Nonlinear Dynamic Analysis of Axially Moving Laminated Shape Memory Alloy Beam with 1:3 Internal Resonance

Abstract

The remarkable properties of shape memory alloys (SMA) are attracting significant technological interest in many fields of science and engineering. In this paper, a nonlinear dynamic analytical model is developed for a laminated beam with a shape memory alloy layer. The model is derived based on Falk’s polynomial model for SMAs combined with Timoshenko beam theory. In addition, axial velocity, axial pressure, temperature, and complex boundary conditions are also parameters that have been taken into account in the creation of the SMA dynamical equation. The nonlinear vibration characteristics of SMA laminated beams under 1:3 internal resonance are studied. The multi-scale method is used to solve the discretized modal equation system, the characteristic equation of vibration modes coupled to each other in the case of internal resonance, as well as the time-history and phase diagrams of the common resonance amplitude in the system are obtained. The effects of axial velocity and initial conditions on the nonlinear internal resonance characteristics of the system were also studied.

Research on One-to-Two Internal Resonance of Sling and Beam of Suspension Sling–Beam System

“…Guillot et al [24] compared the experimental and theoretical results of the 1:2 and 1:3 internal resonances of a homogeneous thin beam equipped with piezoelectric patches and observed the exchanges of energy between the modes in the 1:3 internal resonance. Hao [25] studied the nonlinear vibration characteristics of a Timoshenko beam combined with SMAs under 1:3 internal resonance. Nikpourian [26] investigated the 3:1 internal resonance of a microarch resonator.…”