Nonlinear Vibration Movements of the Mid-Supported Micro-Beam

Abstract

This study analyzes the vibration movements of multi-support micro beams placed in an electrically smooth area using the modified couple stress theory. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. Large number of experiments in recent years have indicated that classical continuum theory is unable to predict the mechanical behavior of microstructure with small size. However, nonclassical continuum theory should be used to accurately design and analyze the microstructures. Modified couple stress theory models the micro and nanomechanical systems with higher accuracy because they employ additional material parameters to the equation considering size dependent behavior. The most general nonlinear motion equations for multi-support microbeams have been obtained by considering the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength, and nonlinear effects resulting from elongations. The nonlinear equations of motion are obtained according to the Hamilton method using the modified couple stress theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent of the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multi-scale method, which is one of the perturbation methods. As a result, an increase occurs in the first mode frequencies ([Formula: see text]) and nonlinear correction effect parameters ([Formula: see text]) with the progress of the center support position gradually towards [Formula: see text] and the increase of the microbeam elasticity coefficient ([Formula: see text]).