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Free vibration analysis of symmetrically laminated fully clamped skew plates using extended Kantorovich method

Fallah, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.4028/www.scientific.net/KEM.471-472.739
  3. Publisher: 2011
  4. Abstract:
  5. In this paper, free vibration analysis of thin symmetrically laminated skew plates with fully clamped edges is investigated. The governing differential equation for skew plate which is a fourth order partial differential equation (PDE) is obtained by transforming the differential equation in Cartesian coordinates into skew coordinates. Based on the multi-term extended Kantorovich method (MTEKM) an efficient and accurate approximate closed-form solution is presented for the governing PDE. Application of the MTEKM reduces the governing PDE to a dual set of ordinary differential equations. These sets of equations are then solved with infinite power series solution, in an iterative manner until convergence was achieved. Results of this study show the fast rate of convergence of the MTEKM. Usually two or three iterations are enough to obtain reasonably accurate results. The frequency parameters of laminated composite plates are obtained for different skew angles and lay-up configuration for different composites laminates skew plates. Comparisons have been made with the available results in the literature which show the accuracy and efficiency of the method
  6. Keywords:
  7. Composite skew plate ; Multi-term extended Kantorovich method ; Cartesian coordinate ; Clamped edge ; Closed form solutions ; Extended Kantorovich method ; Fast rate ; Fourth order partial differential equations ; Free vibration analysis ; Frequency parameters ; Governing differential equations ; Laminated composite plates ; Power series solutions ; Skew angles ; Skew plates ; Approximation theory ; Convergence of numerical methods ; Laminated composites ; Laminating ; Ordinary differential equations ; Partial differential equations ; Plates (structural components) ; Vibration analysis
  8. Source: Key Engineering Materials, 22 March 2011 through 24 March 2011, Kuala Lumpur ; Volume 471-472 , 2011 , Pages 739-744 ; 10139826 (ISSN) ; 9783037850596 (ISBN)
  9. URL: http://www.scientific.net/KEM.471-472.739