Abstract:
The study object is a flexible plate of a mesh structure with an electrical drive with clamped edges. A source of electromotive force is connected to the gate and the plate. The gate is located at some distance below the plate. The volumetric ponderomotive forces of the electric field acting on the plate are modeled by the Coulomb force. The motion equations of a geometrically nonlinear plate, boundary, and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on Kirchhoff's hypotheses. An isotropic, homogeneous material is considered. Scale effects are taken into account using modified couple stress theory. It is assumed that the fields of displacement and rotation are not independent. Geometric nonlinearity is taken into account according to the theory of T. von Karman. The mesh structure of the plate was modeled using the continuum theory of G. I. Pshenichny, which made it possible to replace the regular system of ribs with a continuous layer. The system of partial differential equations describing the nonlinear vibrations of the mesh plate under consideration was reduced to a system of ordinary differential equations using the finite difference method of second-order accuracy. The Cauchy problem was solved by the Runge – Kutta method of fourth-order accuracy. The mathematical model, solution algorithm, and software package were verified by comparing the calculation results with a full-scale experiment. An analysis of the static instability depending on the mesh geometry was carried out, as well as an analysis of the appearance of instability zones depending on the amplitude and frequency of the electrical voltage dynamic part.
Key words:NEMS, mesh plate, electric field, loss of stability, natural oscillations, carbon nanoplate, mathematical modeling.
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