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Research Papers

# Dynamics of a Shell-Type Amplified Piezoelectric Actuator

[+] Author and Article Information
Aman Kumar

Department of Mechanical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, West Bengal, India
e-mail: e.aman.k@gmail.com

Anirvan Dasgupta

Professor
Department of Mechanical Engineering,
Center for Theoretical Studies,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, West Bengal, India
e-mail: anir@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 11, 2017; final manuscript received January 5, 2018; published online March 14, 2018. Assoc. Editor: A. Srikantha Phani.

J. Vib. Acoust 140(4), 041011 (Mar 14, 2018) (9 pages) Paper No: VIB-17-1314; doi: 10.1115/1.4039239 History: Received July 11, 2017; Revised January 05, 2018

## Abstract

A dynamic model for a shell-type amplified piezoelectric actuator (APA) is proposed. The dimensions of the shell of a typical shell-type actuator allow one to model it as a set of connected beams. The contribution of the geometric nonlinearity in the axial direction of the beams due to bending is accounted for in the formulation. Subsequent nonlinear analysis using both analytical and numerical approaches reveals the presence of second harmonic in the response spectrum. This occurrence is also seen experimentally. A frequency regime is also identified within which the effect of quadratic nonlinearity is minimal and the actuator exhibits high fidelity. Dependence of the response spectrum on the actuator geometry has been studied. For a given forcing frequency, a certain geometric configuration is shown to exist, which maximizes the nonlinear effects. The effect of prestressing of the piezoelectric stack on the frequency spectrum is also studied. The obtained results are expected to lead to improved design of such actuators.

## References

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Cedrat Technology, 2008, “ APA120ML,” Cedrat Technologies, Meylan, France, accessed Feb. 19, 2018,

## Figures

Fig. 1

A typical shell-type piezoelectric actuator APA120ML from Cedrat Technologies. The directions of motion of the piezoelectric stack and the shell are indicated.

Fig. 2

Kinematics of beams considering geometric nonlinearity

Fig. 3

Kinematics of the shell considering geometric nonlinearity

Fig. 4

Mode shapes pertaining to first and second modes. () is the undeformed configuration and () is the deformed configuration: (a) first mode shape pertaining to ωn1 = 1381.66 and (b) second mode shape pertaining to ωn1 = 12460.49.

Fig. 5

Schematic representation of the shell with forcing F

Fig. 6

Fast Fourier transform (FFT) plots for increasing nondimensional amplitude of excitation C0, keeping ε fixed (analytical): (a) C0 = 40, (b) C0 = 100, and (c) C0 = 200

Fig. 7

FFT plots for increasing values of ε keeping C0 fixed (analytical): (a) ε = 0.08, (b) ε = 0.1, and (c) ε = 0.2

Fig. 8

FFT plots for increasing values of C0 keeping ε fixed (numerical): (a) C0 = 40, (b) C0 = 100, and (c) C0 = 200

Fig. 9

(a) Variation of A2/A1 with C0. Obtained analytically () for ε=0.06, () for ε=0.07, () for ε=0.08, and numerically, () for ε=0.06, () for ε=0.07, () for ε=0.08. (b) Variation of A2/A1|a obtained analytically with A2/A1|n obtained numerically. “”, “”, “” pertain to ε=0.06, ε=0.07 and ε=0.08, respectively, and () is 45 deg line.

Fig. 10

FFT plots of for different values of Ω keeping C0 fixed: (a) Ω = 0.3, (b) Ω = 0.46, and (c) Ω = 0.92

Fig. 11

Variation of A2/A1 with Ω

Fig. 12

(a) Photograph of the experimental setup. (b) Schematic representation of the experimental setup: 1—piezoelectric actuator (APA120ML from Cedrat Technologies), 2—laser vibrometer (Polytec PDV-100), 3—computer (running LabVIEW) with I/O card (NI PCI-6259), 4—signal amplifier (LA-75), and (c) FFT of the response of the actuator to an input sinusoidal voltage signal of frequency ν = 60 Hz.

Fig. 13

Effect of actuator geometry on its response spectrum: (a) A2/A1 versus θ (rad) for forcing frequencies Ω = 0.154, Ω = 0.278 and Ω = 0.308 denoted by “”, “”, “” respectively. (b) Amplification M versus θ (rad).

Fig. 14

Model of the Actuator with precompressed piezoelectric stack

Fig. 15

FFT plots for increasing values of nondimensional stiffness Ps=keql3/EI (analytical): (a) Ps = 300, (b) Ps = 2000, and (c) Ps = 3000

Fig. 16

FFT plots for increasing values of Ps (numerical): (a) Ps = 300, (b) Ps = 2000, and (c) Ps = 3000

Fig. 17

Variation of A2/A1 with Ps. Obtained analytically “”, and numerically “”. The third-order polynomial fits to the analytical () and numerical () results are also shown.

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