表面效应对多孔纳米梁热屈曲行为影响的辛方法  

Symplectic method for the influence of surface effect on thermal buckling of graded porous nanobeams

作　　者：李清禄[1] 牛晓洁 张靖华[1] LI Qinglu;NIU Xiaojie;ZHANG Jinghua(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《西北工业大学学报》2024年第6期1152-1159,共8页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(12362009);甘肃省自然科学基金重点项目(23JRRA775);甘肃省科技重大专项计划(24ZDCJ001)资助。

摘　　要：为了分析表面效应对多孔纳米梁热屈曲行为的影响,基于Grutin-Murdoch表面弹性理论和Euler梁理论,采用Hamilton体系研究了梯度多孔纳米梁的热屈曲问题。在辛空间中,梯度多孔梁的屈曲问题归结为系统的零本征值问题,纳米梁的屈曲临界温度和屈曲模态对应于Hamilton体系的辛本征值和本征解。假设梯度多孔材料的性能在整个厚度上连续变化,并考虑了孔隙率沿其厚度不均匀分布的2种余弦形式,通过分叉条件及归一化方法解析地给出了屈曲模态和纳米梁发生屈曲的临界屈曲升温。以图表形式呈现了表面效应对梯度多孔纳米梁热屈曲的影响。结果表明:梯度多孔纳米梁具有十分显著的表面效应。考虑表面效应,多孔纳米梁的临界热载荷和临界屈曲升温都会提高,同时,适当的孔隙率系数和孔隙分布方式可以有效地改善多孔纳米梁的力学性能。The influences of surface effect on the thermal buckling behavior of graded porous nano-beams were analyzed.Based on the Grutin-Murdoch surface elasticity theory and Euler beam theory,the thermal buckling of graded porous nano-beams was studied by using Hamilton system.In the symplectic space,the buckling problem of gradient porous beams was reduced to the zero eigenvalue problem of the system,and the critical buckling temperature and buckling mode of nano-beams correspond to the symplectic eigenvalue and eigensolution of the Hamiltonian system.It is assumed that the performance of gradient porous materials varies continuously throughout the thickness,and two cosine forms of uneven distribution of porosity along its thickness are considered.By using bifurcation conditions and normalization methods,the critical buckling temperature rise for buckling modes and nano-beams was analytically determined.Finally,the influence of surface effects on the thermal buckling of gradient porous nano-beams was presented in the form of a chart.The results indicate that graded porous nano-beams have significant surface effects.Considering surface effects,the critical thermal load and critical buckling temperature of porous nano-beams will be increased.At the same time,appropriate porosity coefficients and pore distribution can effectively improve the mechanical properties of porous nano-beams.

关 键 词：梯度多孔材料 纳米梁 表面应力 辛方法 临界屈曲升温 

分 类 号：O312[理学—一般力学与力学基础] V242[理学—力学]