Vibration analysis of a circular arch with variable cross-section using differential transformation and generalized differential quadrature

• Published in: Journal of sound and vibration Vol. 309; no. 1; pp. 9 - 19
• Main Authors: Shin, Young-Jae, Kwon, Kyunng-Mun, Yun, Jong-Hak
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 08.01.2008; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Natural frequency; Curved beam; Quadrature; Variable section; Vibration; Equation of motion; Circular arch; Differential method; Infinitesimal transformation; Modeling; Structural analysis
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2006.08.020

Vibration analysis of circular arches is an important subject in mechanics due to its various applications. In particular, circular arches with variable cross-section have been widely used to satisfy modern architectural and structural requirements. Recently, the generalized differential quadrature method (GDQM) and differential transformation method (DTM) were proposed by Shu and Zhou, respectively. In this study, GDQM and DTM are applied to vibration analysis of circular arches with variable cross-section. The governing equation of motion is derived and the non-dimensional natural frequencies are obtained for various boundary conditions. The concepts of differential transformation and generalized differential quadrature are briefly introduced. The results obtained by these methods are compared with previously published works. GDQM and DTM showed fast convergence, accuracy and validity in solving the vibration problem for circular arches with variable cross-sections.