Vibration reduction in a periodic truss beam carrying locally resonant oscillators

Abstract

A periodic truss beam is designed by connecting an array of identical elements in parallel to gain excellent Bragg band gaps, after which locally resonant (LR) oscillators are attached to the truss beam to form the periodic LR truss beam, which can achieve both an LR gap in low frequency and Bragg gaps in high frequency. Firstly, dynamic models of the periodic LR truss beams in which longitudinal and flexural waves propagate are established. Then, transfer matrices of the periodic elements are derived by using the transfer matrix method and are further used for computing frequency-dependent propagation constants and acceleration frequency response (AFR) on semi-infinite and finite periodic LR truss beams. Furthermore, vibration reduction performance of the periodic structures in the frequency range below 1400 Hz is numerically analyzed in detail. Finally, an experimental setup for measuring AFR on the periodic LR truss beam is carried out to validate the predicted numerical results. Both the numerical simulation and experimental results reveal that the LR gap in low frequency and the Bragg gap in high frequency coexist in the periodic LR truss beam; within the frequency ranges of the two types of band gaps, vibration transmitted in the periodic structure can be substantially attenuated.