Nonlinear dynamic characteristics of FGCNTs reinforced microbeam with piezoelectric layer based on unifying stress-strain gradient framework

A size-dependent model of functionally graded carbon nanotubes (FGCNTs) reinforced microbeam with piezoelectric layer is presented based on unifying nonlocal stress and strain gradient framework. Nonlinear dynamic characteristics of the microbeam arise from electrostatic, piezoelectric actuation and thermal loading, with consideration of quantum and thermal fluctuations induced Casimir force. The nonlinearly dynamic frequency and pull-in instability of FGCNTs reinforced microbeam with damping effect are investigated by perturbation technique and verified by numerical method, where the coupling effects of nonlocal stress gradient and strain gradient parameters on fundamental frequency are described. The results show that the frequency of piezoelectric laminated microbeam-damping system declines with the growth of nonlocal stress gradient parameter while increases with the increment of strain gradient parameter. The pull-in voltage of micro- piezoelectric laminated beam can be tuned by excitation voltage exerted on piezoelectric layer, and the frequency and pull-in voltage decrease with the increase of the excitation voltage exerted on piezoelectric layer. In addition, dissipative effects originating from viscous and structural damping are evaluated. It is found that the pull-in voltage of micro-structures with damping system is higher than that of undamped system. (C) 2016 Elsevier Ltd. All rights reserved.