Computation of the Green's function for the transverse vibration of a composite circular membrane


Yakhno V. G., Ozdek D.

JOURNAL OF ENGINEERING MATHEMATICS, vol.87, no.1, pp.187-205, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1007/s10665-013-9673-2
  • Journal Name: JOURNAL OF ENGINEERING MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.187-205
  • Keywords: Analytical method, Composite circular membrane, Green's functions, Simulation, Transverse vibration, BOUNDARY-ELEMENT ANALYSIS, TIME-DOMAIN BEM, FUNDAMENTAL-SOLUTIONS, AXISYMMETRICAL VIBRATIONS, ANNULAR MEMBRANES, ELASTODYNAMICS, FORMULATION, SCATTERING
  • Dokuz Eylül University Affiliated: Yes

Abstract

A new analytical method is suggested for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a composite circular membrane with piecewise constant varying density and tension. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients and 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 the derived eigenfunctions. A computational experiment confirms the robustness of the method.