Static pull-in instability analysis of a microcantilever under uniformly distributed loading and electrostatic interaction force using shooting method = Phân tích tĩnh cho dạng mất ổn định kéo vào của một dầm công xôn kích thước micro chịu tải phân bố đều và lực tương tác tĩnh điện bằng phương pháp bắn

Abstract

In this study, using the shooting method, the static pull-in instability phenomenon of a microcantilever beam under the effect of uniformly distributed loading and electrostatic interaction force is analyzed within the framework of the Euler-Bernoulli beam theory associated with the modified couple stress theory. The shooting method is a mumerical treatment applied to the boundary value problem using approaches of numerical methods for initial condition problems. For the microcantilever beam under consideration, the shooting method is implemented based on the Runge-Kutta method combined with the Newton-Raphson iteration method. The profit of the present approach is to take advantage of the accuracy of the well-known Runge-Kutta algorithm and the Newton-Raphson method for algebraic equations with fast convergence. Because the governing equation of the beam is nonlinear, a highly accurate method becomes important in determining the pull-in characteristics of micro-electro-mechanical systems (MEMS). The static response of the microbeam is investigated in detail. The pull-in curves are shown to be a good agreement in comparison with those obtained from the finite difference method and experimental data.