Non-linear analysis of wave propagation using transform methods

D. S. Pipkins, S. N. Atluri

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Non-linear wave propagation/transient dynamics in lattice structures is modeled using a technique which combines the Laplace transform and the Finite element method. The first step in the technique is to apply the Laplace transform to the governing differential equations and boundary conditions of the structural model. The non-linear terms present in these equations are represented in the transform domain by making use of the complex convolution theorem. Then, a weak formulation of the transformed equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solutions of the linear parts of the transformed governing differential equations. Numerical results are presented for a viscoelastic rod and von Karman type beam.

Original languageEnglish
Pages (from-to)207-227
Number of pages21
JournalComputational Mechanics
Volume11
Issue number4
DOIs
StatePublished - Jul 1993

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