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Nowadays, thousands of studies have looked into the nonlinear vibration analysis of micro/nanostructures by solving nonlinear partial differential equations; however, there is almost no focus on the solution of the nonlinear boundary condition problems in the micro/nanoscale literature. This work presents the free vibration of a nonlocal functionally graded Euler–Bernoulli beam with a tip nanoparticle and a nonlinear spring constraint using Eringen's nonlocal theory. It is assumed that there is a nonlinear/linear spring and a nanoparticle at one end of the beam while the other is clamped. The effect of various parameters, such as the nonlocal parameter, the nanoparticle mass, and the nonlinear/linear spring constant on the resonance frequencies, is demonstrated and discussed in detail. The presented benchmark tables can be used as an appropriate resource to validate analytical or approximate solutions in future works. Furthermore, the presented results can be useful for those designing micro/nano-electromechanical devices. [ABSTRACT FROM AUTHOR]

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In this paper, the wave propagation approach is presented for free vibration analysis of non-uniform rectangular membranes. Literature reviews reveal that most bodies analyzed by this approach are one dimensional waveguide structures. Firstly, the propagation, reflection and transmission matrices for non-uniform rectangular membranes are derived. Then, these matrices are combined to obtain the natural frequencies of non-uniform rectangular membranes. The solution obtained by this approach is verified by the classical method. Moreover, a set of benchmark results is presented for various geometric parameters. Finally, the behavior of wave reflection and transmission at the section change of the composite rectangular membranes is studied in details for the first time by defining their important parameters. The obtained hints are useful for the analysis of energy transmission in micro/nano devices. [ABSTRACT FROM AUTHOR]