轴向运动超薄梁的非局部动力学分析

基于非局部弹性理论,建立了两端受初始张力的轴向运动超薄梁横向振动的控制方程。与现有的一些仅仅在控制方程中考虑非局部效应的研究不同,该文同时将非局部效应引入到两种典型的边界条件中,考察了非局部参数对超薄梁横向振动行为尤其是固有频率和临界速度的影响。结果表明：超薄性使得轴向运动梁的自由振动固有频率及临界速度降低,经典弹性理论高估了纳米尺度结构的弯曲刚度,轴向运动超薄梁的动力学行为存在明显的非局部尺寸效应。

NONLOCAL DYNAMICAL ANALYSIS ON AXIALLY TRAVELLING ULTRA-THIN BEAMS

Based on the nonlocal elasticity theory, the equation of motion that governs the transverse vibration of an axially travelling ultra-thin beam subjected to initial axial tension is established. Unlike some previous work which only employs nonlocal effects in the governing equation, the nonlocal small scale parameter is also adopted into two typical kinds of boundary conditions to investigate the effects of nonlocal elasticity on vibration behaviors, including the natural frequency and critical velocity. It is shown that the ultra-thin character causes the natural frequency and critical velocity to decrease, and the classical elasticity theory overestimates the bending stiffness of nanostructures. The nonlocal size effects exist obviously in the dynamic properties of such an axially travelling ultra-thin beam.