Farzad Ebrahimi - Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran
Ali Seyfi - Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran
Mostafa Nouraei - Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran
Ali Dabbagh - School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

In present study, the influence of porosity on wave propagation behaviors of functionally graded (FG) nanobeams via a nonlocal strain gradient based shear deformable beam theory is investigated. The porosity influences are regarded within the framework of a newly developed method. The motion equations are obtained by extending the dynamic form of the principle of virtual work for a higher-order beam model. Thereafter, the constitutive relations are modified based on the nonlocal strain gradient theory in order to account for the effects of small scale. Also, Hamilton’s principle is employed to derive kinetic relations. At the end, the dispersion curves are achieved by solving the problem with an analytical method. The obtained results which are provided in a group of figures show that there is a remarkable difference between the results of this homogenization method and those of former simple methods that were utilized to capture porosity effects. Also, it is proven that the presented methodology is efficient enough to estimate the dynamic behaviors of FG nanobeams.

Wave propagation; nonlocal strain gradient elasticity; porosity; refined higher-order beam theory