Errors in response calculations for beams

Abstract

AbstractWhen the finite element method is used to idealize a structure, its dynamic response can be determined from the governing matrix equation by the normal mode method or by one of the many approximate direct integration methods. In either method the approximate data of the finite element idealization are used, but further assumptions are introduced by the direct integration scheme. It is the purpose of this paper to study these errors for a simple structure. The transient flexural vibrations of a uniform cantilever beam, which is subjected to a transverse force at the free end are determined by the Laplace transform method. Comparable responses are obtained for a finite element idealization of the beam, using the normal mode and Newmark average acceleration methods; the errors associated with the approximate methods are studied. If accuracy has priority and the quantity of data is small, the normal mode method is recommended; however, if the quantity of data is large, the Newmark method is useful.