Indirect Time Integration Scheme for Dynamic Analysis of Space Structures Using Wavelet Functions

Mahdavi, Seyed Hossein; Razak, Hashim Abdul

doi:10.1061/(asce)em.1943-7889.0000914

Cited by 8 publications

(10 citation statements)

References 21 publications

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“…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%

“…The families of orthogonal Chebyshev polynomials are classified into two main types. The first kind of Chebyshev polynomials ( ) is obtained by a recursive formulation as follows [5,15,16]:…”

Section: The First Kind Of Chebyshev Waveletmentioning

confidence: 99%

“…where the orthogonality of ( ) is satisfied with respect to the weight function of ( ) = 1/ √ 1 − 2 on | | < 1. Subsequently, Chebyshev wavelets of the first kind (FCW) are constructed by substituting ( ) in (1) as [14,16] , ( )…”

Section: The First Kind Of Chebyshev Waveletmentioning

confidence: 99%

See 2 more Smart Citations

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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“…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: The First Kind Of Chebyshev Waveletmentioning

confidence: 99%

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An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Mahdavi¹,

Razak

2015

Mathematical Problems in Engineering

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“…'Indirect' integration procedures require the reformulation of Eq. ( 26) into an equivalent time-space system which is instead solved [42,122].…”

Section: Numerical Integrationmentioning

confidence: 99%

Beams on elastic foundations – A review of railway applications and solutions

Lamprea-Pineda

Connolly

Hussein

2022

Transportation Geotechnics

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“…Gopikrishna and Shrikhande (2011) presented a hierarchical finite element formulation for the solution of structural dynamic problems. Mahdavi and Razak (2015) used Haar wavelet and Chebyshev wavelet for the dynamic analysis of space structures. In the above methods, it is considered that a function or signal is represented by wavelets basis; however, few mentioned references refer to the number of basis function used, and the selection is usually subjective.…”

Section: Introductionmentioning

confidence: 99%

Wavelet-Galerkin method for reconstruction of structural dynamic responses

Lai

2016

Advances in Structural Engineering

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In this article, the wavelet-Galerkin method is adopted for calculating structural dynamic responses under the framework of multiresolution analysis. At first, the second-order differential equation of motion is transformed into wavelet domain through function expansion with scaling function at the chosen resolution level. The number of basis function is uniquely determined, and the corresponding coefficients are approximated by numerical quadrature method. And then the two-term connection coefficients are derived and computed at various scales. After this, the dynamic responses of the system with single degree of freedom subjected to sinusoidal excitation are obtained and validated. Subsequently, the proposed method is extended to multidegree-of-freedom systems based on mode-superposition method. Finally, the parametric study is performed, and the simulation results show that the identified dynamic responses match the true responses very well with appropriate choice of the resolution level and the wavelet order.

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Indirect Time Integration Scheme for Dynamic Analysis of Space Structures Using Wavelet Functions

Cited by 8 publications

References 21 publications

An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

An Efficient Iterative Scheme Using Family of Chebyshev’s Operations

Beams on elastic foundations – A review of railway applications and solutions

Wavelet-Galerkin method for reconstruction of structural dynamic responses

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