Open Access

ARTICLE

The time-dependent Green's function of the transverse vibration of a composite rectangular membrane

V.G.Yakhno¹, D. Ozdek^2,3

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.
3 Department of Mathematics, Izmir University of Economics, Izmir, TURKEY.

Computers, Materials & Continua 2013, 33(2), 155-173. https://doi.org/10.3970/cmc.2013.033.155

Abstract

A new method for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a multi stepped membrane is suggested. This method is based on generalization of the Fourier series expansion method and consists of the following steps. The first step is finding eigenvalues and an orthogonal set of eigenfunctions corresponding to an ordinary differential operator with boundary and matching conditions. The second step is a regularization (approximation) of the Dirac delta function in the form of the Fourier series with a finite number of terms, using the orthogonal set of eigenfunctions. The third step is an approximate computation of the Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of eigenfunctions. The computational experiment confirms the robustness of the method.

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