This article investigates wave propagation behavior of a multi-phase nanocrystalline nanobeam subjected to a longitudinal magnetic field in the framework of nonlocal couple stress and surface elasticity theories. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, couple stress and surface effects are omitted. Hamilton’s principle is employed to derive the governing equations which are solved by applying an analytical method. The frequencies are compared with those of nonlocal and couple stress-based beams. It is showed that wave frequencies and phase velocities of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, magnetic field, surface effect and nonlocality.

本文在非局部耦合应力和表面弹性理论的框架下研究了纵向磁场作用下的多相纳米晶纳米束的波传播行为。在该模型中，纳入了描述纳米晶纳米束真实材料结构和尺寸效应的基本措施。这种非经典的纳米束模型包含耦合应力效应，以捕获晶粒的微旋转。此外，非局部弹性理论被用来研究粒子之间的非局部和远距离相互作用。如果忽略非局部参数，耦合应力和表面效应，则本模型可以退化为经典模型。利用汉密尔顿原理导出控制方程，该控制方程通过应用解析方法求解。将频率与非局部和基于应力的偶合梁的频率进行比较。结果表明，纳米晶纳米束的波频率和相速度取决于晶粒尺寸，晶粒旋转，孔隙率，界面，磁场，表面效应和非局部性。