Nonlinear dynamics of SMA-fiber-reinforced composite beams subjected to a primary/secondary-resonance excitation

Abstract

In this paper, nonlinear free vibration and primary/secondary resonance analyses of shape memory alloy (SMA) fiber reinforced hybrid composite beams with symmetric and asymmetric lay-up are investigated. The simplified Brinson constitutive model and cosine phase transformation kinetics are utilized to simulate the behavior of the SMA materials and calculate the recovery stress. In order to predict the behavior of the smart laminated beam, Euler–Bernoulli beam theory and nonlinear von-Karman strain field are employed. Two types of micromechanical models, namely Voigt and Reuss models are considered. The Galerkin procedure together with the elliptic function and multi timescales method is adopted to obtain analytical solutions for the nonlinear free vibration and primary/secondary response phenomena. Numerical results reveal that some of the geometrical and physical parameters such as the SMA volume fraction, the amount of prestrain in the SMA fiber, orientation of composite fiber, vibration amplitude and temperature are important factors affecting the free vibration characteristic in the pre/post-buckled region, and primary and secondary resonance of the laminated beams reinforced with SMA fibers. The analytical solutions and results are reported for the first time and can serve as benchmark for researchers to validate their numerical and analytical methods in the future.