Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers

Abstract

This investigation aims to explore the non-conservative instability of a functionally graded material micro-beam subjected to a subtangential force. The functionally graded material micro-beam is integrated with piezoelectric layers on the lower and upper surfaces. To take size effect into account, the mathematical derivations are expanded in terms of three length scale parameters using the modified strain gradient theory in conjunction with the Euler–Bernoulli beam model. However, the modified strain gradient theory includes modified couple stress theory and classical theory as special cases. Applying extended Hamilton’s principle and Galerkin method, the governing equation and corresponding boundary conditions are obtained and then solved numerically by the eigenvalue analysis, respectively. The results illustrated effects of non-conservative parameter, length scale parameter, different material gradient index, and various values of piezoelectric voltage on the natural frequencies, flutter and divergence instabilities of a cantilever functionally graded material micro-beam. It is found that both the material gradient index and applied piezoelectric voltage have significant influence on the vibrational behaviors, divergence and flutter instability regions. Furthermore, a comparison between the various micro-beam theories on the basis of modified couple stress theory, modified strain gradient theory, and classical theory are presented.

On the roles of strain gradient tensors in quasi‐3D nonlinear dynamics of microplate‐type piezoelectric systems of energy harvesting under triangular mechanical actuation

“…Malikan and Nguyen 58 investigated the use of higher-order strain gradient tensors to model the buckling responses of piezo-magnetoelectric nanoplates. Hosseini et al 59 explored size effects on the stability behaviors of piezoelectric micro-beams via coupling the modified strain gradient elasticity with the Euler-Bernoulli beam model. Al shujairi and Mollamahmuto glu 60 utilized nonlocal strain gradient elastic beam formulations to analyze the stability characters of FG composite micro-beams considering thermal effects on their dynamic responses.…”