ABSTRACT
Analytical solutions of the governing differential equations in acoustics can only be obtained if the physical boundaries can be described simply in mathematical terms (Nelson 1998). This is rarely the case in engineering and so it is generally necessary to employ approximate numerical methods. The two most widely used are the finite element method (FEM) and the boundary element method (BEM). Finite element methods were first developed for analysing complex engin-
eering structures. Once the method had been given a firm mathematical foundation, it was only natural that it should be used for analysing other physical problems which could be represented by partial differential equations. The field of acoustics has been no exception. The BEM was first developed to predict the noise radiated from vibrating structures which are immersed in an infinite acoustic medium. Subsequently, it was applied to interior problems. Vibroacoustic problems can be analysed by combining the equations of motion of the vibrating structure, obtained using finite element techniques, with the equations of motion of the acoustic medium, which can be obtained using either FEM or BEM. Both FEM and BEM represent a continuous system, which has an infinite
number of degrees of freedom, by a discrete system having a finite number of degrees of freedom. The accuracy of the solution depends upon the number of degrees of freedom used. The higher the frequency of interest the more degrees of freedom that are required. Therefore, at high frequencies such methods become inefficient. Consequently, they are only used at low frequencies where wavelengths are of similar order of magnitude to the defined geometry. High-frequency acoustic problems are analysed using geometrical or ray-tracing techniques (Pierce 1989), and vibroacoustic problems are handled by means of statistical energy analysis (Lyon and DeJong 1995; Craik 1996). Further details are given in Chapter 11. This chapter is confined to low-frequency analysis in acoustics and vibroacoustics.
