The Random Response of In-Plane Arch of Variable Curvature Subjected to Mulitple Excitation

• Main Authors: Lin, Chia Jung, 林佳蓉
• Other Authors: Tseng Yi Ping
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/96067806958544815160

碩士 === 淡江大學 === 土木工程學系 === 84 === Curved structural elements are usually used in civil , mechanical , and aerospace structures , e.q. arch bridge , ring beam , and reinforced rib in thin shell structures . In general , there are analytical solutions for circular arch ( of constant curvature) . But the arch of variable curvature can not be solved analytically . The main purpose of this thesis is to propoR%璔 dynamic stiffness method associated with a series solution to study the free vibration , transient and random analyses of in-plane arch of variable curvatures,including the effects of rotatary inertic and shear deformation .Firstly , the geometric coefficients are determined for the arch by using Taylor's expansion . Assuming the series form of displacement solution ,the series coefficients can be obtained through the governing equation . In free vibration analysis , the natural frequencies are calculated by using an iteration method in frequency domain . In transient and base excitation analysis , the dynamic stiffness is a function of s-domain through the Laplace transformation of the governing equations . After the solution in s-domain is solved , an accurate time history of displacements and internal forces can be obtained by the Laplace inverse technique . In random response analysis , the statisticial conception is used to obtain the auto-spectrum and variance of structure subjected to correlated multiple excitation .Since the structure is decomposed into several elements , the number of adopted series terms is reduced tremendously to reach accurate results . Besides , the Laplace inversion technique is used in the transient analysis and random response analysis , very accurate response can be then evaluated , which is impossible for the modal super- position method. The vibration characteristics , transient and random response of circular , parabolic , and ellipitic archs are further compared in order to obtain some valuable suggestion for engineering design purposes.