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
Related Articles
- EP ID EP373055
- DOI 10.33108/visnyk_tntu2018.02.060
- Views 71
- Downloads 0
Autonomous power supply system for outdoor illumination of residential areas in the territory of Ukraine
The methodology and the calculation of the autonomous power supply system for outdoor illumination using solar batteries of KV 250M type, Li-ion batteries of LP48100ES type and the control system consisting of the MPPT c...
Structure and corrosion resistance of composite materials Cu-Mo-Zr-Y obtained by electron-beam evaporation-condencation
This research studied the structure of composite materials Cu-Mo-Zr-Y obtained by electron-beam method of evaporation-condensation. It was found that the structure is related to the chemical composition of condensate. Wh...
Contact problem on the wear of the elastic half-plane by canonical form stamps
The problems of contact interaction of the canonical form stamps (cylindrical, elliptical, hyperbolic) with the elastic half-plane taking into account the wastage of material, are solved. The integral equation, based on...
The effect of initial deformations of the thick plate on its contact interaction with the ring punch
The calculation of the structural elements and mechanisms strength is one of the most important stages while their developing. Initial deformations are almost always available in the structural elements and machine parts...
Wave propagation in the pre-deformed compressible elastic layer interacting with a layer of viscous compressible liquid
Based on three-dimensional equations of linearized elasticity theory for finite deformations of elastic body and three-dimensional linearized Navier-Stokes equations for the liquid medium, the problem of propagation of a...