Out-of-plane free vibration analysis of non-hinged arches with Ⅰ-variable cross-section

FENG Canliang; HU Zhenzhi; LU Hanwen; CHEN Zhou

Abstract：For the Ⅰ-shaped thin-walled variable cross-section with the height of the arch section varying according to the exponential function with the natural constant e as the base,by assuming the approximate mode shape that satisfies the clamped boundary conditions,the kinetic energy and elastic potential energy of the system were constructed based on the variable cross-section characteristics and bending-torsion deformation analysis of the arch.The out-of-plane bending-torsion free vibration differential equation of the hingeless arch with Ⅰ-shaped variable cross-section was derived using the Hamiltonian variational principle,and the analytical solution of the out-of-plane natural frequency was given.The analytical solution was compared with the ANSYS finite element modal analysis results to verify the correctness of the analytical solution.Based on this,the paper analyzes the effects of parameters such as the variation coefficient of the cross-section β(ratio of the height of the arch foot to that of the arch top),central angle 2Θ,and out-of-plane slenderness ratio S/ry on the natural frequencies.Results show that the fundamental frequency of out-of-plane vibration corresponds to a single-wave symmetric vibration dominated by lateral displacement,whose frequency ωu decreases with increases in the central angle and out-of-plane slenderness ratio.Another type is a symmetric vibration dominated by torsional angle,whose frequency ωθ increases with the central angle but decreases with the out-of-plane slenderness ratio.Natural frequencies generally increase with the increase of the cross-section variation parameter β.Therefore,designing the arch with larger cross-sectional heights at the springings compared to the crown can enhance the dynamic performance of the arch.