Free Vibrations in a Wave Equation Modeling MEMS

Forced Vibrations for a Nonlinear Wave Equation

Free Vibrations for a Nonlinear Wave Equation and a Theorem of

A new and simpler proof is given of the result of P. Rabinowitz for nontrivial time periodic solutions of a vibrating string equation utt-ux, + g(u) = 0 and Dirichlet boundary conditions on a finite interval. We assume essentially that g is nondecreasing, and g(u)/u+m as Iu(+w. The proof uses a modified form (PS), of the Palais-Smale condition (PS). Let g : R-+R be a continuous nondecreasing fu...

Finite time singularity in a free boundary problem modeling MEMS

An idealized electostatically actuated microelectromechanical system (MEMS) consists of a fixed horizontal ground plate held at zero potential above which an elastic membrane held at potential V is suspended. A Coulomb force is generated by the potential difference across the device and results in a deformation of the membrane, thereby converting electrostatic energy into mechanical energy, see...

Numerical Quenching Solutions of a Parabolic Equation Modeling Electrostatic Mems

In this paper, we study the semidiscrete approximation for the following initial-boundary value problem  ut(x, t) = uxx(x, t) + λf(x)(1− u(x, t))−p, −l < x < l, t > 0, u(−l, t) = 0, u(l, t) = 0, t > 0, u(x, 0) = u0(x) ≥ 0, −l ≤ x ≤ l, where p > 1, λ > 0 and f(x) ∈ C([−l, l]), symmetric and nondecreasing on the interval (−l, 0), 0 < f(x) ≤ 1, f(−l) = 0, f(l) = 0 and l = 1 2 . We find some cond...

A parabolic free boundary problem modeling electrostatic MEMS

The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right hand side that depe...