Mechanical Vibration Analysis and Computation

Newland, David; Soom, A.

doi:10.1115/1.2899551

Cited by 90 publications

(80 citation statements)

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“…The technique using the Sturm sequence property is used in the commercial ÿnite element computer program such as ADINA. However, this technique can only be applied to the eigenproblem without the damping matrix such as the cases of the undamped and proportionally damped system [5].…”

Section: Introductionmentioning

confidence: 99%

Technique of checking missed eigenvalues for eigenproblem with damping matrix

Jung

Kim

Lee

2000

Int. J. Numer. Meth. Engng.

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In the case of the non-proportionally damped system such as the soil-structure interaction system, the structural control system and composite structures, the eigenproblem with the damping matrix should be necessarily performed to obtain the exact dynamic response. However, most of the eigenvalue analysis methods such as the subspace iteration method and the Lanczos method may miss some eigenvalues in the required ones. Therefore, the eigenvalue analysis method must include a technique to check the missed eigenvalues to become the practical tools. In the case of the undamped or proportionally damped system the missed eigenvalues can easily be checked by using the well-known Sturm sequence property, while in the case of the nonproportionally damped system a checking technique has not been developed yet. In this paper, a technique of checking the missed eigenvalues for the eigenproblem with the damping matrix is proposed by applying the argument principle. To verify the e ectiveness of the proposed method, two numerical examples are considered.

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Section: Introductionmentioning

confidence: 99%

Technique of checking missed eigenvalues for eigenproblem with damping matrix

Jung

Kim

Lee

2000

Int. J. Numer. Meth. Engng.

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“…(3) being defective is zero [9]. Nonetheless, defective systems were considered in certain situations [31,32,42,[52][53][54]. A numerical example will be provided to indicate how defective systems can be decoupled.…”

Section: Free Vibration With Mixed Eigenvaluesmentioning

confidence: 99%

The decoupling of damped linear systems in free or forced vibration

Morzfeld

Imam

2010

Journal of Sound and Vibration

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a b s t r a c tThe purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the ''classical decoupling problem.'' Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.

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“…Given the order n s for the state space model (2), generate n d = n s /2 random values for the natural frequencies <&, -, n d random values for the damping ratios (,-, and a random full matrix $ e U" dX " d with columns linearly independent (if the natural frequencies are all distinct, the mode shapes are linearly independent [12]). To ensure the generated random starting point lies inside the unit circle, admissible values for natural frequencies go from 0 to Nyquist frequency, and for damping ratios are comprised between 0 and 1.…”

Section: Procedures To Build Random Starting Valuesmentioning

confidence: 99%

An approach to operational modal analysis using the expectation maximization algorithm

Cara

Carpio

Ruiz

et al. 2012

Mechanical Systems and Signal Processing

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This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points.The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

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Mechanical Vibration Analysis and Computation

Abstract: ning graduate students with some previous background in mechanical vibrations, linear algebra, and dynamic systems analysis.

Cited by 90 publications

References 0 publications

Technique of checking missed eigenvalues for eigenproblem with damping matrix

Technique of checking missed eigenvalues for eigenproblem with damping matrix

The decoupling of damped linear systems in free or forced vibration

An approach to operational modal analysis using the expectation maximization algorithm

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