Nonlinear Forced Vibration of Curved Microbeam Resting on Nonlinear Foundation Using the Modified Strain Gradient Theory

Abstract

The nonlinear forced vibrations of a curved micro-beam resting on a nonlinear foundation are examined. The equations of motion are derived using Hamilton’s principle and the modified strain gradient theory which is capable to examine the size effects in microstructures. The nonlinear partial differential equations of motion are reduced to a time-dependent ordinary differential equation containing quadratic and cubic nonlinear terms. The frequency response of the curved microbeam at the primary resonance is determined using the multiple time scales perturbation method. From the application point of view, the frequency response curves may be useful to select the optimum values of design parameters. The effects of geometry parameters and foundation moduli on the vibration behavior of the curved microbeam are illustrated.