Porosity and deformable boundary effects on the dynamic of nonlocal sigmoid and power-law fg nanobeams embedded in the winkler-pasternak medium

Abstract

ObjectiveThe aim of this study is to solve the free vibrations of embedded functionally graded porous and non-porous nanobeams with different material distributions (power-law and sigmoid) under general elastic boundary conditions to better understand the dynamic properties. This form of model has the benefit of allowing one to handle the rigid or restrained supporting conditions.MethodA solution method using the Fourier sine series and Stokes' transform together is adopted. This method is used to study the effects of deformable boundary conditions as well as rigid boundary conditions, which are common in the literature. In the current study, two sets of equations for both elastic support conditions consisting of infinite series are derived. Then, eigenvalue problems are set up for the analytical solution. The eigenvalues of the established problems give the vibration frequencies of the embedded functionally graded porous/non-porous nanobeams.ConclusionsThe proposed models are effective for studying arbitrary boundary conditions. The accuracy of the model is compared with some results from the literature for rigid boundary conditions. Looking at the frequencies of functionally graded porous/non-porous nanobeams, it is seen that the studied parameters such as foundation parameters, nonlocal parameter, grading index, elastic spring stiffness produce changes that cannot be ignored.