Analysis of out of plane bending and torsional vibration of variable cross-section arch based on ANCF

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (15) : 231-237.

LIU Mao, WANG Zhongmin

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Abstract

Based on the absolute node coordinate formulation (ANCF), vibration characteristics of a homogeneous Euler-Bernoulli arch with variable cross-section were studied. Firstly, a homogeneous vibration model considering out of plane bending and torsion was established. In the global inertial coordinate system, it was divided into several arch elements with variable cross-section. The expressions of element’s kinetic energy, strain energy and potential energy of external forces were derived to obtain element’s mass matrix and stiffness matrix, and furthermore the arch’s mass matrix and stiffness matrix were assembled. Secondly, the arch’s bending-torsional vibration differential equation was established by using Lagrange equation. Finally, the first three order natural frequencies of equal cross-section circular arc arch and variable cross-section circular arc arch fixed at two-end were calculated numerically and the corresponding modal shapes were plotted. Effect laws of variable cross-section circular arc arch’s center angle, radius, height-width ratio and uniformly distributed radial load on its vibration characteristics were analyzed. The first three order natural frequencies of equal cross-section and variable cross-section parabolic type non-circular arc arches fixed at two-end were calculated numerically and the corresponding modal shapes were plotted.

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absolute nodal coordinate formulation (ANCF) / non-circular arch / out-of-plane bending and torsion vibration / variable cross-section

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LIU Mao, WANG Zhongmin. Analysis of out of plane bending and torsional vibration of variable cross-section arch based on ANCF[J]. Journal of Vibration and Shock, 2021, 40(15): 231-237

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