Dynamic analysis and identification of bi-directional functionally graded elastically supported cracked microbeam subjected to thermal shock loads

Abstract

Micro scale structures like beams and plates are used in several micro sensors and actuators, micro level energy harvesters and atomic force microscopes. During their manufacture and in the service condition, micro level voids and cracks are developed on their edges and surfaces. These result-in increasing vibration amplitudes and eventual catastrophic failures. Present work deals with the transient dynamic analysis of bi-directional functionally graded material microbeams with edge cracks resting on nonlinear elastic foundations in the presence of thermal shock loads. The dynamic equations of the beam are derived from Hamilton principle by considering modified couple stress theory and the equations of motion are solved through the finite element model. Natural frequencies of the FG beam are calculated for different boundary conditions and thermal shock response is obtained for different grading indices. Effects of crack parameters, support stiffness and thermal loads on the natural frequencies are studied. The input power flow analysis of the cracked FG microbeam is also conducted. In order to identify the crack depth and location, inverse based optimization methodology is illustrated through minimization of error functions derived from natural frequencies and input power flow. A surrogate scheme with firefly metaheuristic optimization employing back propagation neural network regression model is proposed for obtaining the effective solution.