Nonlinear free vibration and damping analysis of a microbeam with pseudoelastic shape memory alloy layer based on the modified couple stress theory

Abstract

The aim of this investigation is to evaluate the size effects on the nonlinear free vibration of the sandwich composite microbeam with an extensible shape memory alloy layer in the midplane. A one-dimensional constitutive model is considered to simulate the pseudoelastic behavior of the shape memory alloy layer. The governing equation of motion is derived using the Euler–Bernoulli beam theory together with the modified couple stress theory through the Hamilton’s principle. Midplane stretching and phase transformation of the shape memory alloy which are sources of nonlinearity were considered, and a numerical solution method is presented. A damped response of the sandwich composite microbeam is observed because of the hysteresis behavior of the extensible shape memory alloy layer in the midplane. Results are appraised by comparing with the available literature. The influence of material length scale, temperature, and initial velocity on the loss factor and other pivotal vibrational behavior is evaluated. Results show that increasing the material length scale to thickness ratio has a decreasing effect on damping capacity.