as

enhanced damage tolerance. Additionally, an optimized integrated application of this technology may 

provide overall aircraft weight and volume savings over using conventional damping technology systems. 

While our analytical and experimental study, which was conducted using more realistic blade 

specimens combined with blade spin rig experimental test, has resulted demonstrating the feasibility of 

piezoelectric blade damping benefits, still much work is required before it can be in a real engine fan 

blade application applied in a commercial aircraft engine blade system. 

7.0 Future Work

A few technical challenge areas for future work are as follows: (1) the modeling techniques explained 

herein can be extended to real blade specimens, nevertheless a full forced response prediction, by 

applying the CFD aerodynamic results or wind tunnel experimental test data as a forcing function to the 

rotating piezoelectric blade model, would allow for more validations of these methods; (2) challenges 

associated with using piezoelectric actuators embedded in composite fan blades, insuring sufficient

component strength and fatigue properties need to be studied; (3) use of synthetic inductive shunt circuits

or digital control techniques may also be feasible concepts, but still they will require power in the rotating 

frame. The capability to transfer power to the rotating frame using a wireless inductive power transfer 

device needs further development; (4) Newer state-of-the-art high temperature piezoelectric patches 

should be considered for high temperature applications. 

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of Subscale Composite Fan Blades, Proceedings of ASME Turbo Expo 2012: Power for Land, Sea 

and Air GT2012, June 11-15, 2012, Copenhagen, Denmark. 

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transducer, Proceedings of IEEE ultrasonics symposium, Vol. 2, 1999, pp. 1105-1108. 

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25. D. Varelis and D. A. Saravanos: Small-Amplitude Free-Vibration Analysis of Piezoelectric 

Composite Plates Subject to Large Deflections and Initial Stresses, ASME Journal of Vibration and 

Acoustics, Vol. 128, February 2006. 

26. Y.-W. Kim, M. J. Jhung: Mathematical Analysis Using Two Modeling Techniques For Dynamic 

Responses Of A Structure Subjected To A Ground Acceleration Time History, Nuclear Engineering 

And Technology, Vol. 43, August 2011. 
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4. TITLE AND SUBTITLE

Piezoelectric Vibration Damping Study for Rotating Composite Fan Blades 

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Min, James, B.; Duffy, Kirsten, P.; Choi, Benjamin, B.; Provenza, Andrew, J.; Kray, Nicholas 

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WBS 561581.02.08.03.43.04.04 

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John H. Glenn Research Center at Lewis Field 

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14. ABSTRACT

Resonant vibrations of aircraft engine blades cause blade fatigue problems in engines, which can lead to thicker and aerodynamically lower 

performing blade designs, increasing engine weight, fuel burn, and maintenance costs. In order to mitigate undesirable blade vibration 

levels, active piezoelectric vibration control has been investigated, potentially enabling thinner blade designs for higher performing blades 

and minimizing blade fatigue problems. While the piezoelectric damping idea has been investigated by other researchers over the years, 

very little study has been done including rotational effects. The present study attempts to fill this void. The particular objectives of this study 

were: (a) to develop and analyze a multiphysics piezoelectric finite element composite blade model for harmonic forced vibration response 

analysis coupled with a tuned RLC circuit for rotating engine blade conditions, (b) to validate a numerical model with experimental test 

data, and (c) to achieve a cost-effective numerical modeling capability which enables simulation of rotating blades within the NASA Glenn 

Research Center (GRC) Dynamic Spin Rig Facility. A numerical and experimental study for rotating piezoelectric composite subscale fan 

blades was performed. It was also proved that the proposed numerical method is feasible and effective when applied to the rotating blade 

base excitation model. The experimental test and multiphysics finite element modeling technique described in this paper show that 

piezoelectric vibration damping can significantly reduce vibrations of aircraft engine composite fan blades. 

15. SUBJECT TERMS

Piezoelectric; Fan blade; Finite element; Vibration; Damping; Composites; Blade base excitation; Spin testing 

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