Free and Forced Vibrations of Elastically Connected Double-beam Systems

Abstract

The free vibrations and the forced vibrations of a system of two elastically connected parallel upper and lower beams having unequal masses and unequal flexural rigidities are analysed by using a generalized method of finite integral transformation and the Laplace transformation. The natural frequencies and the amplitude ratios for the normal modes of vibration are presented explicitly, and the effects of mass ratio and flexural rigidity ratio of the beams are discussed. It is also shown that a system consisting of a lower beam and coupling springs can be used as a dynamic vibration absorber to reduce the vibrations of the upper beam subjected to a periodic force. An elastically connected multi-beam system is compared with a multi-degree-of-freedom-mass-spring system, and their similarity is pointed out.