Perturbation Methods

Perturbation methods yield approximate analytical solutions that provide physical insight into finite-amplitude sound and benchmarks for computational methods. The acoustic Mach number is employed as the small parameter for the perturbation expansions. The first method presented is the regular perturbation technique leading to a straightforward expansion of the solution in powers of the small parameter, but which is not uniformly valid. Two methods are presented for rendering the solutions uniformly valid, the method of multiple scales and the method of renormalization. Analysis of radiation from a vibrating plate is provided as an example of a multidimensional problem solved by perturbation.