Vol. 3, No. 5, 2008

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ISSN: 1559-3959
Spline-based investigation of natural vibrations of orthotropic rectangular plates of variable thickness within classical and refined theories

Yaroslav M. Grigorenko, Alexander Ya. Grigorenko and Tatyana L. Efimova

Vol. 3 (2008), No. 5, 929–952
Abstract

A spline-collocation approach is proposed for studying the natural vibrations of orthotropic rectangular plates of variable thickness. The approach is based on the spline-approximation method and the method of discrete orthogonalization coupled with the step-by-step search method. The study is carried out within the framework of the classical and refined theories of plates. The dynamic response of the plates is studied depending on the variation of the plate thickness, the mechanical parameters, and the type of boundary conditions.

Keywords
Kirchhoff's theory, Mindlin's theory, anisotropic rectangular plates, spline approximations, natural frequencies, natural vibration modes
Milestones
Received: 18 February 2008
Revised: 99 2999
Accepted: 20 May 2008
Published: 1 July 2008
Authors
Yaroslav M. Grigorenko
S. P. Timoshenko Institute of Mechanics of NAS of Ukraine
Nesterov Street 3
Kiev 03057
Ukraine
Alexander Ya. Grigorenko
S. P. Timoshenko Institute of Mechanics of NAS of Ukraine
Nesterov Street 3
Kiev 03057
Ukraine
Tatyana L. Efimova
S. P. Timoshenko Institute of Mechanics of NAS of Ukraine
Nesterov Street 3
Kiev 03057
Ukraine