Free vibration of spring-mounted beams

Abstract

Abstract In the present work, free vibration characteristics of a spring-mounted beam is studied. The objective is to determine the natural frequencies and mode shapes of this beam. Towards this end, a novel semi-analytical method is developed. The methodology is based on Green’s function of Euler-Bernoulli beam together with a Rayleigh-Ritz method. A minimal set of basis functions for the Rayleigh-Ritz method is found, by generating the beam mode shapes for extreme values (zero and infinity) of the connecting spring stiffnesses. Thus, for a beam with n intermediate spring connections, 2 n beam modes are generated as basis functions. The Green’s function approach is used to extract the beam mode shapes for the extreme values of the connecting spring stiffnesses. The results from the proposed formulation are compared with those from a finite element (FE) simulation. For most cases, the results obtained by the two methods are in excellent agreement. Guidelines for further improvement of the accuracy of the present results have been proposed. Detailed parametric studies on the effect of spring stiffness value and their location have been performed.