An Analytical Solution for In-Plane Free Vibration and Stability of Loaded Arches

• Main Authors: Kuo-Yun Nieh, 聶國昀
• Other Authors: Der-Wen Chang
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/92113919863520873397

博士 === 淡江大學 === 土木工程學系 === 92 === Curved structure elements are usually used in civil, mechanical, and aerospace structures, e.g. arch bridge, ring beam, and reinforced rib in thin shell structures. The main purpose of this thesis is to apply a dynamic stiffness method associated with a series solution to analyze the free vibration and stability of an in-plane loaded arch, including the effects of static deformation, rotatory inertia, and shear deformation. The first known equations governing vibrations of preloaded arches are derived according to a variational principle for dynamic problems concerning an elastic body under equilibrium initial stresses, and considering the effects of the extensibility of the arch centerline, static deformation, rotatory inertia, and shear deformation. The governing equations, which are differential equations with variable coefficients, are solved for arches statically preloaded with a uniformly distributed vertical loading, by obtaining a static solution and an analytical dynamic solution from series solutions along with dynamic stiffness matrixes. Convergence to accurate results is obtained by increasing the number of elements or by increasing both the number of terms in the series solution and the number of terms in the Taylor expansion of the variable coefficients. The accuracy of the proposed solution is somewhat verified with the excellent agreement between the present results and the published ones for the cases neglecting shear deformation and static deformation. Graphs of non-dimensional frequencies and buckling loads are presented for preloaded arches with different geometrical parameters. They show the effects of opening angle and thickness-to-radius ratio on vibration frequencies and buckling loads. The effects of static deformation on vibration frequencies are also investigated.