Optimum time history analysis of SDOF structures using free scale of Haar wavelet

Mahdavi, Seyed Hossein; Shojaee, Saeed

doi:10.12989/sem.2013.45.1.095

Cited by 11 publications

(12 citation statements)

References 11 publications

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“…Subsequently, integration of 2 is obtained by Haar series with new square coefficient matrix of integration 2 as [16,18]…”

Section: Fundamental Of Waveletmentioning

confidence: 99%

“…Considerably, less computational cost of calculations in advanced time history analysis through the compatible wavelet functions makes distinction of this approach over other numerical methods. For instance, for the purpose of time history analysis, a simple basis function of Haar wavelet was indirectly applied on its own freescaled functions [16]. It is inferred that because of the inherent simple shape function of Haar wavelet accuracy of responses was undesirable even employing large-scaled functions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

Mahdavi

Razak

2015

Mathematical Problems in Engineering

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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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“…Subsequently, integration of 2 is obtained by Haar series with new square coefficient matrix of integration 2 as [16,18]…”

Section: Fundamental Of Waveletmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

Mahdavi

Razak

2015

Mathematical Problems in Engineering

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“…In (11), the subscripts of Ψ 2 and 2 denote the dimension of matrices. Accordingly, the 2 × 2 -dimensional operational matrix for FCW and SCW is derived as…”

Section: Product Matrix Of Integrationmentioning

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%

An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Mahdavi¹,

Razak

2015

Mathematical Problems in Engineering

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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.

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“…Therefore, searching for a simple, fast, and accurate earthquake response analysis method is an important area of research that engineers and scholars have been working towards for many years [6]. Currently, the dynamic response with a time history for a portal frame structure under the action of an earthquake is generally calculated by a finite element software [7,8], such as ANSYS [9] or MIDAS; unfortunately, for the complex civil structure with a large number of degrees of freedom, the computational work load is heavy, which cause long calculation times and low calculation efficiencies.…”

Section: Introductionmentioning

confidence: 99%

Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

Ding

Zhuang

Wang

2014

Advances in Mechanical Engineering

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Portal frame structures are widely used in industrial building design but unfortunately are often damaged during an earthquake. As a result, a study on the seismic response of this type of structure is important to both human safety and future building designs. Traditionally, finite element methods such as the ANSYS and MIDAS have been used as the primary methods of computing the response of such a structure during an earthquake; however, these methods yield low calculation efficiencies. In this paper, the mechanical model of a single-story portal frame structure with two spans is constructed based on the transfer matrix method of multibody system (MS-TMM); both the transfer matrix of the components in the model and the total transfer matrix equation of the structure are derived, and the corresponding MATLAB program is compiled to determine the natural period and seismic response of the structure. The results show that the results based on the MS-TMM are similar to those obtained by ANSYS, but the calculation time of the MS-TMM method is only 1/20 of that of the ANSYS method. Additionally, it is shown that the MS-TMM method greatly increases the calculation efficiency while maintaining accuracy.

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Optimum time history analysis of SDOF structures using free scale of Haar wavelet

Cited by 11 publications

References 11 publications

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

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