Efficient computation of modal sensitivities for systems with repeated frequencies

Ojalvo, I. U.

doi:10.2514/3.9897

Cited by 89 publications

(34 citation statements)

References 6 publications

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“…Nelson [14] presented a method where only the eigenmode of interest was required to determine the eigenmode sensitivity. These methods have been extended to allow for eigensolution sensitivities of asymmetric non-conservative systems [15] and systems with repeated eigenfrequencies [16]. In our present work which is to find a systematic way to control the eigensolutions, conservative systems will be considered as a first step.…”

Section: Introductionmentioning

confidence: 99%

Control of the Eigensolutions of a Harmonically Driven Compliant Structure

Peters¹,

Tiso²,

Goosen³

et al. 2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The motion amplitude of a harmonically driven compliant structure is maximized if the driving frequency equals one of the structural resonance frequencies. For practical use of resonating compliant structures control of the eigensolutions, i.e. eigenfrequencies and eigenmodes, is often required. In this work, a systematic way to control the eigensolutions of harmonically driven structures is presented while maintaining the advantages of a resonating structure. This control is realized using local structural modifications. Eigensolution sensitivities for these local structural modifications are used to indicate the locations for the most effective structural modifications, minimizing the required control power. This method uses the modal basis of the structure as the preferred basis. A simple harmonically driven compliant structure is used to show how local structural modifications are selected to obtain a desired change in the eigensolutions. The proposed method is found to be a convenient tool to determine effective local structural modifications to control the eigensolutions of resonating compliant structures. During the design phase it provides valuable insights in the possibilities and limitations of controlling specific eigensolutions.

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Section: Introductionmentioning

confidence: 99%

Control of the Eigensolutions of a Harmonically Driven Compliant Structure

Peters¹,

Tiso²,

Goosen³

et al. 2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…The subject of repeated eigenvalues has recently received attention in the literature, 6 " 9 and it is of importance here since Nelson's method will fail when X 1 is repeated. The authors view repeated eigenvalues as a rare occurrence for most complex structures, but structures possessing multiple planes of symmetry, cyclic symmetry, or axisymmetry (which cannot undergo model simplification based on symmetry) certainly merit concern.…”

Section: Repeated Eigenvaluesmentioning

confidence: 99%

Mode tracking issues in structural optimization

1995

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Within the context of optimization of the structural dynamics properties of finite element models, methodology is developed for the tracking of eigenpairs through changes in the structural eigenvalue problem. The goal is to eliminate difficulties caused by "mode switching" (i.e., frequency crossing). Out of several candidate methods, two methods for mode tracking are successful. The first method, the higher order eigenpair perturbation algorithm, is based on a perturbation expansion of the eigenproblem. It iteratively computes changes in the eigenpairs due to parameter perturbations with the important feature of maintaining the correspondence between the baseline and perturbed eigenpairs. The second method is a cross-orthogonality check method, which uses mass orthogonality to reestablish correspondence after a standard reanalysis.

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“…[23] it was shown that, under special circumstances, the treatment of Ref. [22] is not necessary to obtain the partial derivatives of repeated eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

“…Sizing optimization problems to maximize the buckling capacity of structures have also been found to frequently encounter repeated buckling load eigenvalues and modes that are not simply associated with the symmetry of structures [21]. In [22] the physical origin and ambiguity of repeated eigenvalues were discussed, and a treatment was presented to obtain partial derivatives of repeated eigenvalues. In Ref.…”

Section: Introductionmentioning

confidence: 99%

A symmetry reduction method for continuum structural topology optimization

Kosaka

Swan

1999

Computers & Structures

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It is considered that asymmetrical material layout design solutions are caused by numerical roundo and the convexity characteristics of alternative topology design formulations. Emphasis is placed here not on analyzing potential instabilities that lead to asymmetrical designs, but on a method to stabilize topology design formulations. A novel symmetry reduction method is proposed, implemented and studied. While enforcing symmetry and signi®cantly reducing the size of the optimization problem, the symmetry reduction method is shown to have the added bene®t of greatly simpli®ed design sensitivity analysis of non-simple repeated vibrational eigenvalues which occur in many symmetrical structures. #

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Efficient computation of modal sensitivities for systems with repeated frequencies

Cited by 89 publications

References 6 publications

Control of the Eigensolutions of a Harmonically Driven Compliant Structure

Control of the Eigensolutions of a Harmonically Driven Compliant Structure

Mode tracking issues in structural optimization

A symmetry reduction method for continuum structural topology optimization

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