Size-dependent pull-in analysis of a composite laminated micro-beam actuated by electrostatic and piezoelectric forces: Generalized differential quadrature method

In this paper, a size-dependent model of clamped-clamped composite laminated electrostatic Euler Bernoulli microbeams with piezoelectric layers attached was proposed based on a new modified couple stress theory for anisotropic elasticity. With the aid of Hamilton's principle, the nonlinear differential governing equation was established and solved by utilizing the generalized differential quadrature method. The present model, which can be reduced to the isotropic beam model takes the residual stresses, fringing effects and midplane stretching effects into consideration. A good agreement exists between numerical results of the present reduced model and those of available literature. Numerical analysis reveals that the size effect is significant when geometry sizes of a beam are comparable to the internal material length scale parameter (hereafter referred to as MLSP). Furthermore, the pull-in voltage dependence of the residual stress, midplane stretching, MLSP as well as the voltage applied to the piezoelectric layers are also investigated. The present model can accurately predict the static behavior and guide the design of composite laminated micro-beam actuated by both the electrostatic and piezoelectric forces. (C) 2017 Elsevier Ltd. All rights reserved.