Modeling of vibration, sound, and stresses using the virtual source approach

Abstract

Analytical solutions of acoustical, vibration, or stress problems are available only for some simple structural systems, e.g., a rectangular simply supported plate or a parallelepipedic cavity. An usual way of finding a solution where complex systems are concerned is to apply field discretization in conjunction with some numerical methods such as FE or BE. Yet the use of analytical models is desirable for its simplicity and better physical understanding of phenomena concerned. On top of this, analytical models give the possibility of assessing quantities like energy flow which are linked to higher spatial derivatives, the latter being difficult to model numerically. The method of virtual sources enables one to obtain analytical solutions of systems of rather simple but non-trivial geometry. A key advantage of the method is the full control over the computation error. The method consists in applying a layer of virtual sources to a simple mother system of known analytical solution. These sources are adjusted in such a way as to produce particular boundary conditions on a target part of the mother system. The target part can be given a complex geometry which cannot be directly treated analytically. The paper will be accompanied by a number of examples which illustrate the approach.