Transverse Vibration of an Undamped Elastically Connected Double-Beam System with Arbitrary Boundary Conditions

Abstract

This paper presents a semianalytical method to analyze the natural frequencies and mode shapes of an undamped double-beam system, which is composed of two beams joined by a uniformly distributed connecting elastic layer, with arbitrary beam mass, beam flexural rigidity, and arbitrary boundary conditions. The classical modal expansion method is further applied to determine the forced vibration responses in the double-beam system based on the natural frequencies and mode shapes obtained from the free vibration analysis. A specific orthogonality condition for the double-beam system is derived, and then applied to decouple and simplify the motion differential equations. Numerical examples are presented and discussed in detail to verify and illustrate the efficiency of the proposed semianalytical method that can further help characterize the dynamic responses and design work for double-beam structures.