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TECHNICAL PAPERS

Analysis of Static Deformation, Vibration and Active Damping of Cylindrical Composite Shells with Piezoelectric Shear Actuators

[+] Author and Article Information
Senthil S. Vel

Department of Mechanical Engineering

Brian P. Baillargeon

 Department of Mechanical Engineering, University of Maine, Orono, Maine 04469

J. Vib. Acoust 127(4), 395-407 (Aug 05, 2004) (13 pages) doi:10.1115/1.1898337 History: Received August 26, 2003; Revised August 05, 2004

An analytical solution is presented for the static deformation and steady-state vibration of simply supported hybrid cylindrical shells consisting of fiber-reinforced layers with embedded piezoelectric shear sensors and actuators. The piezoelectric shear actuator, which is poled in the circumferential direction, will induce transverse shear deformation of the hybrid shell when it is subjected to an electric field in the radial direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the governing equations of static deformation and steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations in the radial coordinate, which are solved by employing the Frobenius method. Natural frequencies, mode shapes, displacements, electric potential, and stresses are presented for four-layer hybrid laminates consisting of a piezoelectric shear sensor and actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using a positive position feedback controller. Frequency response curves for different controller frequencies, controller damping ratio, and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is demonstrated that vibration suppression of thickness modes is also feasible using the piezoelectric shear actuator.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

N-layer hybrid piezoelectric shell

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Figure 2

A four-layer hybrid shell with piezoelectric sensor and actuator sandwiched between fiber-reinforced composite layers

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Figure 3

Comparison of analytical static electric potential, circumferential displacement, circumferential stress, and transverse shear stress with finite element results for an electric potential ϕ(θ,t)=ϕ0cosπθ∕Θ applied to the piezoelectric actuator of a four layer hybrid shell

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Figure 4

First nine mode shapes for a [0° Gr-Ep/PZT-5A/PZT-5A//0° Gr-Ep] hybrid shell, electrically closed, R=0.25m, R∕H=5: (a) ω1(1)=683.229Hz, (b) ω1(2)=2393.43Hz, (c) ω2(1)=2858.45Hz, (d) ω2(2)=4780.83Hz, (e) ω3(1)=5254.74Hz, (f) ω3(2)=7156.76Hz, (g) ω4(1)=7636.58Hz, (h) ω5(1)=9984.92Hz, and (i) ω1(3)=10223.9Hz

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Figure 5

The displacement and electric potential as a function of the radial coordinate for the first nine modes of a [0° Gr-Ep/PZT-5A/PZT-5A/0° Gr-Ep] hybrid shell, R=0.25m, R∕H=5: (a) ω1(1)=683.229Hz, (b) ω1(2)=2393.43Hz, (c) ω2(1)=2858.45Hz, (d) ω2(2)=4780.83Hz, (e) ω3(1)=5254.74Hz, (f) ω3(2)=7156.76Hz, (g) ω4(1)=7636.58Hz, (h) ω5(1)=9984.92Hz, and (i) ω1(3)=10223.9Hz

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Figure 6

The stresses as a function of the radial coordinate for the first nine modes of a [0° Gr-Ep/PZT-5A/PZT-5A/0° Gr-Ep] hybrid shell, R=0.25m, R∕H=5: (a) ω1(1)=683.229Hz, (b) ω1(2)=2393.43Hz, (c) ω2(1)=2858.45Hz, (d) ω2(2)=4780.83Hz, (e) ω3(1)=5254.74Hz, (f) ω3(2)=7156.76Hz, (g) ω4(1)=7636.58Hz, (h) ω5(1)=9984.92Hz, and (i) ω1(3)=10223.9Hz

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Figure 7

Magnitude and phase of radial deflection as a function of frequency of a harmonic distributed radial load for a [0° Gr-Ep/PZT-5A/PZT-5A/0° Gr-Ep] hybrid shell with PPF control, R=0.25m, R∕H=5: (a), (b) ςc=0.05,g=5(10−8)s2, (c), (d) ωc=ω1(1),g=5(10−8)s2, (e), (f) ωc=ω1(1),ςc=0.05

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Figure 8

Magnitude of electric potential to actuator as a function of frequency of a harmonic distributed radial load for a [0° Gr-Ep/PZT-5A/PZT-5A/0° Gr-Ep] hybrid shell with PPF control, R=0.25m, R∕H=5: (a) ςc=0.05,g=5(10−8)s2, (b) ωc=ω1(1),g=5(10−8)s2, (c) ωc=ω1(1),ςc=0.05

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Figure 9

Magnitude and phase frequency response curves of radial deflection for a harmonic distributed radial load for a [0° Gr-Ep/PZT-5A/PZT-5A/0° Gr-Ep] hybrid shell with PPF Control, R=0.25m, R∕H=5: (a), (b) ςc=0.05,g=5(10−9)s2, (c), (d) ωc=ω1(3),g=5(10−9)s2, (e), (f) ωc=ω1(3),ςc=0.05

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