Open Access

ARTICLE

Computation of the Time-Dependent Green's Function for the Longitudinal Vibration of Multi-Step Rod

by V.G.Yakhno¹, D. Ozdek²

1 Electrical and Electronics Engineering Department, Dokuz Eylul University, Izmir, Turkey.
2 Department of Mathematics, The Graduate School of Natural and Applied Sciences, Dokuz Eylul University, Izmir, Turkey.

Computer Modeling in Engineering & Sciences 2012, 85(2), 157-176. https://doi.org/10.3970/cmes.2012.085.157

Abstract

The present paper describes computation of the time-dependent Green's function for the equations of longitudinal vibration of a multi-step rod with a piecewise constant varying cross-section. This computation is based on generalization of the Fourier series expansion method. The time-dependent Green's function is derived in the form of the Fourier series. The basic functions of this series are eigenfunctions of an ordinary differential equation with boundary and matching conditions. Constructing the eigenvalues and eigenfunctions of this differential equation and then derivation of the Fourier coefficients of the Green's function are main steps of the method. Computational experiments confirm the robustness of the method.

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