A comparative study on optimal structural dynamics using wavelet functions

Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational...

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Main Authors: Mahdavi, S.H., Razak, H.A.
Format: Article
Language:English
Published: 2015
Subjects:
Online Access:http://eprints.um.edu.my/13743/1/A_Comparative_Study_on_Optimal_Structural_Dynamics_Using.pdf
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author Mahdavi, S.H.
Razak, H.A.
author_facet Mahdavi, S.H.
Razak, H.A.
author_sort Mahdavi, S.H.
collection UM
description Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational technique is developed by using free scale of simple Haar wavelet, initially. Later, complex and continuous Chebyshev wavelet basis functions are presented to improve the time history analysis of structures. Free-scaled Chebyshev coefficient matrix and operation of integration are derived to directly approximate displacements of the corresponding system. In addition, stability of responses has been investigated for the proposed algorithm of discrete Haar wavelet compared against continuous Chebyshev wavelet. To demonstrate the validity of the wavelet-based algorithms, aforesaid schemes have been extended to the linear and nonlinear structural dynamics. The effectiveness of free-scaled Chebyshev wavelet has been compared with simple Haar wavelet and two common integration methods. It is deduced that either indirect method proposed for discrete Haar wavelet or direct approach for continuous Chebyshev wavelet is unconditionally stable. Finally, it is concluded that numerical solution is highly benefited by the least computation time involved and high accuracy of response, particularly using low scale of complex Chebyshev wavelet.
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spelling um.eprints-137432015-07-22T01:44:31Z http://eprints.um.edu.my/13743/ A comparative study on optimal structural dynamics using wavelet functions Mahdavi, S.H. Razak, H.A. T Technology (General) TA Engineering (General). Civil engineering (General) Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational technique is developed by using free scale of simple Haar wavelet, initially. Later, complex and continuous Chebyshev wavelet basis functions are presented to improve the time history analysis of structures. Free-scaled Chebyshev coefficient matrix and operation of integration are derived to directly approximate displacements of the corresponding system. In addition, stability of responses has been investigated for the proposed algorithm of discrete Haar wavelet compared against continuous Chebyshev wavelet. To demonstrate the validity of the wavelet-based algorithms, aforesaid schemes have been extended to the linear and nonlinear structural dynamics. The effectiveness of free-scaled Chebyshev wavelet has been compared with simple Haar wavelet and two common integration methods. It is deduced that either indirect method proposed for discrete Haar wavelet or direct approach for continuous Chebyshev wavelet is unconditionally stable. Finally, it is concluded that numerical solution is highly benefited by the least computation time involved and high accuracy of response, particularly using low scale of complex Chebyshev wavelet. 2015 Article PeerReviewed application/pdf en http://eprints.um.edu.my/13743/1/A_Comparative_Study_on_Optimal_Structural_Dynamics_Using.pdf Mahdavi, S.H. and Razak, H.A. (2015) A comparative study on optimal structural dynamics using wavelet functions. Mathematical Problems in Engineering. p. 10. ISSN 1024-123X, DOI https://doi.org/10.1155/2015/956793 <https://doi.org/10.1155/2015/956793>. http://www.hindawi.com/journals/mpe/2015/956793/ Doi 10.1155/2015/956793
spellingShingle T Technology (General)
TA Engineering (General). Civil engineering (General)
Mahdavi, S.H.
Razak, H.A.
A comparative study on optimal structural dynamics using wavelet functions
title A comparative study on optimal structural dynamics using wavelet functions
title_full A comparative study on optimal structural dynamics using wavelet functions
title_fullStr A comparative study on optimal structural dynamics using wavelet functions
title_full_unstemmed A comparative study on optimal structural dynamics using wavelet functions
title_short A comparative study on optimal structural dynamics using wavelet functions
title_sort comparative study on optimal structural dynamics using wavelet functions
topic T Technology (General)
TA Engineering (General). Civil engineering (General)
url http://eprints.um.edu.my/13743/1/A_Comparative_Study_on_Optimal_Structural_Dynamics_Using.pdf
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