Recent Research on Vibration of Structures Using Boundary Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method

Abstract

Vibration analysis of arbitrary shaped structures has been of interest to structural designers for several decades. Dynamic behavior of these structures is strongly dependent on boundary conditions, geometrical shapes, material properties, different theories, and various complicating effects. Closed-form solutions are possible only for a limited set of simple boundary conditions and geometries. For analysis of arbitrary shaped structures, several numerical methods, such as finite element method, finite difference method, boundary element method, and so on, are usually applied. Although such discretization methods provide a general framework for general structures, they invariably result in problems with a large number of degrees of freedom. This deficiency is overcome by using the Rayleigh-Ritz method. Recently, a tremendous amount of work has been done by using the newly developed method of boundary characteristic orthogonal polynomials, first proposed in 1985, with the Rayleigh-Ritz method. This method provides better accuracy of results, is more efficient and simple, and is easier for computer implementation. This paper gives a survey of the research that has been done for the analysis of vibration of various structures with different effects using this method. More than a hundred papers have been reported and discussed that use this method over the past 12 years.