Applied Dynamics

Schiehlen, Werner; Eberhard, Peter

doi:10.1007/978-3-319-07335-4

Cited by 54 publications

(56 citation statements)

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“…The main objective of the Section 3 consists in determining the advanced kinematic parameters from each kinetic ensemble. Unlike the classical approaches [31][32][33], few formulations based on time derivatives of the locating matrices is developed. For this purpose, in Figure 1 a sequence of two kinetic ensembles (i − 1) → (i) , from the mechanical structure of a serial robot, subjected to kinematical study is considered.…”

Section: θ(T); · · · ;mentioning

confidence: 99%

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A New Approach in Analytical Dynamics of Mechanical Systems

2020

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This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.

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Section: θ(T); · · · ;mentioning

confidence: 99%

“…As mentioned in the scientific literature [17,18,33], in 1879, Gibbs defined the differential equations of motion, on which, later in 1899, Paul Appell, performed an elaborate study. Therefore, the Gibbs-Appell equations were determined.…”

Section: The Matrix Expressions Of the Acceleration Energiesmentioning

confidence: 99%

A New Approach in Analytical Dynamics of Mechanical Systems

2020

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“…Within each reduction method, the most expensive step, with respect to the need of memory as well as to the runtime, is often solving a sparse system of linear equations. With the projection matrix, a reduced system of linear equations can be calculated and included into the MBS according to the theory described in [2,3].…”

Section: Institute Of Engineering and Computational Mechanics Univermentioning

confidence: 99%

Model Order Reduction of Large-Scale Finite Element Systems in an MPI Parallelized Environment for Usage in Multibody Simulation

Volzer

Eberhard

2016

Archive of Mechanical Engineering

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The use of elastic bodies within a multibody simulation became more and more important within the last years. To include the elastic bodies, described as a finite element model in multibody simulations, the dimension of the system of ordinary differential equations must be reduced by projection. For this purpose, in this work, the modal reduction method, a component mode synthesis based method and a momentmatching method are used. Due to the always increasing size of the non-reduced systems, the calculation of the projection matrix leads to a large demand of computational resources and cannot be done on usual serial computers with available memory. In this paper, the model reduction software Morembs++ is presented using a parallelization concept based on the message passing interface to satisfy the need of memory and reduce the runtime of the model reduction process. Additionally, the behaviour of the Block-Krylov-Schur eigensolver, implemented in the Anasazi package of the Trilinos project, is analysed with regard to the choice of the size of the Krylov base, the blocksize and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.

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“…Multibody systems (MBS) are well suited to simulate the kinematics and dynamics of mechanical systems composed by a number of rigid bodies that undergo large, nonlinearly described motions [4]. In many engineering tasks, e.g.…”

Section: Contact Simulation Based On Elastic Multibody Systemsmentioning

confidence: 99%

Influence of Uncertainties on the Stability of a Self-Excited Elastic Multibody System

Iroz¹,

Hanss²,

Eberhard³

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. In this paper, uncertainty analyses based on fuzzy arithmetic are performed and illustrated for a disc brake affected by friction-induced vibrations and modeled as an elastic multibody system. By the use of fuzzy-valued model parameters, the nominal results of conventional, crisp-valued models are extended to the inclusion of uncertainties, and valuable conclusions on the overall effect as well as on the individual influence of uncertain parameters on the output of the model can be drawn. For the definition, the simulation and the evaluation of the fuzzy-parameterized model, the software package FAMOUS is used and coupled to the multibody simulation program Neweul-M 2 .

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Applied Dynamics

Cited by 54 publications

References 0 publications

A New Approach in Analytical Dynamics of Mechanical Systems

A New Approach in Analytical Dynamics of Mechanical Systems

Model Order Reduction of Large-Scale Finite Element Systems in an MPI Parallelized Environment for Usage in Multibody Simulation

Influence of Uncertainties on the Stability of a Self-Excited Elastic Multibody System

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