Nonlinear Vibration of a Microbeam on a Winkler Foundation and Subjected to an Axial Load using Modified Couple Stress Theory

In this paper, nonlinear vibration analysis of a microbeam on Winkler type of foundation and subjected to an axial compressive load on its both ends is investigated. The partial differential governing equation of motion in transverse direction for the Euler-Bernoulli microbeam considering the Hook’s law based on the couple stress theory and applying the Hamilton principle is derived. Using Galerkin method, the partial differential equation of vibration in lateral direction is converted to an ordinary differential equation and then is analytically solved using the He’s nonlinear method to obtain frequency response of the microbeam. Effect of changes of various parameters such as geometrical size scale of microbeam, stiffness of Winkler foundation and axial compressive load on the nonlinear and linear natural frequencies are all investigated. It is seen that by increasing the axial compressive load, the dimensionless ratio of nonlinear frequency to linear frequency increases and the value of this ratio for the pinned-pinned microbeam is greater than the one for a clamped-clamped microbeam.