Comment on "Reduction of Structural Frequency Equations"

Flax, Alexander H.

doi:10.2514/3.49797

Cited by 23 publications

(3 citation statements)

References 5 publications

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“…Over the years, a number of researchers have proposed improvements or alterations to the Guyan reduction, including Downs (1980), Flax (1975), Johnson et al (1980), Kidder (1973, Kim (1985), Kuhar and Stahle (1974), Leung (1978), Miller ( 1980), Paz ( 1983Paz ( , 1984, and Suarez and Singh (1992). In these works, discussed in more detail by Young (1994), the transformation connecting the master and secondary coordinates has not been improved on very much, and Guyan reduction is still the industry standard for doing direct model reduction.…”

Section: Background and Related Researchmentioning

confidence: 99%

On the Reduction of Nonlinear Structural Dynamics Models

Burton

Rhee

2000

Journal of Vibration and Control

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The authors analyze the problem of model reduction in structural dynamics for unforced conser vative systems having static, cubic nonlinearities. The framework is the classical one of partitioning the coordinate vector into subsets of so-called master and slave coordinates, with the reduced dynamic model to contain only the masters. The objective is to compare the quality of two model-reduction methods: (1) a re duction based on the leading order calculation of the nonlinear master-slave state transformation defining the manifold containing the modes to be represented in the reduced model ("NNM-based reduction") and (2) a "linear-based reduction" utilizing the exact for the linear case master-slave state transformation; the linear- based reduction is equivalent to a modal analysis, but the reduced model is defined in terms of the physical, rather than the modal, coordinates. For the simple, low-order oscillator systems considered as examples, the authors have found the NNM-based reduction, which one would expect to be superior, to suffer degradation in quality in the presence of near (and not so near) three to one internal resonance conditions. The linear-based reduction is much simpler to implement and seems to provide competitive results over wide ranges in the system parameters. This conclusion may not carry over to other, higher degree-of-freedom systems.

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Section: Background and Related Researchmentioning

confidence: 99%

On the Reduction of Nonlinear Structural Dynamics Models

Burton

Rhee

2000

Journal of Vibration and Control

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“…This process can be repeated until the number of master DOFs reaches the desired magnitude. An approach similar to this algorithm was proposed by Shah and Raymund [10], based on the discussions of Kidder [11,12] and Flax [13], where the number of master DOFs is controlled by iteratively eliminating the DOFs for which the ! s is larger than a predefined cutoff frequency !…”

Section: Introductionmentioning

confidence: 99%

Node Sampling for Nonlinear Vibration Analysis of Structures with Intermittent Contact

et al. 2010

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“…This process can be repeated until the number of master DOF reaches the desired number. An approach similar to this algorithm was proposed by Shah and Raymund 10 based on the discussion of Kidder and Flax, [11][12][13] where the number of master DOF is controlled by iteratively eliminating the DOF whose ω s is larger than the pre-defined cut-off frequency ω c that is chosen to be approximately three times the highest significant frequency in the frequency range of interest. Independently from the work by Henshell and Ong, Grinenko and Mokeev developed an order reduction technique named frequencydynamic condensation, 14 which also proposed a criterion to select master DOF.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Reduced Order Modeling Technique for Nonlinear Vibration Analysis of Structures with Intermittent Contact

Saito

Castanier

Pierre

2009

50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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In this paper, a reduced order modeling framework for nonlinear vibration problems of elastic structures involving intermittent contact is proposed. Of particular interest is a vibration problem of plate-like elastic structures with a crack with a large number of degrees of freedom involved on the crack surfaces. Due to the localized nature of such nonlinearity, the number of degrees of freedom on the surfaces greatly affects the computational time of the analysis. Therefore, reducing the number of degrees of freedom on the crack surfaces without significantly sacrificing the accuracy of the results is a critical issue for conducting vibration analysis of such structures in a reasonable amount of time. The focus is placed on the development of an efficient algorithm to select a set of nodes on the crack surfaces, where nonlinear boundary conditions are imposed. The method is developed based on a procedure for selecting master degrees of freedom for Guyan reduction. The accuracy, efficiency, and optimality of the method are discussed in detail and compared with those aspects of previous methods. The advantages of the new method are demonstrated in terms of the accuracy of the frequency response and the resonant frequencies.

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Comment on "Reduction of Structural Frequency Equations"

Cited by 23 publications

References 5 publications

On the Reduction of Nonlinear Structural Dynamics Models

On the Reduction of Nonlinear Structural Dynamics Models

Node Sampling for Nonlinear Vibration Analysis of Structures with Intermittent Contact

An Efficient Reduced Order Modeling Technique for Nonlinear Vibration Analysis of Structures with Intermittent Contact

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