Nonlinear dynamic analysis of microbeam containing graded shape memory microwires

Abstract

This study investigates the nonlinear dynamic response of the microbeam containing shape memory alloy (SMA) microwires laid along its length. The microwires are arranged in five different forms in the direction of the thickness of the microbeam. The modified couple stress theory is used to consider the size effect on the matrix material and the Hernandez-Lagoudas formulation is applied to model and capture the size effect for the SMA. The governing equation is derived for Timoshenko microbeam using the Hamilton’s principle considering the Von Karman strains. Using the nonlinear finite element method and return mapping algorithm, the governing equations are solved. By comparing some of the results obtained with the reference papers, the accuracy of the present work is examined. After confirming the accuracy of this study, the effect of parameters such as considering the nonlinear strain field, the diameter of the SMA microwires and their arrangement forms and the length-scale factor on the vibration damping rate of the microbeam is studied. Some results show that by increasing the diameter of the SMA microwires and also by reducing the length-scale factor, the effect of using the SMA on the vibration damping of the microbeam increases.