A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation

Anh, Nguyen Dong; Zakovorotny, V. L.; Hieu, Nguyen N.; Diep, D. V.

doi:10.1007/s00707-012-0738-5

Cited by 21 publications

(19 citation statements)

References 27 publications

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“…The dual criterion of stochastic linearization method appears from an idea that the original nonlinear system can be replaced by an equivalent linearization system, and then this equivalent system is replaced by another nonlinear system that belongs to the same class of the original nonlinear system. Some obtained results using the dual criterion are presented in works of Anh et al [27,28] for single-and multi-degree-of-freedom systems subjected to random excitations. Naturally, the dual criterion of stochastic linearization needs to be developed in investigating continuous systems under random excitation.…”

Section: A Dual Criterion For Modal Equations Of Beammentioning

confidence: 99%

“…, M) are non-dimensional linearization coefficients determined from a specified criterion of stochastic linearization. We here utilize the dual criterion [27,28] for determining coefficients k eq,m (m = 1, 2, . .…”

Section: A Dual Criterion For Modal Equations Of Beammentioning

confidence: 99%

“…It is noted that, to calculate higher-order moments in Eqs. (28) and (29), we employ the following generalized formula expressed in terms of second-order moments of Gaussian random processes with zero-mean [30]…”

Section: Equivalent Linearization Coefficientsmentioning

confidence: 99%

“…Using Eqs. (43) and (28) for M = 1, we get the following single-mode approximate mean-square response E w 2 1 depending upon the nonlinear parameter 1/R in the following form…”

Section: The Case Of Single-modementioning

confidence: 99%

“…The authors showed that the accuracy of the mean-square response obtained by the dual criterion is significantly improved when the nonlinearity is increasing. This dual approach is then extended to cases of multi-degree-of-freedom systems [28].…”

Section: Introductionmentioning

confidence: 99%

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Vibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearizationVibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearization

2016

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In this paper responses of beams subjected to random loading are analyzed by the dual approach of the equivalent linearization method. The external random loading is assumed to be a space-wise and time-wise white noise in which the exact solutions of the modal equations can be found. A system of nonlinear algebraic equations for linearization coefficients of the modal linearized system is obtained in a closed form and is solved by the fixed-point iteration method. Results obtained from the proposed dual criterion are compared with the exact solution and those obtained from other approaches including energy method, and conventional linearization method. It is observed that the solution obtained by the dual criterion is in good agreement with the exact solution, especially, in the case of strong nonlinearity of beam.

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Section: A Dual Criterion For Modal Equations Of Beammentioning

confidence: 99%

Section: A Dual Criterion For Modal Equations Of Beammentioning

confidence: 99%

Section: Equivalent Linearization Coefficientsmentioning

confidence: 99%

“…Using Eqs. (43) and (28) for M = 1, we get the following single-mode approximate mean-square response E w 2 1 depending upon the nonlinear parameter 1/R in the following form…”

Section: The Case Of Single-modementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearizationVibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearization

2016

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Identification of weak nonlinearities in MDOF systems based on reconstructed constant response tests

2019

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A novel strategy to characterize and identify structural nonlinearities in MDOF systems based on reconstructing constant response tests from constant excitation tests is developed in this paper. Constant displacement frequency response functions (FRFs) can be measured by a stepped sine test where the displacement is controlled at every frequency of interest. In these FRFs the nonlinear restoring force is effectively linearized and natural frequencies can be estimated by linear modal analysis. Using a series of constant displacement tests, the relationship of equivalent stiffness versus displacement can be established by curve fitting and hence the nonlinear stiffness characterized. This paper proposes a method to reconstruct the constant displacement FRFs from stepped sine tests with constant excitation; this avoids the requirement to control either the response or force amplitude, leads to a faster and more stable testing programme. Similarly, damping nonlinearities in structures can be characterized and identified by constant velocity tests reconstructed in a similar way. This approach of FRF reconstruction is mathematically simple and suitable for structures with weak nonlinearities. The method is demonstrated on a framed structure with unknown weak nonlinearities, and the nonlinear stiffness and damping parameters of the structure are identified and validated. The results demonstrate the feasibility and effectiveness of the approach, and also show the potential for practical applications in engineering.

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Improving the accuracy of SOD for modal parameters estimation of damped systems

Rezaee

Yam

2014

Acta Mech

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A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation

Cited by 21 publications

References 27 publications

Vibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearizationVibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearization

Vibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearizationVibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearization

Identification of weak nonlinearities in MDOF systems based on reconstructed constant response tests

Improving the accuracy of SOD for modal parameters estimation of damped systems

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