Spline collocation method for free vibration analysis of laminated shallow shells
Journal Title: Вісник Тернопільського національного технічного університету - Year 2018, Vol 90, Issue 2
Abstract
The presented study deals with free vibration of cross-ply symmetrically laminated composite doubly-curved panels with constant thickness. Based on the first-order shear deformation theory (FSDT) the equations of motion are derived by applying the Hamilton’s principle. Spline function approximation technique, which includes B-splines of the third order, is used to reduce two-dimensional system of coupled differential equations in terms of displacement and rotational functions to one-dimensional. A generalized eigenvalue problem is obtained by applying a point collocation method with suitable boundary conditions. The vector-matrix form of the governing equations with different boundary conditions, from which values of a frequency parameter is obtained, is presented. These systems of ordinary differential equations are solved using the Godunov's discrete orthogonalization method. The effects of curvature ratio and thickness-to-length ratio on the fundamental natural frequencies of composite doubly-curved panels with all sides simply supported are investigated. In order to verify the accuracy of the employed method the frequency parameters are evaluated in comparison with the previous paper available in the literature. Good agreement with other available data demonstrates the capability and reliability of the spline collocation method and the adopted composite doubly-curved shell model used.
Authors and Affiliations
Oleg Pavlenko
Keywords
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- EP ID EP373055
- DOI 10.33108/visnyk_tntu2018.02.060
- Views 69
- Downloads 0
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