Reducing Huge Gyroscopic Eigenproblems by Automated Multi-level Substructuring

Elssel, Kolja; Voß, Heinrich

doi:10.1007/s00419-006-0013-0

Cited by 11 publications

(4 citation statements)

References 22 publications

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“…Besides the classical methods, which are available and have been employed successfully in the past for reducing the original number of degrees of freedom of a complex mechanical system, a new class of coordinate reduction methods has also been developed recently, which presents certain computational advantages (Kropp and Heiserer, 2003;Kim and Bennighof, 2006;Elssel and Voss, 2006;Papalukopoulos and Natsiavas, 2007). The basic steps of these methods are briefly illustrated in this section.…”

Section: Substructuring Methodsmentioning

confidence: 99%

“…Apart from increasing the computational efficiency and speed, the reduction of the system dimensions makes amenable the subsequent application of numerical techniques for determining the dynamic response of complex systems, which are applicable and efficient for low order systems. For instance, this method has already been applied successfully to the solution of the real eigenproblem and the prediction of periodic response of large scale linear models with nonclassical damping (Kim and Bennighof, 2006;Papalukopoulos and Natsiavas, 2007), large order gyroscopic systems (Elssel and Voss, 2006) and broadband vibro-acoustic simulations of vehicle models (Kropp and Heiserer, 2003). In addition, the same method has also facilitated determination of the transient response of large scale nonlinear models (Papalukopoulos and Natsiavas, 2007;Theodosiou and Natsiavas, 2009).…”

Section: Introductionmentioning

confidence: 95%

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Periodic steady state response of large scale mechanical models with local nonlinearities

Theodosiou

Sikelis

Natsiavas

2009

International Journal of Solids and Structures

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a b s t r a c tLong term dynamics of a class of mechanical systems is investigated in a computationally efficient way. Due to geometric complexity, each structural component is first discretized by applying the finite element method. Frequently, this leads to models with a quite large number of degrees of freedom. In addition, the composite system may also possess nonlinear properties. The method applied overcomes these difficulties by imposing a multi-level substructuring procedure, based on the sparsity pattern of the stiffness matrix. This is necessary, since the number of the resulting equations of motion can be so high that the classical coordinate reduction methods become inefficient to apply. As a result, the original dimension of the complete system is substantially reduced. Subsequently, this allows the application of numerical methods which are efficient for predicting response of small scale systems. In particular, a systematic method is applied next, leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. An appropriate continuation scheme is also applied, leading to evaluation of complete branches of periodic solutions. In addition, the stability properties of the located motions are also determined. Finally, respresentative sets of numerical results are presented for an internal combustion car engine and a complete city bus model. Where possible, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models. Moreover, emphasis is placed in comparing results obtained by employing the nonlinear or the corresponding linearized models.

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Section: Substructuring Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Periodic steady state response of large scale mechanical models with local nonlinearities

Theodosiou

Sikelis

Natsiavas

2009

International Journal of Solids and Structures

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“…Optionally, by this switch the extraction of eigenvalues around or below the shift value can An alternative numerical technique for the efficient computation of large scale quadratic eigenproblems is provided by automated multi-level sub-structuring (AMLS) techniques, cf. [3,4] for general structural dynamics and [7] especially for gyroscopic systems. By this approach the eigenvalue problem is projected into a much smaller subspaces.…”

Section: Algorithm For Large Scale Eigenvalue Problems Of Gyroscopic mentioning

confidence: 99%

An approach for large-scale gyroscopic eigenvalue problems with application to high-frequency response of rolling tires

Brinkmeier

Nackenhorst

2007

Comput Mech

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The transient dynamic response of rolling tires is of essential importance for comfort questions, e.g. noise radiation. Whereas finite element models are well established for stationary rolling simulations, it lacks computational methods for the treatment of the high frequency response. One challenge is the large mode density of tire structures that is up to the acoustic frequency domain and another lies on the physically correct description of rolling (gyroscopic) structures. Despite that the eigenvalue analysis of gyroscopic systems, described by complex-valued quadratic eigenvalue systems, seems to be well understood in general, specific problems arise for the computability of large scale three-dimensional tire models. In this presentation an overall computational strategy for the high frequency response of FE-tire models is outlined, where special emphasis is placed upon the efficient numerical treatment of the complex-valued eigenproblems for large scale gyroscopic systems. The practicability of the proposed approach will be demonstrated by the analysis of detailed finite element tire models. The physical interpretation of the computational results is also discussed in detail.Keywords Finite element method · Arbitrary Lagrangian Eulerian · Gyroscopic effects · Large scale quadratic eigenvalue problem · Rolling noise · Tire models M. Brinkmeier (B) · U. Nackenhorst

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“…Numerical techniques for forward gyroscopic eigensystems have been discussed in [10, 22, 36], but the attention mostly is on the damping free case, i.e., C = G is skew-symmetric. A hybrid optimization method employing genetic algorithms and simulated annealing to identify bearing parameters of rotating machinery from bearing forces [4] is somewhat close to an inverse problem, but we have found no discussion on the gyroscopic inverse eigenvalue problem.…”

Section: When M C and K Are A Mixture Of Linear Typesmentioning

confidence: 99%

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

2009

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In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs.

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Reducing Huge Gyroscopic Eigenproblems by Automated Multi-level Substructuring

Cited by 11 publications

References 22 publications

Periodic steady state response of large scale mechanical models with local nonlinearities

Periodic steady state response of large scale mechanical models with local nonlinearities

An approach for large-scale gyroscopic eigenvalue problems with application to high-frequency response of rolling tires

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

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