Modified Mathematical Model of Vibrations of a Long-Sized Plate and its Application to the Analysis of MEMS Structures

The research and analysis of wave processes in micro- and nanoscale structures are closely related to searching for precise analytical solutions of mathematical physics problems that simulate vibrations in such type systems. Classical models of mechanics don't allow us to describe the nature of the wave process adequately. The main disadvantage of such approaches to modeling MEMS-systems is the lack of precise methods for research. In the paper, wave processes in long-scaled constructions under the action of external forces are considered as a two-point in time problem for a nonhomogeneous wave equation in an unbounded domain. There is proposed a precise method for constructing a solution in this mathematical model. The method is illustrated to describe the vibration processes of the infinite membrane. There is possible to model the behavior of the oscillations properly and also to control the parameters of such type systems due to the presented method.