The Use of the Strain Gradient Elasticity Theory in the Electrically Actuated Microbeam Problem: An Investigation on the Static and the Dynamic Response

The main goal of this work is to investigate the static and the dynamic behaviour of an electrically-actuated microbeam modelled by means of the strain gradient elasticity theory. Considering the nonlinearities due to the mid-plane stretch and of the applied electric force, a numerical solution for the static response is obtained by the differential quadrature method including also the features introduced by the non-classical continuum theory. A parametric analysis confirms the well-known hardening effect generated by a tensile applied axial load and highlights the variation of the deflection with respect to the high-order material parameters. The reliability of the considered 1-d model is improved by taking also into account a correction for the electrical fringing field effects that slightly modifies the solution. Regarding the dynamics, a single-degree-of-freedom model is studied and the variation of the eigenfunction, used in the discretized problem, with respect to the higher-order length scale parameters, is analysed. The results, carried out from the 4th order Runge-Kutta numerical integration, show the softening/hardening behaviour of the device varying the beam model parameters.