An evaluation of higher-order modal methods for calculating transient structural response

Camarda, Charles J.; Haftka, Raphael T.; Riley, Michael F.

doi:10.1016/0045-7949(87)90184-2

Cited by 36 publications

(15 citation statements)

References 7 publications

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“…The force-derivative method corresponds to the limiting subcase of uj* -> 0, so that in the second-orderrepresentation (4.35) through (4.37) reduce to Using the first three terms of (4.53) through (4.55), the first three terms of (4.56) through (4.58), T~2 -¥ Q~2, 3 -» A, a,<* -» 0, and fj ->■ f for the slow time a// in (4.23) reproduces (38) of Ref. [38, p. 29].…”

Section: Force Derivative As a Submethodsmentioning

confidence: 99%

“…The force derivative method is another example of a model reduction hybrid, in this case for extending modal reduced basis approximations. With linear FEM models of mechanical systems as a benchmark, comparisons [36,37,38] between several reduced basis methods based on computed responses of the resulting reduced dynamical models, seem to favor the force-derivative [37,39,38] and the (closely related) Lanczos [24,27,26,40] methods. This is evidence supporting the utility of hybrid extensions to model reduction methods.…”

Section: Introductionmentioning

confidence: 99%

“…Its importance is underscored by the fact that it provides both a foundation and extension to the popular Craig-Bampton [43] version of component mode synthesis [44], as shown by Suarez and Singh [45]. The conventional version of the force derivative method is a convolution integral formulation [39,38], from which higher order corrections are derived via repeated integration by parts of the integral. This integrationby-parts development of the series is apparently serendipitous; a direct systematic development in terms of a generic perturbation methodology is neither mentioned nor used as an alternative.…”

Section: Introductionmentioning

confidence: 99%

“…This is evidence supporting the utility of hybrid extensions to model reduction methods. The force-derivative method encompasses [39,38] the older mode-displacement and mode-acceleration methods [41,42] as zeroth and first-order submethods, respectively. It is essentially a modal basis method that is systematically corrected by terms containing residual mode information.…”

Section: Introductionmentioning

confidence: 99%

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A Generic Bilevel Formalism for Unifying and Extending Model Reduction Methods

Flippen¹

2000

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. 12b. DISTRIBUTION CODE ABSTRACT (Maximum 200 words)An abstract, algebraic bilevel version of conventional multigrid methods has been developed that formally unifies and extends the reduced basis, substructuring, smoothing/homogenization, and frequency window methods of model reduction. Within the context of this formalism, a given model reduction method synthesizes a reduced model that plays the role of a "coarse grid" model. Another original-model approximation, conjugate to the model reduction method, plays the role of a "fine grid" model. Conventional multigrid methods can be thought of as an extension of the coarse grid model beyond the original scope of its accuracy through the alternating use of "fine-grid-error-smoothing" and "coarse-grid-correction" steps. Analogously fashioned, abstract versions of these steps extend the particular model reduction method used beyond the original scope of its accuracy. In addition to the development of the mathematical formalism, a generic continuation is proposed and developed as the conjugate approximation for use in the abstract version of the fine-grid-error-smoothing step. For generality, the nature of the parameter-embedding of the continuation is deliberately left unspecified; a particular parameter-embedding is chosen by the analyst to complement the particular model and model reduction method (or class thereof) in a given case. As an example, a particular submethod of this formalism is constructed by specializing the parameter-embedding to a temporal, biscale perturbational parameter-embedding for the case of a generic set of coupled ordinary differential equations with constant coefficients. The initial iteration of this submethod is a general, combined transient/frequency-window methodology for linear finite-element method applications. It is shown to encompass both the force derivative and Lanczos/Ritz vector methods for the limiting case of a zero frequency, singlepoint window for the "fast" time scale. To put this in perspective, the force derivative and Lanczos/Ritz vector methods are two leading approaches for extending/replacing modal reduced basis methods. Current frequency window methods, in turn, are very efficient for extensive time-harmonic «analysis of the system.

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Section: Force Derivative As a Submethodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Generic Bilevel Formalism for Unifying and Extending Model Reduction Methods

Flippen¹

2000

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“…Improved results can be obtained with the force derivative methods (FDM), whose correction is built as a series expansion [5,6]. This requires the knowledge of successive time derivatives of the excitation, which are not always available, therefore limiting the practical applicability of the method.…”

Section: Introductionmentioning

confidence: 99%

A new modal correction method for linear structures subjected to deterministic and random loadings

Palmeri

Lombardo

2011

Computers & Structures

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Citation: PALMERI, A. and LOMBARDO, M., 2011. A new modal correction method for linear structures subjected to deterministic and random loadings. Computers and Structures, AbstractIn the general framework of linear structural dynamics, modal corrections methods allow improving the accuracy of the response evaluated with a reduced number of modes. Although very often neglected by researchers and practitioners, this correction is particularly important when strains and stresses are computed. Aimed at overcoming the main limitations of existing techniques, a novel dynamic modal acceleration method (DyMAM) is presented and numerically validated. The proposed correction involves a set of additional dummy oscillators, one for each dynamic loading, and can be applied, with a modest computational effort, to discrete and continuous systems under deterministic and random inputs.

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Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

D'Aveni

Muscolino

2001

Earthq Engng Struct Dyn

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A step-by-step approximate procedure taking into consideration high-frequency modes, usually neglected in the modal analysis of both classically and non-classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the modeacceleration method and the dynamic correction method, which are very e ective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the ÿrst step, the number of di erential equations of motion are reduced and consequently solved by using the ÿrst few undamped mode-shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of di erential equations, formally similar to the original di erential equations of motion. The di erence between the two groups of di erential equations lies in the forcing vector, which is evaluated in such a way as to correct the e ects of modal truncation on applied loads.

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An evaluation of higher-order modal methods for calculating transient structural response

Cited by 36 publications

References 7 publications

A Generic Bilevel Formalism for Unifying and Extending Model Reduction Methods

A Generic Bilevel Formalism for Unifying and Extending Model Reduction Methods

A new modal correction method for linear structures subjected to deterministic and random loadings

Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

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