A wave-based computational method for free vibration, wave power transmission and reflection in multi-cracked nanobeams

In this paper, the wave propagation method and the nonlocal elasticity theory are utilized to analyze the vibration, wave power transmission and reflection in multi-cracked Euler-Bernoulli nanobeams. This aim is pursued by deriving the propagation, reflection and transmission matrices and comparing the natural frequencies obtained by these matrices with the available results in the literature. Then, the nonlocal and crack-severity effects on the natural frequencies are presented for some combinations of the boundary conditions. Finally, the effects of nonlocal and crack-severity parameters on the reflected and transmitted power of a wave incident upon a crack location are studied in details for cracked nanobeams. The results obtained via the reflection and transmission matrices will provide valuable insights into the subject of wave power reflection and transmission analysis in nanoscale structures for the future. The computer coding of the proposed method is much easier than the classical vibration analysis methods for similar analyses which makes it more appropriate in implementation.