剪切变形与转动惯量对层合金属厚壁短管振动模态的影响  

Effects of shear deformation and rotary inertia on the vibration of laminated thick-walled short tubes

作　　者：郭建英[1] 白艳艳[2] 

机构地区：[1]太原理工大学矿业工程学院,太原030024 [2]太原理工大学机械工程学院,太原030024

出　　处：《振动与冲击》2017年第21期107-116,共10页Journal of Vibration and Shock

基　　金：山西省自然科学基金(2013011025-2);山西省研究生教育改革研究课题(2016JG40)

摘　　要：对层合金属厚壁短管进行振动分析必须考虑非匀质、剪切变形和转动惯量效应。基于Timoshenko理论,推导了两端简支、两端固支、两端自由和悬臂四种边界条件下,层合金属厚壁短管弯曲振动的频率函数与模态振型函数的表达式。采用计算机代数系统MAPLE对四种边界条件下铜钢层合厚壁短管的固有频率进行求解,并绘制振型曲线。采用锤击实验法并结合有限元模态分析法,测得了铜钢层合厚壁短管在两端自由条件下弯曲振动的固有频率。理论解与实测值相比的最大误差为-4.56%,理论解与有限元解相比的最大误差为-0.76%。求解了剪切变形与转动惯量对铜钢层合厚壁短管固有频率的影响系数,并分析了该频率影响系数与管子的振型曲线随边界条件、阶序、层合管长径比、以及壁厚比等参数的变化规律。The effects of non-homogeneit,shear deformation and rotary inertia are necessary to be taken into account in the vibration analysis of laminated metal thick-walled short tubes. Based on the Timoshenko＇s beam theory,the analytical expressions of the frequencies and modal functions of laminated metal tubes were deduced under four kinds of boundary conditions： hinged-hinged,clamped-clamped,free-free and clamped-free. The natural frequencies of coppersteel laminated tubes were solved and the mode shapes were mapped by use of the computer algebra system MAPLE for these four cases. The natural frequencies of three copper-steel laminated tubes with different lengths were also measured by using both the method of hammer tests and the finite element modal analysis. The theoretical solutions of the first three natural frequencies of the copper-steel tubes were compared with the measured values, the maximum error being-4. 56%,and also compared with the finite element results,the maximum error being-0. 76%. The influential coefficients of shear deformation and rotary inertia on the frequencies of laminated metal thick-walled short tubes were solved. The variations of the frequency influential coefficients and modal shapes along with the boundary condition,frequency order,aspect ratio,non-homogeneous material parameter of laminated metal tubes were also investigated.

关 键 词：层合金属厚壁短管 剪切变形 转动惯量 频率影响系数 模态振型 

分 类 号：TB123[理学—工程力学]