A wavelet-based approach for vibration analysis of framed structures

Mahdavi, Seyed Hossein; Razak, Hashim Abdul

doi:10.1016/j.amc.2013.06.026

Cited by 11 publications

(14 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To simplify this equation, constant quantities are approximated by Chebyshev wavelets in each step. For this purpose, the unity is being expanded by the Chebyshev wavelet as [10,15,16] 1…”

Section: The Proposed Methods For Operation Of Derivativementioning

confidence: 99%

“…This global interval is dividing into the many subdivisions according to the degree of the corresponding wavelet. The idea of discretizing the global domain into the multiple partitions appropriate to the global-scaled-frequency analysis is known as Segmentation Method (SM) [10]. The main purpose of SM is to define several collocation points on the main setting domain (global points of along the global domain) and therefore to convey components of those to the new alternative domain of the analysis (i.e., local points in frequency domain).…”

Section: A Brief Background Of Family Of Chebyshev Operationsmentioning

confidence: 99%

“…Considerably, the effective characteristics of wavelets such as localization properties and multiresolution analysis have been the focus of considerations among researchers. There are several studies available for application of this powerful tool in dynamical problems [10,11] and integral equations [12,13]; however, there are less reports received in the literature for development of iterative methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Mahdavi¹,

Razak

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper presents an efficient iterative method originated from the family of Chebyshev’s operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavelet functions of the first and second kind, initially. Later, Chebyshev’s iterative method is improved by approximation of the first and second derivatives. The analysis of convergence demonstrates that the method is at least fourth-order convergent. The effectiveness of the proposed scheme is numerically and practically evaluated. It is concluded that it requires the less number of iterations and lies on the best performance of the proposed method, especially for highly varying nonlinear problems.

show abstract

“…To simplify this equation, constant quantities are approximated by Chebyshev wavelets in each step. For this purpose, the unity is being expanded by the Chebyshev wavelet as [10,15,16] 1…”

Section: The Proposed Methods For Operation Of Derivativementioning

confidence: 99%

Section: A Brief Background Of Family Of Chebyshev Operationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Mahdavi¹,

Razak

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…where positive integer denotes the value of transition, indicates the time, is degree of Chebyshev polynomials for the first kind, and denotes the considered scale of wavelet. Chebyshev wavelets are formulated with substituting the first kind with relevant weight functions for each scale and transition in (11) as follows [22,25]:…”

Section: Fundamental Of Waveletmentioning

confidence: 99%

“…However, it is reported that stability of results computed by Chebyshev wavelet are independent from initial accelerations. Furthermore, compatibility is being satisfied through the capturing of broad frequency of complex excitations by oscillated shape functions of free-scaled Chebyshev wavelet [25].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

Mahdavi

Razak

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

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.

show abstract