Investigation on characteristics of energy transfer of flexural vibration in a Y-shaped bifurcated beam imposed lumped mass

Abstract

A Y-shaped bifurcated beam that is comprised of one tapered part and two uniform parts is investigated in this article. The wave propagation method and Timoshenko beam theory are utilized to investigate the characteristics of energy transfer of flexural vibration. Transmission and reflection matrices at Y-shaped bifurcated interface with variable propagation directions of flexural incident wave are derived; the proportions of transmitted and reflected power caused by flexural wave in semi-infinite beam are obtained. The results show that both bifurcation position and angles between three sub-beams at Y-shaped bifurcated interface influence proportions of transmitted and reflected power. In order to investigate the power transfer coefficient of forced vibration in a finite Y-shaped bifurcated beam, the propagation relations of wave vectors in the coupled beam imposed lumped mass are deduced. Moreover, the analytical solution of power transfer coefficient is obtained. Numerical results indicate that increase of local mass can reduce power transfer coefficient at specific range of frequency domain in Y-shaped bifurcated beam. The investigation proposes the characteristics of energy transfer affected by bifurcation position, angles between sub-beams, variation coefficient of tapered beam and lumped mass, which is useful to optimal vibration control of flexural forced vibration in Y-shaped bifurcated beam.