Analysis of a Mathematical Model of Plate Structures Oscillations in MEMS

A mathematical model of describing the oscillations of longitudinal plate structures MEMS is proposed. This model contains a partial differential equation of second order in time and fourth order in spatial variables with conditions which describe the behavior of the plate at two time points. The conditions of existence and uniqueness of the solution of the problem are investigated, and the method of constructing an accurate analytical solution of a two-point time problem is developed. On the basis of this, processes in micro- and nanoscale plate structures and dependence their horizontal deflections on the material properties and parameters are studied. Specific examples show the application of the developed method.