Stabilization of a vibrating non-classical micro-cantilever using electrostatic actuation

A closed-loop control methodology is investigated for stabilization ofa vibrating non-classical micro-scale euler-bernoulli beam with nonlinear electrostaticactuation. the dimensionless form of governing nonlinear partial dierential equation(pde) of the system is introduced. the galerkin projection method is used to reduce thepde of system to a set of nonlinear ordinary dierential equations (ode). in non-classicalmicro-beams, the constitutive equations are obtained based on the non-classical continuummechanics. in this work, proper control laws are constructed to stabilize the free vibrationof non-classical micro-beams whose governing pde is derived based on the modied straingradient theory as one of the most inclusive non-classical continuum theories. numericalsimulations are provided to illustrate the eectiveness and performance of the designedcontrol scheme. also, the results have been compared with those obtained by the classicalmodel of micro-beam.