In-plane free vibration analysis for arches of variable cross- section and variable curvature

• Main Authors: Lin, Yih-Wenn, 林毅文
• Other Authors: Tseng Yi-Ping
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/86877155622508967057

碩士 === 淡江大學 === 土木工程學系 === 84 === The free vibration analysis for circular arches of uniform cross-section h ave obtained exact solution, but arches of variable curvature and cross sectio n have seldom analytical solution, and multiple-span arches also can not be so lved analytically. This paper adopts dynamic stiffness method in which the tim e dependent displacements are expressed in a form of harmonic and modal displa cements. The partial differential eqution then reduces to ordinary ones. The v ariations of geometric shape and cross section are expressed in a series form. Therefore, the modal displacements can be solved by a series method from the o rdinary differential eqution. Based on the Mindlin arch theory with the effect of axial de- formation, sh ear deformation and rotary inertia, a series method and dynamic stiffness meth od are combined to formulate the element dynamic stiffness. The global dynamic stiffness can be then estab-lished, which relates the modal nodal displacement s to modal nodal loadings. Finally, one can solve the natural frequencies by i ter-ation method. As the number of series terms is sufficient, the proposed me thod can be regarded as analytical solution. In the paper, the free vibration analysis of circular arches, parabolic ar ches and elliptic arches have been accomplished. The convergence study are pre sented for the number of elements, series solution terms and geometry function terms taken in the series . For the par-abolic arches with various boundary co nditions, the effects of rise-to-span ratio and cross-section slender ratio on natural frequencies are also investigated as a reference of practical engineer ing problems.