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

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (21) : 107-116.

论文

郭建英1 白艳艳2

作者信息 +

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

GUO Jian-ying1 BAI Yan-yan 2

Author information +

文章历史 +

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。

Abstract

Non-homogeneous, shear deformation and rotary inertia effects must be taken into account in vibration analysis of laminated metal thick-walled short tubes. Based on Timoshenko’s beam theory, the analytical expressions of the frequency and modal function of laminated metal tubes are deduced for four boundary conditions: hinged-hinged, clamped-clamped, free-free and clamped-free. The natural frequencies of copper-steel laminated tubes are solved and mode shapes are mapped by used of computer algebra system MAPLE for these four cases. The natural frequencies of three copper-steel laminated tubes with different length are also measured by method of hammer tests combined with finite element modal analysis. The theoretical solutions of the first three natural frequencies of copper-steel tubes are compared with the measured values, the maximum error of -4.56%, compared with the finite element, the maximum error of -0.76%. The frequency influence coefficients of shear deformation and rotary inertia on the laminated metal thick-walled short tubes are solved. The variations of the frequency influence coefficients and modal shapes with the boundary condition, frequency order, the aspect ratio, the non-homogeneous material parameter of laminated metal tubes are also investigated.

导出引用

郭建英1 白艳艳2. 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[J]. 振动与冲击, 2017, 36(21): 107-116

GUO Jian-ying1 BAI Yan-yan 2 . Effects of shear deformation and rotary inertia on vibration of laminated thick-walled short tubes[J]. Journal of Vibration and Shock, 2017, 36(21): 107-116

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