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.
Issue Section:
Technical Papers
Keywords:
finite element analysis,
acoustic wave propagation,
acoustic wave scattering,
plates (structures),
laminates,
eigenvalues and eigenfunctions,
shear deformation,
closed loop systems,
vibration control,
vibrations,
structural acoustics,
FLPT,
SVD,
PEP,
high frequency,
open-loop control,
closed-loop control,
wave scattering
Topics:
Actuators,
Composite materials,
Computation,
Eigenvalues,
Fracture (Materials),
Modeling,
Plates (structures),
Polynomials,
Scattering (Physics),
Sensors,
Wave propagation,
Waves,
Displacement,
Finite element analysis,
Stress,
Shear deformation,
Finite element model,
Delamination,
Boundary-value problems,
Cantilevers,
Vibration control
1.
Kuhlemeyer
, R.
, and Lysmer
, J.
, 1973, “Finite Element Accuracy for Wave Propagation Problems
,” J. Soil Mech. Found. Div.
0044-7994, 99
(SM5
), pp. 421
–427
.2.
Doyle
, J.
, 1997, Wave Propagation in Structures
, Springer
, New York.3.
Gopalakrishnan
, S.
, Martin
, M.
, and Doyle
, J.
, 1992, “A Matrix Methodology for Spectral Analysis of Wave Propagation in Multiple Connected Timoshenko Beam
,” J. Sound Vib.
0022-460X, 158
, pp. 11
–24
.4.
Mahapatra
, D. R.
, 2003, “Development of Spectral Finite Element Models for Wave Propagation Studies, Health Monitoring and Active Control of Waves in Laminated Composite Structures
,” Ph.D. thesis, Indian Institute of Science, Bangalore, pp. 73
–95
.5.
Danial
, A.
, 1994, “Inverse Solutions in Folded Plate Structures
,” Ph.D. thesis, Purdue University.6.
Chakraborty
, A.
, and Gopalakrishnan
, S.
, 2004a, “A spectrally formulated finite element for wave propagation analysis in layered composite media
,” Int. J. Solids Struct.
0020-7683, 41
(18–19
), pp. 5155
–5183
.7.
Chakraborty
, A.
, and Gopalakrishnan
, S.
, 2004b, “Wave Propagation in Inhomogeneous Layered Media: Solution of Forward and Inverse Problems
,” Acta Mech.
0001-5970, 169
(1–4
), pp. 153
–185
.8.
Chakraborty
, A.
, and Gopalakrishnan
, S.
, 2005, “A Spectrally Formulated Plate Element for Wave Propagation Analysis in Anisotropic Material
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 194
(42–44
), pp. 4425
–4446
.9.
Bao
, G.
, and Cai
, H.
, 1997, “Delamination Cracking in Functionally Graded Coating/Metal Substrate Systems
,” Acta Mater.
1359-6454, 45
(3
), pp. 1055
–1066
.10.
Pindera
, M.
, Aboudi
, J.
, and Arnold
, S.
, 2002, “Analysis of Spallation Mechanism in Thermal Barrier Coatings with Graded Bond Coats Using the Higher-Order Theory of FGMS
,” Eng. Fract. Mech.
0013-7944, 69
, pp. 1587
–1606
.11.
Garg
, A.
, 1988, “Delamination-a damage model in composite structures
,” Eng. Fract. Mech.
0013-7944, 29
, pp. 557
–584
.12.
Ochoa
, O.
, and Reddy
, J.
, 1992, Finite Element Analysis of Composite Laminates
, Kluwer
, Dordrecht.13.
Simitses
, G.
, Sallam
, S.
, and Yin
, W.
, 1985, “Effect of Delamination of Axially Loaded Homogeneous Laminated Plate
,” AIAA J.
0001-1452, 23
(9
), pp. 1437
–1444
.14.
Karadomateas
, G.
, and Schmueser
, D.
, 1988, “Buckling and Postbuckling of Delaminated Composites Under Compressive Loads Including Transverse Shear Effects
,” AIAA J.
0001-1452, 26
(3
), pp. 337
–342
.15.
Barbero
, E.
, and Reddy
, J.
, 1991. “Modeling of Delamination in Composite Laminates Using a Layer-Wise Plate Theory,” Int. J. Solids Struct.
0020-7683, 28
(3
), pp. 373
–388
.16.
Point
, N.
, and Sacco
, E.
, 1996, “A delamination model for laminated composites
,” Int. J. Solids Struct.
0020-7683, 33
(4
), pp. 483
–509
.17.
Finn
, S.
, and Springer
, G.
, 1993, “Delaminations in composite plates under transverse static or impact loads - A model
,” Comput. Struct.
0045-7949, 23
, pp. 177
–190
.18.
