Vibration Analysis of Locally Resonant Beams with L-Joint Using an Exact Wave-Based Vibration Approach

This paper employed and developed the wave-based vibration approach to analyze the band-gap characteristics of a locally resonant (LR) beam with L-joint, which is common in engineering practices. Based on the proposed modular approach, where the discontinuities on the beam are created as modules, the design and modeling work for such an LR beam can be simplified considerably. Then, three kinds of LR beams with an L-joint suspended with transverse-force type resonators and two cells of longitudinal-force-moment type resonators are analyzed, respectively, to show their suppression ability on the axial wave’s propagation and widened effect on the low-frequency band-gaps, where the longitudinal-force-moment type resonators at the 3rd–4th cells can better suppress the propagation of the axial waves. Meanwhile, the proposed analysis results are compared with the ones obtained with the finite element method and further verified the accuracy and efficiency of the wave-based vibration approach. The aim of this paper is to provide an efficient method for the analysis and design of the LR beam with L-joint for low-frequency vibration attenuation in engineering practices.