Free vibration, wave power transmission and reflection in multi-cracked nanorods

Abstract

Abstract In this paper, the wave propagation method and the differential constitutive law consequent (not equivalent) to the Eringen strain-driven integral nonlocal elasticity model are utilized to analyze the free vibration, wave power transmission and reflection in multi-cracked nanorods. 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, crack-severity, and crack location effects on the natural frequencies are presented for two combinations of the boundary conditions. Finally, the paper presents the effects that the reflected and transmitted power of a wave incident on a crack location receive from the nonlocal and crack-severity parameters. 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 which makes it more appropriate in implementation.