Chattopadhya
, A.
, and Gu
, H.
, 1994, “New Higher-Order Plate Theory in Modeling Delamination Buckling of Composite Laminates
,” AIAA J.
0001-1452, 32
(8
), pp. 1709
–1716
.19.
Williams
, T.
, and Addessio
, F.
, 1997, “A General Theory for Laminated Plates with Delaminations
,” Int. J. Solids Struct.
0020-7683, 34
(16
), pp. 2003
–2024
.20.
Williams
, T.
, 1999, “A Generalized Multilength Scale Nonlinear Composite Plate Theory with Delamination
,” Int. J. Solids Struct.
0020-7683, 36
, pp. 3015
–3050
.21.
Greco
, F.
, Lonetti
, P.
, and Zinno
, R.
, 2002, “An Analytical Delamination Model for Laminated Plates Including Bridging Effects
,” Int. J. Solids Struct.
0020-7683, 39
(9
), pp. 2435
–2463
.22.
Rice
, J.
, and Levy
, N.
, 1972, “The Part-Through Surface Crack in an Elastic Plate
,” ASME J. Appl. Mech.
0021-8936, 39
, pp. 183
–194
.23.
Krawczuk
, M.
, Palacz
, M.
, and Ostachowicz
, W.
, 2004, “Wave Propagation in Plate Structures for Crack Detection
,” Finite Elem. Anal. Design
0168-874X, 40
, pp. 991
–1004
.24.
Chakraborty
, A.
, 2004, “Wave Propagation in Anisotropic and Inhomogeneous Structures
,” Ph.D. thesis, Indian Institute of Science, Bangalore.25.
Mahapatra
, D. R.
, Gopalakrishnan
, S.
, and Balachandran
, B.
, 2001, “Active Feedback Control of Multiple Waves in Helicopter Gearbox Support Struts
,” Smart Mater. Struct.
0964-1726, 10
, pp. 1046
–1058
.26.
Mahapatra
, D. R.
, and Gopalakrishnan
, S.
, 2003a, “Optimal Spectral Control of Broadband Waves in Composite Beams with Distributed Sensor-Actuator Configuration
,” SPIE Symposium on Smart Materials and MEMS
, Melbourne, Australia, Dec. 13–15.27.
Lancaster
, P.
, 1966, Lambda Matrices and Vibrating Systems
, Pergamon Press
, N. Y.28.
Lancaster
, P.
, 1969, Theory of Matrices
, Academic Press
, N.Y.29.
Golub
, G.
, and Loan
, C. V.
, 1989, Matrix Computations
, The Johns Hopkins University Press
, Baltimore.30.
Reddy
, J. N.
, 1997, Mechanics of Laminated Composite Plates
, CRC Press
, Boca Raton, FL.31.
Tisseur
, F.
, and Higham
, N. J.
, 2001, “Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
,” SIAM J. Matrix Anal. Appl.
0895-4798, 23
(1
), pp. 187
–208
.32.
Reddy
, J.
, 1999, “On Laminated Composite Plates with Integrated Sensors and Actuators
,” Eng. Struct.
0141-0296, 21
, pp. 568
–593
.33.
Khadem
, S.
, and Rezaee
, M.
, 2000, “Introduction of Modified Comparison Functions for Vibration Analysis of a Rectangular Cracked Plate
,” J. Sound Vib.
0022-460X, 236
(2
), pp. 245
–258
.34.
Anderson
, B.
, and Moore
, J.
, 1990, Optimal Control
, Prentice–Hall
, Englewood Cliff, N. J.35.
LS-DYNA
, 2003, Livermore Software Technology Corporation, California.36.
Kumar
, D.
, RoyMahapatra
, D.
, and Gopalakrishnan
, S.
, 2004, “A Spectral Finite Element for Wave Propagation and Structural Diagnostic Analysis of Composite Beam with Transverse Crack
,” Finite Elem. Anal. Design
0168-874X, 40
(13–14
), pp. 1729
–1751
.37.
Mahapatra
, D. R.
, and Gopalakrishnan
, S.
, 2003b, “A Spectral Finite Element Model for Analysis of Axial-Flexural-Shear Coupled Wave Propagation in Laminated Composite Beams
,” Compos. Struct.
0263-8223, 59
(1
), pp. 67
–88
.38.
Point
, N.
, and Sacco
, E.
, 1996, “A Delamination Model for Laminated Composites
,” Int. J. Solids Struct.
0020-7683, 33
(4
), pp. 483
–509
.39.
Shivakumar
, K.
, and Whitcomb
, J.
, 1985, “Buckling of a Sublaminate in Quasi-Isotropic Composite Laminate
,” J. Compos. Mater.
0021-9983, 19
(1
), 2
–18
.Copyright © 2006
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