Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis
Open Access
- 14 December 2015
- journal article
- research article
- Published by Hindawi Limited in Mathematical Problems in Engineering
- Vol. 2015, 1-15
- https://doi.org/10.1155/2015/541276
Abstract
It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: () the boundary splitting and () the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.
Keywords
Funding Information
- National Research Foundation of Korea (NRF-2015R1A2A2A01003653)
This publication has 18 references indexed in Scilit:
- Frequency-dependent vibration analysis of symmetric cross-ply laminated plate of Levy-type by spectral element and finite strip proceduresApplied Mathematical Modelling, 2013
- Free and transient vibration analysis of an un-symmetric cross-ply laminated plate by spectral finite elementsActa Mechanica, 2012
- Dynamic stiffness elements and their applications for plates using first order shear deformation theoryComputers & Structures, 2011
- Wave propagation in plate structures for crack detectionFinite Elements in Analysis and Design, 2004
- Spectral-Element Method for Levy-Type Plates Subject to Dynamic LoadsJournal of Engineering Mechanics, 1999
- CALCULATION OF WAVE PROPAGATION IN RIB-STIFFENED PLATE STRUCTURESJournal of Sound and Vibration, 1996
- Dynamic stiffness analysis of laminated composite platesThin-Walled Structures, 1996
- Analysis of orthotropic plate structures by the direct-dynamic stiffness methodMechanics Research Communications, 1995
- Application of the dynamic stiffness method to the free and forced vibrations of aircraft panelsJournal of Sound and Vibration, 1989
- A spectral element method for fluid dynamics: Laminar flow in a channel expansionJournal of Computational Physics, 1984