Abstract

The objective of this study is to apply Gram-Schmidt orthogonalization procedure for generating displacement functions. This procedure allows us to obtain numerically stable functions to be used in vibration analysis of novel composite beams via the Ritz method. Within this study, the theoretical modeling based on third-order shear deformation beam theory is derived to deal with free and forced vibration of functionally graded graphene nanoplatelet-reinforced composite beams subjected to multiple moving loads. To solve the problems of the beams with various end supports, the Ritz method-based Gram-Schmidt polynomial series is adopted to obtain the accurate results. In forced vibration due to the applied multiple moving loads, the time integration technique of Newmark is also employed to find out time history of dynamic deflection of such beams associated with several parametric studies such as patterns of reinforcement, weight fraction of graphene nanoplatelets, and the number of moving loads. According to the numerical results, it is found that the composite beams with low content of graphene nanoplatelets can result in enhancing performance of dynamic bending resistance. Increasing number of moving loads on the beams yields the increases of dynamic deflection and critical velocity.

摘要

本研究的目的是应用 Gram-Schmidt 正交化程序来生成位移函数。该程序使我们能够通过 Ritz 方法获得用于新型复合梁振动分析的数值稳定函数。在这项研究中，基于三阶剪切变形梁理论的理论模型被推导出来处理功能梯度石墨烯纳米片增强复合梁在多个移动载荷下的自由和受迫振动。为解决具有多种端部支撑的梁的问题，采用基于Ritz方法的Gram-Schmidt多项式级数来获得准确的结果。在由于施加的多个移动载荷引起的强迫振动中，Newmark 的时间积分技术也被用于找出与几个参数研究相关的此类梁的动态偏转的时间历史，例如增强模式、石墨烯纳米片的重量分数和移动载荷的数量。根据数值结果，发现石墨烯纳米片含量低的复合梁可以提高动态抗弯性能。梁上移动载荷数量的增加导致动态挠度和临界速度的增加。研究发现，石墨烯纳米片含量低的复合梁可以提高动态抗弯性能。梁上移动载荷数量的增加导致动态挠度和临界速度的增加。研究发现，石墨烯纳米片含量低的复合梁可以提高动态抗弯性能。梁上移动载荷数量的增加导致动态挠度和临界速度的增加。