摘要
基于分层法对石墨烯增强功能梯度Timoshenko梁的动力特性问题进行有限元分析。在有限元建模过程中,首先将Timoshenko梁沿厚度方向分成若干层,然后利用改进的Halpin-Tsai细观力学模型计算各层的弹性模量,相应的泊松比和密度则根据混合率法则进行计算,最后对各层均采用4节点四边形板单元离散。通过数值算例分析分层数和单元尺寸比例的合理性,探究石墨烯片的分布形式、质量含量、几何形状和尺寸等因素对Timoshenko梁动力特性的影响。结果表明,添加少量的石墨烯能显著提高Timoshenko梁自由振动的频率,尤其在梁的上下部位分布较多正方形石墨烯片时效果最佳。随着石墨烯片长厚比的增加,Timoshenko梁的自由振动基频不断增大。当石墨烯片长厚比超过1 000之后,梁的基频变化不明显。
Based on the layered method,the finite element analysis was carried out for the dynamic characteristics of the graphene reinforced functionally graded Timoshenko beams.In the process of finite element modeling,the Timoshenko beam was first divided into several layers along the thickness direction,and then the elastic modulus of each layer was calculated by using the improved Halpin-Tsai micromechanical model,Poisson's ratio and density were calculated according to the mixing rate rule,and finally each layer was discrete using a 4-node quadrilateral plate element.Through numerical examples,the rationality of the number of layers and the proportion of element size was analyzed,and the influence of the distribution form,weight fraction,geometric shape and size of graphene sheets on the dynamic characteristics of Timoshenko beams was explored.The numerical example shows that the free vibration frequency of the Timoshenko beam can be significantly increased by adding a small amount of graphene.Compared with other distribution forms and geometric shapes of graphene sheets,the distribution forms of more graphene sheets in the upper and lower parts of the beam and the square graphene sheets can increase more greatly the frequency of free vibration of the Timoshenko beam.The frequency of the Timoshenko beam increases with the increase of the length thickness ratio.With the increase of graphene sheet length thickness ratio,the frequency of Timoshenko beam increases.However,when the length thickness ratio exceeds 1000,the frequency increase is not obvious.
作者
黄立新
周小云
滕靓媚
HUANG Lixin;ZHOU Xiaoyun;TENG Jingmei(College of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China;Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education,Guangxi University,Nanning 530004,China)
出处
《武汉科技大学学报》
CAS
北大核心
2024年第1期71-80,共10页
Journal of Wuhan University of Science and Technology
基金
国家自然科学基金资助项目(12002093)。
