Alternative Approach for Free Vibration of Beams Carrying A Number of Two-Degree of Freedom Spring-Mass Systems

Abstract

The purpose of this paper is to determine the natural frequencies and mode shapes of beams carrying any number of two-degree of freedom (DOF) spring-mass systems by means of two finite element methods FEM1 and FEM2. For convenience, a beam without attachment is called the unconstrained (or bare) beam and that carrying attachment(s) is called the constrained (or loading) beam. FEM1 is the conventional finite element method (FEM), in which each two-DOF spring-mass system is considered as a finite element and then the assembly technique is used to establish the overall property matrices of the constrained beam. FEM2 is an alternative approach, in which each two-DOF spring-mass system is replaced by four effective springs with spring constants