Nonlocal elasticity theory for transverse vibration of composite nanobeams based on wave approach

Wave approach provides a powerful technique for the vibration analysis of macrostructures and micro/nanostructures. This method exhibits the essence of mechanical behavior excellently through describing waves propagating within structures in matrix form. In this article, wave approach is combined with nonlocal elasticity theory to systematically investigate the composite nanobeams subjected to transverse vibration. Initially, the transfer matrix is derived and combined with the conventional method to capture the general characteristic equation. Then, the propagation, reflection and coordination matrices are assembled for achieving the exact solution of the composite nanobeams. In order to validate the feasibility of the proposed method in investigating the resonance behavior, the nonlocal frequency predicted by wave approach is examined by the available published data. Numerical comparisons are conducted to illustrate the natural characteristic of composite nanobeams with various boundary constraints by employing conventional method and wave approach. Finally, the effects of some parameters such as boundary condition, nonlocal parameter and material parameter on the fundamental frequency are also discussed cautiously.