ABSTRACT

This chapter directly deals with the main idea of the book. Here we shall develop the algebraic eigenvalue formulations in the boundary element method (BEM), which have been a highly researched area in recent years. Even though the algebraic eigenvalue formulation in BEMmay appear involved, it leads to an elegant and simple computational methodology. In the sections that follow we shall develop the earliest boundary element (BE) algebraic eigenvalue formulation which combines the BE formulation with finite element discretization. The finite element discretization of the domain is utilized specifically to formulate the mass matrix. The method, which is designated here as the Internal Cell Method (ICM), is developed first using the acoustics Helmholtz equation (6.1). Examples of the application of ICM are presented in which the natural frequencies and modes of vibration of plates are computed [113]. The subsequent chapters will deal with more recent BE algebraic eigenvalue formulations such as Dual Reciprocity and Particular Integral Methods (DRM and PIM).