Size-dependent behaviors of viscoelastic axially functionally graded Timoshenko micro-beam considering Poisson effects  

考虑泊松效应的黏弹性轴向功能梯度Timoshenko微梁的尺寸依赖行为

作　　者：Zhou Bo Zheng Xueyao Kang Zetian Xue Shifeng 周博;郑雪瑶;康泽天;薛世锋(中国石油大学(华东)储运与建筑工程学院,青岛266580)

机构地区：[1]College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China

出　　处：《Journal of Southeast University(English Edition)》2020年第2期170-180,共11页东南大学学报（英文版）

基　　金：The National Science and Technology Major Project(No.2017ZX05009-003);the National Key Research and Development Program of China(No.2017YFC0307604);the Talent Foundation of China University of Petroleum(No.Y1215042)。

摘　　要：A size-dependent continuum-based model is developed for the functionally graded(FG)Timoshenko micro-beams with viscoelastic properties,in which material parameters vary according to the power law along its axial direction.The size effect is incorporated by employing the modified couple stress theory and Kelvin-Voigt viscoelastic model,so that viscous components are included in the stress and the deviatoric segments of the symmetric couple stress tensors.The components of strain,curvature,stress and couple stress are formulated by combining them with the Timoshenko beam theory.Based on the Hamilton principle,the governing differential equations and boundary conditions for the micro-beam are expressed with arbitrary beam section shape and arbitrary type of loads.The size effect,FG effect,Poisson effect,and the influence of the beam section shape on the mechanical behaviors of viscoelastic FG micro-beams are investigated by taking the simply supported micro-beam subjected to point load as an example.Results show that the size effect on deflection,normal stress and couple stress are obvious when the size of the micro-beam is small enough,and the FG effects are obvious when the size of the micro-beam is large enough.Moreover,the Poisson ratio influences the size effect significantly and the beam section shape is also an important factor influencing the mechanical behavior of the micro-beam.建立了黏弹性功能梯度(FG)Timoshenko微梁的尺寸依赖连续模型,其材料参数沿轴向随幂律变化.为研究微梁的尺寸效应,利用修正偶应力理论和Kelvin-Voigt黏弹性模型将材料的黏性项纳入应力和偶应力张量的偏离分量中;结合Timoshenko梁理论导出了应变、曲率、应力和偶应力的分量;基于哈密顿原理,给出了任意截面形状的微梁在任意荷载作用下的控制微分方程和边界条件.然后,以点荷载作用下的简支微梁为例,研究了尺寸效应、功能梯度效应、泊松效应以及截面形状对黏弹性微梁力学行为的影响.结果表明:当微梁尺寸足够小时,其转角、正应力和偶应力的尺寸效应明显;当微梁尺寸足够大时,微梁的功能梯度效应较为明显;此外,泊松比对尺寸效应影响较大,梁截面形状也是影响微梁力学性能的重要因素.

关 键 词：viscoelastic functionally graded micro-beam size-dependent behaviors size effect functionally graded effect Poisson effect space 

分 类 号：TP324[自动化与计算机技术—计算机系统结构]