Vibration analysis of periodic viscoelastic sandwich beams by the wave method

This study investigates a sandwich beam with discrete viscoelastic cores, proposing a novel method to analyze its steady-state vibration response by considering the cores' linear coupling effects on the upper and lower beams. Based on the wave vector method, this study first establishes the reflection and transmission matrices for flexural waves in the sandwich beam with a core, as well as the iterative calculation formulas for the ends of a segment of the sandwich beam. Subsequently, the vibration propagation characteristics are analyzed. Finally, the influence of the coupling strength of periodically arranged cores, the asymmetry of the upper and lower beams and the loss factor of the core on the propagation relationship of flexural waves and their bandgap characteristics is investigated in detail. The results show that for the upper and lower beams of sandwich beams, the beam with higher Young's modulus dominate the energy transfer of flexural waves in sandwich beams; The coupling strength of the core significantly affects the position and width of the bandgap. The asymmetry of the upper and lower beams not only changes the energy transmission relationship, but also promotes the formation of the band gap. The loss factor attenuates vibrational waves, especially near the bandgap, without affecting its position or width. This study provides important theoretical guidance for the structural design and vibration performance optimization of periodic viscoelastic sandwich beams, as well as the control of flexural wave bandgap.