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Parametric instability of conical shells by the Generalized Differential Quadrature method
Author(s) -
Ng T. Y.,
Hua Li,
Lam K. Y.,
Loy C. T.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990228)44:6<819::aid-nme528>3.0.co;2-0
Subject(s) - instability , quadrature (astronomy) , conical surface , isotropy , mathematical analysis , mathematics , nyström method , parametric statistics , boundary value problem , inertia , geometry , mechanics , classical mechanics , physics , statistics , quantum mechanics , optics
The parametric instability of truncated conical shells of uniform thickness under periodic edge loading is examined. The material considered is homogeneous and isotropic. This is the first instance that the Generalized Differential Quadrature (GDQ) method is used to study the effects of boundary conditions on the parametric instability in shells. The formulation is based on the dynamic version of Love's first approximation for thin shells. A formulation is presented which incorporates the GDQ method in the assumed‐mode method to reduce the partial differential equations of motion to a system of coupled Mathieu–Hill equations. The principal instability regions are then determined by Bolotin's method. Assumptions made in this study are the neglect of transverse shear deformation, rotary inertia as well as bending deformations before instability. Copyright © 1999 John Wiley & Sons, Ltd.