Coupled-field FEM nonlinear dynamics analysis of continuous microsystems by non-incremental approach

摘要

This paper deals with numerical prediction of the nonlinear dynamic behaviour of electromechanical continuous microsystems, in presence of large displacements. Finite Element Method (FEM) is applied, by following so-called "sequential" approach, based on the solution in series of coupled electromechanical problem. In spite of tested approaches available in the literature, a "non-incremental" method is developed to enhance the performances of numerical tools. In practice, for microelectrostatic beam actuators, the total voltage may be applied once, in only one step, instead of by small increments. Non-incremental approach is based on two features. A special non-incremental beam element is introduced to deal with so-called geometrical nonlinearity of microbeam, caused by large displacement. It allows computing the total displacement of a cantilever microbeam, by integrating local rotation and axial deformation of cross-section, by avoiding to refer to the assumption of small displacement. Proposed procedure includes a preliminary static nonlinear analysis, to find the equilibrium condition, then a computation of nodal voltages for the deformed shape and of electric load. Equations of motion are integrated in time, by Newmark's method, while at each step, Newton-Raphson approach finds the instantaneous equilibrium, by applying the total voltage, instead of a small incremental value. Results evidenced a fast convergence even for large initial deflection. Moreover, typical peculiarities of nonlinear dynamic system, like softening effect in frequency response and amplitude jumping are observed. The whole proposed approach is currently under experimental validation and improvement to include damping effects, to study the dynamic stability of the microsystem.