Response of a Shape Memory Alloy Beam Model under Narrow Band Noise Excitation

Abstract

To describe the hysteretic nonlinear characteristic of the strain-stress relation of shape memory alloy (SMA), a Van-der-Pol hysteretic cycle is applied to simulate the hysteretic loops. Then, the model of a simply supported SMA beam subject to transverse narrow band noise excitation with nonlinear damping was proposed. The deterministic and the stochastic responses are studied, respectively, applying the multiple scale method. The stability of the steady state responses is analyzed by Floquet theory and the moment method. The numerical simulation results quite agree with the theoretical analysis.