When a layer of a semicrystalline polymer is subject to a tensile force in its plane and a voltage through its thickness, the deformation of the layer is initially homogeneous, but it then localizes. The electromechanical instability sets in when the force and the voltage reach critical conditions. The critical conditions are determined in this paper and are related to the following two special...

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...

This paper addresses the static and dynamic stabilities of a parametrically excited torsional micro-actuator. The system is composed of a rectangular micro-mirror symmetrically suspended between two electrodes and acted upon by a steady (dc ) while simultaneously superimposed to an (ac ) voltage. First, the stability of the system subjected to a quasi-statically applied (dc ) voltage is investi...

Periodically, some group of asset prices rises at a rapid pace that is matched neither by general price inflation nor seemingly by the relevant fundamental asset values. This situation rightfully causes great consternation at central banks, as it has dangerous implications for the stability of inflation and full employment and for financial stability. Some asset prices, such as those for housin...

The pull-in voltage instability associated with a simple MEMS device, consisting of a thin dielectric elastic membrane supported above a rigid conducting ground plate, is analyzed. The upper surface of the membrane is coated with a thin conducting film. In a certain asymptotic limit representing a thin device, the mathematical model consists of a nonlinear partial differential equation for the ...