Examination of the High-Frequency Behavior of Functionally Graded Porous Nanobeams Using Nonlocal Simple Higher-Order Shear Deformation Theory

The primary objective of this paper is to examine the free vibration behaviors of functionally graded nanobeams with porosity while considering nonlocal parameters. The nanobeams are built of functionally graded materials, having material features that change smoothly over the beam’s thickness. To illustrate how porosity is distributed throughout the body of the beams, four different forms of porosity distribution are taken into consideration. Eringen’s nonlocal parameter elasticity theory and Hamilton’s principle are used to establish the governing equations of the motion of the functionally graded porous nanobeams. Then, the closed-form solution of Navier is used to solve the eigenvalue problems to find the frequencies of the functionally graded porous nanobeams. A comprehensive parametric study is also carried out to demonstrate the influence of geometric parameters, material gradient index, and nonlocal parameters on low- and high-frequency vibration behaviors of the functionally graded porous nanobeams. The results of the vibration of the functionally graded porous nanobeams undergoing the low- and high-frequency conditions can serve as benchmarks for applications of such structures in engineering and for future work.