Free and forced vibration analysis of a Z-shaped structure with multi-span elastic supports

In this paper, an in-plane Z-shaped structure with multi-span elastic supports is proposed to investigate the natural frequency and transmission response through employing in-plane governing equation and transfer matrix method. Based on the solutions of transverse vibration and torsional vibration, the total transfer matrix for the Z-shaped structure with multi-span elastic supports is derived. Furthermore, natural frequencies and mode shapes of the Z-shaped structure are calculated. Finite element simulation method (FEM) is conducted here to verify the theoretical results. In order to effectively evaluate the vibration reduction performance, transmission response of the Z-shaped structure under different boundary supports and multi-span elastic supports is analyzed. This work is significant for the vibration reduction of in-plane Z-shaped structure, especially the multi-span elastic support case in engineering applications.