Nonlinear Spectral Finite Element Model for Analysis of Wave Propagation in Solid with Internal Friction and Dissipation
 D. Roy Mahapatra,
 S. Gopalakrishnan
 … show all 2 hide
Abstract
A geometrically nonlinear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study nonlinear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to nonlinear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.
 Samsonov, A.M.: Strain Solitons in Solids, Monographs and Surveys in Pure and Applied Mathematics. 117 (2001) Chapman & Hall/CRC
 Clarkson, P.A., Kruskal, M.D. (1989) New similarity reduction of Boussinesq equation. J. Mathematical Physics 30: pp. 22012213 CrossRef
 Clarkson, P.A., Winternitz, P. (1991) Physica D 49: pp. 257 CrossRef
 Pupkins, D.S., Atluri, S.N. (1993) Nonlinear analysis of wave propagation using transform methods. Computational Mechanics 11: pp. 207227 CrossRef
 Roy Mahapatra, D., Gopalakrishnan, S. (2003) A spectral finite element model for analysis of axialflexuralshear coupled wave propagation in laminated composite beams. Composite Structures 59: pp. 6788 CrossRef
 Balachandran, B., Khan, K.A. (1996) Spectral analysis of nonlinear interactions. Mechanical Systems and Signal Processing 10: pp. 711727 CrossRef
 Rushchitsky, J.J. (1999) Interaction of waves in solid mixtures. Appl. Mech. Rev. 52: pp. 3574 CrossRef
 Vollmann, J., Dual, J. (1997) Highresolution analysis of the complex wave spectrum in a cylindrical shell containing and viscoelastic medium. Part I. Theory and experimental results. J. Acoust. Soc. America 102: pp. 896920 CrossRef
 McDanel, J.G., Dupont, P., Salvino, L. (2000) A wave approach to estimating frequencydependent damping under transient loading. J. Sound and Vibration 231: pp. 433449 CrossRef
 Zakharov, V.E., Shabat, A.B. (1972) Exact theory of twodimensional focusing and onedimensional selfmodulation in nonlinear media. Soviet Physics, JETP 34: pp. 6269
 Ostrovsky, L.A., Potapov, A.I. (1999) Modulated Waves. Johns Hopkins University Press, Washington
 Doyle, J.F.: Wave Propagation in Structures. SpringerVerlag, 1997
 Roy Mahapatra, D. and Gopalakrishnan, S.: A spectral finite element for analysis of wave propagation in uniform composite tubes, J. of Sound and Vibration (in press) 2003
 Title
 Nonlinear Spectral Finite Element Model for Analysis of Wave Propagation in Solid with Internal Friction and Dissipation
 Book Title
 Computational Science and Its Applications — ICCSA 2003
 Book Subtitle
 International Conference Montreal, Canada, May 18–21, 2003 Proceedings, Part II
 Pages
 pp 745754
 Copyright
 2003
 DOI
 10.1007/3540448438_81
 Print ISBN
 9783540401612
 Online ISBN
 9783540448433
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2668
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Vipin Kumar ^{(4)} ^{(5)}
 Marina L. Gavrilova ^{(6)}
 Chih Jeng Kenneth Tan ^{(7)} ^{(8)}
 Pierre L’Ecuyer ^{(9)}
 Editor Affiliations

 4. Army High Performance Computing Research Center
 5. Department of Computer Science and Engineering, University of Minessota
 6. Department of Computer Science, University of Calgary
 7. Heuchera Technologies Inc.
 8. School of Computer Science, The Queen’s University of Belfast
 9. Département d’informatique et de recherche opérationelle, Université de Montréal
 Authors

 D. Roy Mahapatra ^{(10)}
 S. Gopalakrishnan ^{(10)}
 Author Affiliations

 10. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, INDIA
Continue reading...
To view the rest of this content please follow the download PDF link above.