Parametric eigenvalue analysis for flexible multibody systems

Palomba, Ilaria; Wehrle, Erich; Vidoni, Renato; Gasparetto, Alessandro

doi:10.1007/978-3-030-20131-9_410

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…The typical approach to the modal analysis of FLMSs consists of the interpolation of several static modal analyses, which span large displacements of the multibody system [18]. A parametric representation as an approximation of the eigenvalues (and eigenvectors) of second-order mechanical systems is proposed by Wittmuess et al [19], which is adapted to ERLS and validated by Palomba et al in [20,21]. This parameteric approximation is used in the optimization here.…”

Section: Introductionmentioning

confidence: 99%

An Approximation-Based Design Optimization Approach to Eigenfrequency Assignment for Flexible Multibody Systems

et al. 2021

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The use of flexible multibody simulation has increased significantly over recent years due to the increasingly lightweight nature of mechanical systems. The prominence of lightweight engineering design in mechanical systems is driven by the desire to require less energy in operation and to reach higher speeds. However, flexible lightweight systems are prone to vibration, which can affect reliability and overall system performance. Whether such issues are critical depends largely on the system eigenfrequencies, which should be correctly assigned by the proper choice of the inertial and elastic properties of the system. In this paper, an eigenfrequency assignment method for flexible multibody systems is proposed. This relies on a parametric modal model which is a Taylor expansion approximation of the eigenfrequencies in the neighborhood of a configuration of choice. Eigenfrequency assignment is recast as a quadratic programming problem which can be solved with low computational effort. The method is validated by assigning the lowest eigenfrequency of a two-bar linkage by properly adding point masses. The obtained results indicate that the proposed method can effectively assign the desired eigenfrequency.

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Section: Introductionmentioning

confidence: 99%

An Approximation-Based Design Optimization Approach to Eigenfrequency Assignment for Flexible Multibody Systems

et al. 2021

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“…In this approach, the parametric representation of the eigenpairs is inferred from an iterative Taylor series expansion of the eigenvalue problem associated to the linearized system matrices about a parametric operating point. A first extension and application of the approach proposed by Wittmuess et al to FMBSs characterized by small deformation and negligible damping and velocity-dependent terms has been proposed by the authors in [30,31]. In particular, in [31], the authors performed a preliminary investigation on the method capability to approximate the modal content over a wide range of the FMBS parameters, including not only the rigid motion coordinates, but also the payload handled by a two-degree-of-freedom (dof) planar robot carrying out a pick-and-place trajectory.…”

Section: Introductionmentioning

confidence: 99%

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

Palomba¹,

Vidoni²

2019

Applied Sciences

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The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

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Parametric eigenvalue analysis for flexible multibody systems

Cited by 2 publications

References 9 publications

An Approximation-Based Design Optimization Approach to Eigenfrequency Assignment for Flexible Multibody Systems

An Approximation-Based Design Optimization Approach to Eigenfrequency Assignment for Flexible Multibody Systems

Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

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