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TECHNICAL PAPERS

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

[+] Author and Article Information
A. Chakraborty1

Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, Indiaabir.chakraborty@gm.com

S. Gopalakrishnan

Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, India

1

Author to whom correspondence should be addressed. Presently in India Science Lab, GM R&D. This work was done while a student in the Department of Aerospace Engineering, Indian Institute of Science, Bangalore.

J. Vib. Acoust 128(4), 477-488 (Feb 03, 2006) (12 pages) doi:10.1115/1.2203338 History: Received July 18, 2005; Revised February 03, 2006

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

The plate element and associated DOF

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Figure 2

Real part of wave numbers, symmetric ply sequence

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Figure 3

Imaginary part of wave numbers, symmetric sequence

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Figure 4

Real part of wave numbers, asymmetric ply sequence

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Figure 5

Imaginary part of wave numbers, asymmetric sequence

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Figure 6

Lamina with surface electrodes (St top surface, Sb bottom surface)

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Figure 7

The plate element with transverse and nonpropagating crack

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Figure 8

Variation of nondimensional flexibility at the crack location

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Figure 9

Sensor-actuator element configuration for ASPE

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Figure 10

Broadband pulse loading, inset shows time domain data

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Figure 11

Transverse velocity due to transverse load

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Figure 12

Plate with ply drop

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Figure 13

Response of plate with ply-drop: SPE

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Figure 14

Cantilever bimorph plate for open loop control

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Figure 15

Composite cantilever plate with surface bonded actuator and noncollocated velocity feedback sensor for broadband local control at the tip

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Figure 16

Open loop control of transverse velocity (arrow indicates decreasing E direction)

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Figure 17

Open loop control of transverse velocity (arrow indicates decreasing E direction)

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Figure 18

Closed-loop axial displacement at the tip under unit impulse excitation, La∕L=0.1,xs∕L=1.0

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Figure 19

Closed-loop transverse displacement at the tip under unit impulse excitation, La∕L=0.1,xs∕L=1.0

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Figure 20

Scattering due to transverse crack: Broadband pulse

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Figure 21

Scattering due to transverse crack: Modulated pulse

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