Forced and free dynamic responses of functionally graded porous Rayleigh small-scale beams on Kerr foundation under moving force

Abstract

As a first attempt, free and forced vibrations of functionally graded (FG) porous nanoscale beams embedded in a Kerr foundation under a moving force with constant speed and acceleration are studied analytically and numerically based on the nonlocal strain gradient Rayleigh beam model. It is assumed that the material characteristics of the nanobeam across the thickness are graded according to the power-law function involving different porosity distribution patterns. The governing equation for the motion of the nanobeam is derived by utilizing the extended Hamilton’s principle. With the help of the Galerkin decomposition approach, natural frequencies and dynamic responses of the system are acquired. Several comparative studies are performed with published data in the open literature for validation purposes. Finally, the effects of various parameters such as gradient index, porosity characteristics, foundation properties, and size-dependent parameters on forced and free vibrations of the system are clarified. The results declared that the critical force speed decreases with increasing the gradient index. It is also inferred that for the system with a uniform porosity distribution, the cancellation and critical force speeds increase/decrease for low/high values of the gradient index as the porosity volume fraction increases. Meanwhile, it is indicated that by accurately adjusting the properties of the FG porous material, undesirable vibration of the system can be eliminated. The outcomes of the present investigation could be beneficial in the optimum design of inhomogeneous small-scale transportation systems.