Stabilization of a Vibrating Non-Classical Micro-Cantilever Using Electrostatic Actuation

A closed-loop control methodology is investigated for stabilization of a vibrating non-classical micro-scale Euler-Bernoulli beam with nonlinear electrostatic actuation. The dimensionless form of governing nonlinear partial differential equation (PDE) of the system is introduced. The Galerkin projection method is used to reduce the PDE of system to a set of nonlinear ordinary differential equations (ODE). In non-classical micro-beams، the constitutive equations are obtained based on the non-classical continuum mechanics. In this work، proper control laws are constructed to stabilize the free vibration of non-classical micro-beams whose governing PDE is derived based on the modified strain gradient theory as one of the most inclusive non-classical continuum theories. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme. Also، the results have been compared with those obtained by the classical model of micro-beam.