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A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis

DSpace at IIT Bombay

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Title A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis
 
Creator SONEKAR, P
MITRA, M
 
Subject finite-element-analysis
approximate method
supported beams
vibration
homogenization
periodic structures
wave propagation
daubechies wavelet
finite element
 
Description In this paper, a wavelet-based method is developed for wave-propagation analysis of a generic multi-coupled one-dimensional periodic structure (PS). The formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite-element (FE) or other numerical methods. Here, unlike its conventional definition, the dynamic stiffness matrix is obtained in the wavelet domain through a Daubechies wavelet transform. The proposed numerical scheme enables both time-and frequency-domain analysis of PSs under arbitrary loading conditions. This is in contrast to the existing Fourier-transform-based analysis that is restricted to frequency-domain study. Here, the dispersion characteristics of PSs, especially the band-gap features, are studied. In addition, the method is implemented to simulate time-domain wave response under impulse loading conditions. The two examples considered are periodically simply supported beam and periodic frame structures. In all cases, the responses obtained using the present periodic formulation are compared with the response simulated using the FE model without the periodicity assumption, and they show an exact match. This validates the accuracy of the periodic assumption to obtain the time- and frequency-domain wave responses up to a high-frequency range. Apart from this, the proposed method drastically reduces the computational cost and can be implemented for homogenization of PSs.
 
Publisher ROYAL SOC
 
Date 2011-08-27T11:29:33Z
2011-12-26T12:57:54Z
2011-12-27T05:45:59Z
2011-08-27T11:29:33Z
2011-12-26T12:57:54Z
2011-12-27T05:45:59Z
2010
 
Type Article
 
Identifier PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 466(2113), 263-281
1364-5021
http://dx.doi.org/10.1098/rspa.2009.0369
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11652
http://hdl.handle.net/10054/11652
 
Language en