We analyze the nonlinear elliptic problem ∆u = λf(x) (1+u)2 on a bounded domain Ω of R with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at −1. When a voltage –represented here by λ– is applied, the membrane d...

A novel single-stage push–pull electronic ballast with high input power factor is presented in this paper. The proposed electronic ballast combines the front-end power-factor corrector and push–pull converter into a single-stage converter. Compared to the single-stage class-D electronic ballast, the proposed circuit does not require an isolated driver. The control of the circuit is easier and t...

Accurate determination of the pull-in, or the collapse voltage is critical in the design process. In this paper an analytical method is presented that provides a more accurate determination of the pull-in voltage for MEMS capacitive devices with clamped square diaphragm. The method incorporates both the linearized modle of the electrostatic force and the nonlinear deflection model of a clamped ...

The reproducibility of the pull-in voltage of a single side clamped free-standing beam has been investigated for application as a DC voltage reference. A 2 mm long beam has been fabricated in an epipoly process with, at the tip, poly-poly electrodes extending into the axial direction for electrostatic lateral deflection and a combdrive operating in the normal lateral beam direction. The DC volt...

in the current study the effect of casimir force and squeezed film damping on the pull-in instability and dynamic behavior of electrostatically actuated nano and micro electromechanical systems is investigated separately. linear elastic membrane theory is used to model the static and dynamic behavior of system for strip, annular and disk geometries. squeezed film damping effect is modeled using...

We study the regularity of the free boundary in the obstacle for the p-Laplacian, min { −∆pu, u − φ } = 0 in Ω ⊂ R. Here, ∆pu = div ( |∇u|p−2∇u ) , and p ∈ (1, 2) ∪ (2,∞). Near those free boundary points where ∇φ 6= 0, the operator ∆p is uniformly elliptic and smooth, and hence the free boundary is well understood. However, when ∇φ = 0 then ∆p is singular or degenerate, and nothing was known ab...

Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem related to plasma confinement. The associated energy functional is nondifferentiable, and therefore standard variational methods cannot be used directly to prove...

In this paper, the sloshing response of liquid in a two dimensional rigid rectangular tank with rigid baffles is investigated using boundary element technique. A baffle is a supplementary structural element which supplies a kind of passive control on the effects of ground shaking. The complicated liquid domain is divided into two simple sub-domains so that the liquid velocity potential in each ...

This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric...

We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The new aspect considered in this paper, with respect to other control problems involving free boundaries, is that here the cost functional explicitly depends...