Quasi-static data recovery for dynamic analyses of structural systems

Gu, Jianmin; Ma, Zheng-Dong; Hulbert, Gregory M.

doi:10.1016/s0168-874x(01)00070-1

Cited by 7 publications

(10 citation statements)

References 6 publications

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“…However, we found that consideration of multiple center frequencies (more than one for several frequency domains) is possible; a similar observation was already made . In , the Ritz vectors are generated with multiple center frequencies where in , the bases of the mode superposition method are generated with multiple center frequencies. Therefore, the alternative QSRV method can be modified as follows:

φ_{s MathClass-punc, 1} MathClass-rel\equiv {(bold-italicK (ω_{c MathClass-punc, s}) MathClass-bin- ω_{c MathClass-punc, s}^{2} bold-italicM (ω_{c MathClass-punc, s}))}^{MathClass-bin- 1} bold F (ω_{c MathClass-punc, s})

φ_{s MathClass-punc, j} MathClass-rel\equiv {(bold-italicK (ω_{c MathClass-punc, s}) MathClass-bin- ω_{c MathClass-punc, s}^{2} bold-italicM (ω_{c MathClass-punc, s}))}^{MathClass-bin- 1} (bold-italicM (ω_{c MathClass-punc, s}) φ_{s MathClass-punc, j MathClass-bin- 1})

ω_{c MathClass-punc, s} (MathClass-rel= \frac{ω_{s MathClass-punc, start} MathClass-bin+ ω_{s MathClass-punc, end}}{2}) MathClass-punc, s MathClass-rel= 1 MathClass-punc, MathClass-punc. MathClass-punc. MathClass-punc. MathClass-...

…”

Section: Development Of a Multifrequency Quasi‐static Ritz Vector Methodssupporting

confidence: 73%

“…This research develops a so‐called multifrequency quasi‐static Ritz vector (MQSRV) method applicable to frequency‐dependent acoustic systems that extends the frameworks of existing RV and QSRV methods that are applicable to general engineering problems . Frequency response analysis is a basic tool for both diagnosing processes of mechanical systems and design processes.…”

Section: Introductionmentioning

confidence: 99%

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Toward a multifrequency quasi‐static Ritz vector method for frequency‐dependent acoustic system application

Yoon

2011

Numerical Meth Engineering

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SUMMARYComputational issues concerning the calculation of acoustic responses of a complex finite element (FE) model for various noise and vibration inputs have become prevalent. Such a model requires a significant amount of computation time because of repeated inversions of dynamic stiffness matrices. Thus, even stateof-the-art computer hardware and software often face limitations where a model order reduction (MOR) scheme can help. The established MOR schemes such as Ritz vector or quasi-static Ritz vector methods are efficient for general engineering systems, but these MOR methods become inaccurate for frequency response analyses in some acoustic systems with frequency-dependent mass and stiffness matrices and force vectors (hereinafter frequency-dependent acoustic systems). To cope with the inaccurate prediction by these methods for frequency-dependent acoustic systems, this research presents and applies the multifrequency quasi-static Ritz vector method. Unlike the Ritz vector or quasi-static Ritz vector methods, the present multifrequency quasi-static Ritz vector method employs direct Krylov subspace bases without an orthonormal procedure at multiple center frequencies. In comparison with the existing MOR scheme, a significant gain in computational efficiency is achieved, as well as enhanced accuracy. A comparison of these methods based on criteria such as efficiency, accuracy, and reliability was also conducted.

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φ_{s MathClass-punc, 1} MathClass-rel\equiv {(bold-italicK (ω_{c MathClass-punc, s}) MathClass-bin- ω_{c MathClass-punc, s}^{2} bold-italicM (ω_{c MathClass-punc, s}))}^{MathClass-bin- 1} bold F (ω_{c MathClass-punc, s})

φ_{s MathClass-punc, j} MathClass-rel\equiv {(bold-italicK (ω_{c MathClass-punc, s}) MathClass-bin- ω_{c MathClass-punc, s}^{2} bold-italicM (ω_{c MathClass-punc, s}))}^{MathClass-bin- 1} (bold-italicM (ω_{c MathClass-punc, s}) φ_{s MathClass-punc, j MathClass-bin- 1})

ω_{c MathClass-punc, s} (MathClass-rel= \frac{ω_{s MathClass-punc, start} MathClass-bin+ ω_{s MathClass-punc, end}}{2}) MathClass-punc, s MathClass-rel= 1 MathClass-punc, MathClass-punc. MathClass-punc. MathClass-punc. MathClass-...

…”

Section: Development Of a Multifrequency Quasi‐static Ritz Vector Methodssupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Toward a multifrequency quasi‐static Ritz vector method for frequency‐dependent acoustic system application

Yoon

2011

Numerical Meth Engineering

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“…The third class of methods is the Ritz vector methods (e.g., see Gu, 2000;Gu et al, 2000;Joo et al, 1989;Lanczos, 1950;Leger, 1988Leger, , 1989Leger et al, 1986;Clough, 1984, 1985;Wilson and Bayo, 1986;Wilson et al, 1982) developed to eliminate the need to compute costly eigenvalue problems and to improve the accuracy in cases where eigenvectors are not the best choice; these methods can be regarded as a generalized approach replacing the eigenvectors by more generally defined Ritz vectors. Gu et al (2001) used the data recovery techniques in dynamic analyses to recover the physical response from the modal response obtained by using the mode-displacement method and they developed the technique upon a QSC technique that is applicable for any banded frequency of interest. Cunedioglu et al (2006) investigated some popular model order reduction and superelement techniques in frequency and time domains.…”

Section: Introductionmentioning

confidence: 99%

Analyses of Laminated Cantilever Composite Beams by Model Order Reduction Techniques

Cunedioĝlu

2011

Mechanics Based Design of Structures and Machines

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In this study, a laminated cantilever composite beam is studied in frequency domain by using some popular model order reduction techniques. In the analyses, component mode synthesis (CMS) and quasi-static mode synthesis (QSM1, QSM2) methods are applied to semi-discrete finite element equations to obtain reduced order models for structural analyses. The performance of the model order reduction methods is compared. In addition, fiber orientation, stacking sequence, ply thickness, and its location effects on the number of modes of the methods and on the natural frequencies are investigated. Results reveal that the performance of the QSM2 method is found to be better than the others. It is observed that the fiber orientation, stacking sequence, ply thickness, and its location parameters affect the natural frequency values and the number of modes of the methods.

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“…The third class of methods is the Ritz vector methods (e.g., see [1,[19][20][21][22][23][24][25][26][27][28]10]) developed to eliminate the need to compute costly eigenvalue problems and to improve the accuracy in cases where eigenvectors are not the best choice; these methods can be regarded as a generalized approach replacing the eigenvectors by more generally defined Ritz vectors. Gu et al in [29] used the data recovery techniques in dynamic analyses to recover the physical response from the modal response obtained by using the mode-displacement method and they developed the technique upon a quasi-static compensation technique that is applicable for any banded frequency of interest. The forth class of methods studied extensively in this paper is component mode synthesis (CMS) methods [1,16,17], that combine the first three classes of methods.…”

Section: Introductionmentioning

confidence: 99%

“…The forth class of methods studied extensively in this paper is component mode synthesis (CMS) methods [1,16,17], that combine the first three classes of methods. Based on CMS methods, quasi-static mode synthesis (QSM) methods are developed having improved performance in [16][17][18][19]1,29].…”

Section: Introductionmentioning

confidence: 99%