In this paper, the wave propagation approach is combined with nonlocal elasticity theory to analyze the buckling and free vibrations of Euler–Bernoulli nanobeams. This method gives the propagation and reflection matrices which are useful for the analysis of mechanical energy transmission and reflection in micro/nano devices. Firstly, the propagation and reflection matrices for nanobeams are derived. Then, these matrices are combined to provide a concise and exact approach for obtaining the natural frequencies of the nanobeams for any possible combination of boundary conditions. Then, the natural frequencies obtained by this method are compared with the results in the literature and a set of benchmark results is presented for any combination of boundary conditions in a practical range of nonlocal parameter and axial preload parameter. Finally, the effect of nonlocal and preload parameters on the reflected power of an incident wave upon different boundary conditions is studied in details for the first time.
Composite Structures – Elsevier
Published: Dec 15, 2015
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