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Vibration Analysis for Circular Arches with Variable Cross-section by using Differential Transformation and Generalized Differential Quadrature  

Shin, Young Jae (안동대학교 기계공학부)
Kwon, Kyung Mun (DAEWOO POWERTRAIN(주))
Yun, Jong Hak (안동대학교 대학원)
Yoo, Yeong Chan (안동대학교 건축공학부)
Lee, Ju Hyung (서울정수기능대학)
Publication Information
Journal of Korean Society of Steel Construction / v.16, no.1, 2004 , pp. 81-89 More about this Journal
Abstract
The vibration analysis of the circular arch as a member of a structure has been an important subject of mechanics due to its various applications to many industrial fields. In particular, circular arches with variable cross section are widely used to optimize the distribution of weight and strength and to satisfy special architectural and functional requirements. The Generalized Differential Quadrature Method (GDQM) and Differential Transformation Method (DTM) were recently proposed by Shu and Zou, respectively. In this study, GDQM and DTM were applied to the vibration analysis of circular arches with variable cross section. The governing equations of motion for circular arches with variable cross section were derived. The concepts of Differential Transformation and Generalized Differential Quadrature were briefly introduced. The non-dimensionless natural frequencies of circular arches with variable cross section were obtained for various boundary conditions. The results obtained using these methods were compared with those of previous works. GDQM and DTM showed fast convergence, accuracy, efficiency, and validity in solving the vibration problem of circular arches with variable cross section.
Keywords
inextensible condition; Differential Transformation Method; Generalized Differential Quadrature Method;
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