An analytical method for free vibration analysis of FGM/SMA actuator beam

Abstract

A nonlinear free vibration analysis of a simply supported functionally graded (FG) actuator beam integrated with two uniformly distributed actuator layers made of Shape Memory Alloy (SMA) material on the top and bottom surfaces is presented in this paper. The material properties of the functionally graded core beam are assumed to be graded in the thickness direction according to the power law distribution in terms of the volume fractions of the constituents. Classical beam theory was used in the analysis and Navier type solution method was used to obtain frequencies. Also, the effects of actuator temperature, volume fraction and SMA layer thickness on natural frequencies are investigated. This study will be useful in analyzing functionally graded beams with sensor and actuator capability and it can serve as a basis for investigating smart FG structures. The analytical results are validated by comparing the obtained resonant frequencies of the SMA coupled FG beam with those of an isotropic core beam. The good agreement between the results of this paper and those in literatures validated the presented approach.