Summary
Oscillations of the electrically actuated micro and nano beams and plates are considered, described by strongly nonlinear PDEs. One of the essentially nonlinear effects is the pull-in phenomenon, i.e., the transition of the oscillatory regime to the attraction one. We propose a simple and physically justified algorithm to determine the voltage values at which the system collapses. It is based on the detection of voltage leading to the merging of stable (central) and unstable (saddle) equilibrium points. Comparison with the results of calculations based on other methods as well as with experimental results shows sufficient accuracy of the proposed algorithm. The electrically activated oscillations are considered taking into account the geometric nonlinearity within the framework of the Kirchhoff’s and Berger’s models. Neglecting of geometrical nonlinearity leads to large quantitative error. It is shown that van der Waals forces have a greater influence on the pull-in value than Casimir forces. The effect of compression/extension on the pull-in value has been studied. Common errors when taking this factor into account are indicated. Dynamic scenarios for the collapse of the considered systems are studied. Analytical estimation for the initial values which guarantee oscillatory character of motion is obtained.
