A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

• Published in: Mathematical problems in engineering Vol. 2015; no. 2015; pp. 1 - 10
• Main Authors: Mahdavi, Seyed Hossein, Abdul Razak, Hashim
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015; John Wiley & Sons, Inc
• Subjects: Accuracy; Algorithms; Basis functions; Chebyshev approximation; Colleges & universities; Comparative studies; Computation; Continuity (mathematics); Dynamic structural analysis; Dynamics; Finite element analysis; Mathematical models; Mathematical problems; Methods; Nonlinear dynamics; Ordinary differential equations; Partial differential equations; Wavelet; Wavelet analysis; Wavelet transforms
• ISSN: 1024-123X; 1026-7077; 1563-5147; 1563-5147
• DOI: 10.1155/2015/956793

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.