An approach to the vibration problem of homogeneous, non-homogeneous and composite membranes based on the boundary element method

✍ Scribed by J. T. Katsikadelis; E. J. Sapountzakis

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 840 KB
• Volume: 26
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620261106

✦ Synopsis

In this paper a boundary element approach is presented to establish the eigenfrequencies and the mode shapes of the free vibrations of flexible membranes with arbitrary shape. The membranes may be of homogeneous, non-homogeneous or composite material, while their boundaries may be fixed or elastically supported. The implementation of the method is mainly based on the development of both a boundary element technique to compute numerically the Green function for the Laplace equation and a numerical procedure to solve domain integral equations using two-dimensional Gauss integration on regions of arbitrary shape. The efficiency of the method presented is demonstrated by applying it to study the free vibrations of membranes consisting of homogeneous, non-homogeneous and composite material, fixed or elastically supported on the boundary, and having various shapes, such as circular, rectangular, triangular, or elliptical, or being L-shaped or of arbitrary shape.