Dynamic Pull-In Instability of a Thermoelectromechanically Loaded Micro-Beam Based on "Symmetric Stress" Gradient Elasticity Theory

The dynamic pull-in instability of a thermoelectromechanically loaded micro-beam is investigated based on the “symmetric stress” gradient elasticity theory and Euler–Bernoulli beam theory. The beam is subjected to the combined action of an electric voltage, axial static force and a uniform temperature change. By employing Galerkin’s method, the nonlinear partial differential governing equation is decoupled into a set of nonlinear ordinary differential equations, which are then solved using Runge–Kutta method. Numerical results show that compared with the size-dependent micro-beam model, the classical elasticity theory in which the size effect is ignored underestimates the pull-in voltage. The effects of size, temperature change, axial force, geometric nonlinearity, fringe effect, initial gap, beam length and width on the pull-in instability of the micro-beam are discussed in detail.