Vibration Analysis of a Finite Lightweight Locally Resonant Beam Suspended with Periodic Force-Moment-Type Resonators inside Using an Exact Wave-Based Approach

Abstract

This paper employs and develops the exact wave-based vibration analysis approach to investigate the propagation properties of a designed finite lightweight locally resonant (LR) beam with two-degree-of-freedom (2-DOF) force-moment-type resonators attached periodically inside. By deriving the propagation, reflection, and transmission matrices of the structural discontinuities, the vibration of the LR beam can be described as structural waves. By assembling wave relations into the beam, the approach shows high efficiency because the forced vibration problem of the lightweight LR structure is turned to be the solution to a related set of matrix equations. The accuracy of the developed approach is validated with two examples carried out using the finite element method. In addition, the influence of the main parameters of the LR beam is studied and we found that the increase in the mass of the resonator and the stiffness of the spring are more sensitive in broadening the width and increasing the center frequency of the band gap of the designed lightweight LR beam. The proposed structure and analysis approach in this paper may provide an exact and efficient means for the design and analysis of structures in which damping and lightweight properties are required, such as space-arm and the framework of antennas in the field of aerospace.