Transversal vibration of a multi-span axially moving beam with multiple elastic supports

Abstract

Using the transfer matrix method for multibody systems (MSTMM), this paper presents a dynamical model of a multi-span axially moving system with multiple elastic supports under different boundary conditions. The complex transfer matrices of an axially moving beam and a spring-damping supporting element are derived. According to the system topology, the overall transfer equation is acquired for vibration characteristic analysis. However, when dealing with multi-span systems that involve a large number of components, numerical instability may arise due to the instability of the corresponding boundary value problems. To address this issue, the reduced complex transfer matrix method (RCTMM) is developed. The state vector is artificially partitioned corresponding to the boundary condition of the system input. Numerical simulation results show that the developed method has the same computational accuracy as the MSTMM. More importantly, the RCTMM exhibits superior numerical stability, as indicated by the condition numbers of the system transfer matrix. It will provide an efficient tool for the design of mechanical multi-span axially moving systems.