X.L. Jia

Pull-in instability of nano-switches using nonlocal elasticity theory

This paper investigates the pull-in instability of nano-switches subjected to an electrostatic force due to an applied voltage and intermolecular force within the framework of nonlocal elasticity theory to account for the small scale effect. Both the nonlinear governing equation and boundary conditions with nonlocal effect are derived. A linear distributed load model is proposed to approximate the nonlinear intermolecular and electrostatic interactions. Closed-form solutions of critical pull-in parameters are obtained for cantilever and fixed-fixed nano-beams. The freestanding behaviour of nano-beams, which is a special case in the absence of electrostatic force, is also studied. It is found that the small scale effect contributes to the pull-in instability and freestanding behaviour of cantilever and fixed-fixed nano-beams in quite different ways. The effects of gap ratio, slenderness ratio and intermolecular force are discussed in detail as well.

Free vibration of geometrically nonlinear micro-switches under electrostatic and Casimir forces

This paper investigates the free vibration characteristics of micro-switches under combined electrostatic, intermolecular forces and axial residual stress, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching and the influence of Casimir force. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. The Euler-Bernoulli beam theory with von Karman type nonlinear kinematics is applied in the theoretical formulation. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using the differential quadrature method. The natural frequencies and mode shapes of micro-switches for four different boundary conditions (i.e. clamped-clamped, clamped-simply supported, simply supported and clamped-free) are obtained. The solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted to show the significant effects of geometric nonlinearity, Casimir force, axial residual stress and material composition for the natural frequencies.

Characterization of FGM micro-switches under electrostatic and casimir forces

This paper aims to investigate the nonlinear pull-in characteristics of the micro-switches made of either homogeneous material or non-homogeneous functionally graded material (FGM) with two material phases under the combined electrostatic and intermolecular Casimir force. Principle of virtual work is used to derive the governing differential equation which is then solved using differential quadrature method (DQM). Pull-in voltage and pull-in deflection are obtained for micro-switches with three different boundary conditions (i.e. fixed-fixed, simple-fixed, and simply supported). The present solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted to show the significant effects of material composition, gap ratio, slenderness ratio, Casimir force, axial residual stress on the pull-in instability.

ELECTROMECHANICAL DYNAMICS FOR MICRO BEAMS

In this paper, an electromechanical coupled dynamic equation of a micro beam under an electrostatic force as well as under an electromechanical coupled force is presented. The linearization of above dynamic equation is made, allowing the equation to be divided into a linear dynamic equation for dynamic displacement and a static balance equation for static displacement. Using the balance equation, the changes of the voltage along with displacement are studied. It is shown that there is a critical voltage at which the micro beam will buckle. From the linear dynamic equation, natural frequencies and vibration modes of the micro beam, and its forced responses to voltage excitation are derived. The results show that the natural frequencies and vibrating magnitudes of the micro beam are affected by mechanical and electric parameters. Smaller beam length and voltage as well as larger beam thickness and clearance should be selected in order to obtain smaller vibrating magnitudes. It is also shown that for higher vibration modes, more positions of the peak dynamic displacements occur.

Nonlinear vibration and dynamic response of three-dimensional braided composite plates

This paper studies the nonlinear vibration and dynamic response of three-dimensional braided composite plates produced by the four-step procedure. It is assumed that the yarn is transversely isotropic and the matrix is isotropic. A fiber inclination model is applied to predict the effective stiffness matrix of the braided composite plate. Theoretical formulations are based on Reddys higher-order shear deformation plate theory and von Kármán-type nonlinear kinematics. Asymptotic solutions are obtained for simply supported rectangular plates by using an improved perturbation approach and Galerkin technique.Numerical illustrations are given in both tabular and graphical forms, showing the effects of the fiber volume fraction, the braiding angle, and the inclination angle on the linear and nonlinear vibration frequencies and the dynamic response of braided composite plates.