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

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (21) : 107-116.

GUO Jian-ying1 BAI Yan-yan 2

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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.

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laminated metal thick-walled short tubes / shear deformation / rotary inertia / frequency influence coefficient / mode shape

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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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