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李清禄,赵煊贺,张靖华.梯度多孔金属材料梁的屈曲和屈曲基础上的振动[J].计算力学学报,2024,41(3):415~420
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梯度多孔金属材料梁的屈曲和屈曲基础上的振动
Buckling of beams made of graded porous metal materials and times new vibration on the basis of buckling
投稿时间:2022-10-26  修订日期:2022-12-15
DOI:10.7511/jslx20221026001
中文关键词:  梯度多孔材料  孔隙率  随从载荷  临界载荷  频率
英文关键词:graded porous material  porosity  follower force  critical load  frequency
基金项目:国家自然科学基金(12062010;12362009);甘肃省自然科学基金重点项目(23JRRA775)资助.
作者单位E-mail
李清禄 兰州理工大学 理学院, 兰州 730050 lqu2008@163.com 
赵煊贺 兰州理工大学 理学院, 兰州 730050  
张靖华 兰州理工大学 理学院, 兰州 730050  
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中文摘要:
      为研究梯度多孔金属材料梁的屈曲以及屈曲附近的振动特性,首先建立了随从分布压力下梯度多孔材料梁的动力学控制方程,得到了描述后屈曲的静态控制微分方程和描述屈曲前后振动响应的控制方程。通过打靶法数值求解两组强非线性方程,获得了简支-固支梯度多孔梁的屈曲临界载荷以及屈曲前后振动频率与载荷之间的关系曲线。分析了孔隙率系数和孔隙分布方式对屈曲临界载荷和屈曲前后振动频率的影响。结果表明,随着孔隙率系数e0的增加,发生屈曲时的临界载荷减小;各阶固有频率也减小。屈曲前,各阶振动频率随载荷增大而减小,屈曲后,除三阶频率外,一阶和二阶频率随载荷增大而增大。
英文摘要:
      In order to study the buckling of a graded porous metal beam and its vibration characteristics near buckling,the governing equations of motion of the gradient porous metal beam under the distributed follower pressure were first established,and the governing differential equations of static equilibrium describing post-buckling and the governing equations describing the vibration response before and after buckling were obtained.Two sets of strongly nonlinear equations were solved numerically by shooting method,and the critical buckling load of hinged-fixed graded porous beams and the relationship between the vibration frequency and the load before and after buckling were obtained.The effects of porosity coefficient and porosity distribution on critical buckling load and vibration frequency before and after buckling were analyzed.The results show that the critical load decreases with the increase of porosity coefficient;the natural frequencies also decrease.Before buckling,the natural vibration frequencies decrease with the increase of load.After buckling,the first-and second-order frequencies increase with the increase of load,except for the third order frequencies.
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