Abstract

In this work, the nonlinear flexural free vibration behavior of size-dependent curved nano/micro beams with reinforcement of graphene platelets is studied using the nonlocal elasticity theory along with a trigonometric shear flexible beam theory. The governing equations through the finite element model are derived in terms of displacements using the dynamic version of principle of virtual work. The formulation extends the von-Karman model to account for both large deflections and rotations in the strain displacement relationship. Direct iterative procedure is used to solve the nonlinear eigenvalue problem. This methodological study aims to analyze the influence of various design parameters like slenderness ratio of the beam, curved beam included angle, distribution pattern of porosity and graphene platelets, nonlocal parameter, and boundary conditions on the free vibration behavior of curved nano/micro beams by studying the amplitude frequency response curves. The present work also highlights the variation in modeshapes with reference to axial/transverse directions.

摘要

在这项工作中，使用非局部弹性理论和三角剪切柔性梁理论研究了具有石墨烯薄片增强的尺寸相关弯曲纳米/微米梁的非线性弯曲自由振动行为。通过有限元模型的控制方程是使用虚功原理的动态版本根据位移导出的。该公式扩展了 von-Karman 模型，以考虑应变位移关系中的大变形和旋转。直接迭代过程用于解决非线性特征值问题。本方法研究旨在分析各种设计参数的影响，如梁的长细比、弯曲梁夹角、孔隙率和石墨烯薄片的分布模式、非局部参数、通过研究幅频响应曲线对弯曲纳米/微米梁的自由振动行为和边界条件进行研究。目前的工作还强调了振型在轴向/横向方面的变化。