A Variational Method for Solving Vibration Problems
Abstract Rayleigh-Ritz and Galerkin methods are frequently used in engineering to solve boundary value and eigenvalue problems. The success in applying these methods depends entirely on the construction of a variational entity called the functional, and the choice of a system of elements known as the basis functions. This in some cases greatly narrows down the class of problems to which the above methods may be applied. Here, we present a specific but sufficiently general method known as the Methods of Moments for constructing the elements going into the expansion of the approximate solution. The Method of Moments has been shown to posses the capability of generating the basis functions successfully. The Method of Moments in its various forms has been widely used in electromagnetism. Due to generality involved in the construction of these basis functions, the Method of Moments may be readily used to solve a large variety of problems arising in discrete as well as continuous vibrating systems. This idea forms the central theme of this article.