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According to the present literature review, the axial vibration of the axially functionally graded (FG) tapered nanorod with attached nonlinear spring has not been addressed so far. In this study, the axial vibration of the FG tapered nanorod is studied based on Eringen's nonlocal theory, in which one end of the nanorod is clamped and the other end is attached to a nonlinear spring and a nanoparticle. The influence of different parameters such as the nonlinear spring constant, mass of the nanoparticle, and the nonlocal parameter on the natural frequencies is presented in detail. The solutions via Tables can be utilized as a reliable reference for evaluating the validity of future researches. The presented nonlocal solutions can be helpful for those who are interested in designing micro/nano electromechanical systems. [ABSTRACT FROM AUTHOR]

Wave propagation is one of the famous approaches for analyzing the vibration of solid structures. Literature reviews show that most bodies analyzed with this approach are one-dimensional waveguide structures. In this paper, the free vibration of annular circular and sectorial membranes are analyzed using the wave propagation approach. Firstly, the propagation and reflection matrices are derived. Then, a concise and systematic approach for obtaining the natural frequencies is presented which can be a reference for future studies. The solution obtained by this method is exactly the same as those derived by the classical method. [ABSTRACT FROM AUTHOR]