Steady-state, nonlinear analysis of large arrays of electrically actuated micromembranes vibrating in a fluid

Abstract

This paper describes a robust and efficient method to obtain the steady-state, nonlinear behaviour of large arrays of electrically actuated micromembranes vibrating in a fluid. The nonlinear electromechanical behavior and the multiple vibration harmonics it creates are fully taken into account thanks to a multiharmonic finite element formulation, generated automatically using symbolic calculation. A domain decomposition method allows to consider large arrays of micromembranes by efficiently distributing the computational cost on parallel computers. Two-and three-dimensional examples highlight the main properties of the proposed method.

A frequency domain method for scattering problems with moving boundaries

“…Let us remark that, similarly to [33], the spatial Jacobian ∂x ∂x of x appears in (9). In the following, we provide a frequency domain method to solve the modified wave equation (9).…”

“…In the present paper, we propose an original frequency domain method to address this problem, which leads to the solution of coupled systems of Helmholtz-type equations. First, we transform the constant coefficients wave equation in the moving domain as a new wavelike equation in a fixed domain but with variable coefficients related to the metric change (a similar approach was used for quasi-static electromagnetic models in [33]). Since we are studying the micro-Doppler problem (small amplitude and low frequency oscillations of the scatterer) for a high frequency radar, we can then expand the solution in the Fourier domain in time as a Fourier series expansion centered around the radar frequency, modulated by the low frequency perturbation induced by the scatterer movement.…”

“…Let us remark that, depending on the problem, other high frequency numerical methods may also be adapted like for example fast integral equations solvers [19] or even asymptotic adpproximation techniques [5]. Finally, let us notice that the finite Fourier expansion method which leads to the coupled system of PDEs has also been used in the past under the name of the harmonic-balance method or the multi-harmonic approach [6,11,32,33,35,41,46]. It has been proved to be particularly efficient for engineering problems, including situations related to wave-like equations [22,26,47].…”

Time- and Frequency-Domain Steady-State Solutions of Nonlinear Motional Eddy Currents Problems

“…The HB method has been applied to shielding and welding problems [30], laminated cores [31], and induction heating [32]. Multiphysics simulations for microelectromechanical systems (MEMS) using the HB method have been proposed [33]. Electrical machines with linear material characteristics have been modeled in 2D [34,35].…”