Traverse Vibration of Axially Moving Laminated SMA Beam considering Random Perturbation

Abstract

The nonlinear random vibration of axially moving shape memory alloy (SMA) laminated beam under transverse loads is investigated. Considering the effects of axial movement and random perturbation, the dynamic equation of the SMA laminated beam is established by means of physical equation, force balance conditions, deformation compatibility equation, and the constitutive relation by polynomial function. The transverse vibration differential equation of axially moving SMA laminated beam with two simply‐supported edges is obtained through the Galerkin method. The amplitude‐frequency response equation under primary resonance and the probability density function under random perturbation are derived by using the averaging method and stochastic averaging method, respectively, and the theoretical results are numerically validated. In addition, under the combination of the harmonic excitation and random perturbation, the effects of axial movement velocity and random perturbation intensity on system steady‐state response are analyzed.