Dynamics of Flexible Mechanical Systems Using Vibration and Static Correction Modes

Yoo, Wan-Suk; Haug, Edward J.

doi:10.1115/1.3258733

Cited by 104 publications

(40 citation statements)

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“…An interface DOF is a nodal DOF in which the flexible body can be loaded by an external force: forces due to constraints in the multibody model or due to other external sources of body loading. Yoo and Haug show that the inclusion of static deformation patterns is vital for the accuracy of the reduced model in case of concentrated loads [14], which is often the case in multibody systems. Especially if one is interested in stress estimation in the case of localized loads, deformation patterns compensating for the quasi-static contribution of the omitted (higher-frequency) normal modes are indispensable [15].…”

Section: Body Flexibility Model Reductionmentioning

confidence: 99%

Static modes switching for more efficient flexible multibody simulation

Heirman

Tamarozzi

Desmet

2011

Numerical Meth Engineering

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SUMMARYBody flexibility is of ever-increasing importance in multibody simulation. The current state-of-the-art simulation techniques typically have difficulties with systems in which flexible bodies can be loaded in many degrees of freedom (DOFs). However, in many applications, loading is possible in many DOFs but only few are loaded simultaneously at any given moment, such that at any moment only a low-dimensional part of the reduced body flexibility description contributes to the solution. Static Modes Switching, the methodology proposed in this paper, exploits this by judiciously choosing the body flexibility mode set and at any moment only including those modes that contribute to the solution. Static Modes Switching does not improve simulation accuracy; however, it can significantly reduce simulation times. In a numerical experiment, results using Static Modes Switching match results for a conventional model using the same mode set. The approximation errors are negligible compared to the accuracy loss encountered when using a mode set without compensation for the quasi-static response of the high-frequency dynamics, while both simulation results are obtained at a comparable computational cost. Static Modes Switching numerically introduces discontinuities when removing a mode from the mode set. This is overcome by time integration schemes exhibiting high-frequency numerical damping.

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Section: Body Flexibility Model Reductionmentioning

confidence: 99%

Static modes switching for more efficient flexible multibody simulation

Heirman

Tamarozzi

Desmet

2011

Numerical Meth Engineering

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“…These coefficients are the finite element mass matrix M f f , the vibration modes used in the modal matrix X and the corresponding natural frequencies used in matrix K. Equation (12) represents a linear system of equations for which the unknowns are the second-order time derivatives of generalized coordinates. It should be noted that though only the modes of vibration associated with body coordinates systems fixed to the body center of mass are used in this procedure, other modes such as the static correction modes can also be used [20]. In the same manner, the use of the mean axis condition [21] could also be considered in order to improve numerical precision and the efficiency of the mode component synthesis.…”

Section: Coordinate Reduction By the Component Mode Synthesismentioning

confidence: 99%

Sensitivity analysis of flexible multibody systems using composite materials components

Neto

Ambrósio

Leal

2008

Numerical Meth Engineering

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SUMMARYIn this paper, a general formulation for the computation of the first-order analytical sensitivities based on the direct method using automatic differentiation of flexible multibody systems is presented. The direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible multibody systems of composite materials with respect to the design variables, which are the ply orientations of the laminated. In order to appraise the benefits of the approach suggested and to highlight the risks of the procedure, the analytical sensitivities are compared with the numerical results obtained by using the finite difference method. For the beam composite material elements, the section properties and their sensitivities are found using an asymptotic procedure that involves a two-dimensional (2-D) finite element analysis of their cross section. The equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems. The equations of motion and the sensitivities of the flexible multibody system are solved and the accelerations, velocities and the sensitivities of accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm. Through the application of the methodology to two simple flexible multibody systems the difficulties and benefits of the procedure, with respect to finite difference approaches or to the direct implementation of the analytic sensitivities, are discussed.

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“…For a more detailed discussion on the selection of the modes used the interested reader is referred to Refs. [15][16][17][18][19][20]46]. …”

Section: Flexible Multibody Equations Of Motionmentioning

confidence: 99%

“…Different formulations for the description of flexible multibody systems have been proposed in the literature presenting relative advantages, and also drawbacks, with respect to the formulation used here [9][10][11][12][13]. However, the flexible multibody descriptions based on generalized elastic coordinates relative to body fixed frame not only use the standard linear finite element mass and stiffness matrices directly but also allow for the reduction of the number of elastic degrees of freedom, either by applying substructuring techniques [14], the Craig-Bampton method [3,15], the mode superposition technique [8,[16][17][18][19][20] or other reduction techniques [21], leading to simpler and computationally efficient models.…”

Section: Introductionmentioning

confidence: 99%

Optimization of a complex flexible multibody systems with composite materials

2007

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The paper presents a general optimization methodology for flexible multibody systems which is demonstrated to find optimal layouts of fiber composite structures components. The goal of the optimization process is to minimize the structural deformation and, simultaneously, to fulfill a set of multidisciplinary constraints, by finding the optimal values for the fiber orientation of composite structures. In this work, a general formulation for the computation of the first order analytical sensitivities based on the use of automatic differentiation tools is applied. A critical overview on the use of the sensitivities obtained by automatic differentiation against analytical sensitivities derived and implemented by hand is made with the purpose of identifying shortcomings and proposing solutions. The equations of motion and sensitivities of the flexible multibody system are solved simultaneously being the accelerations and velocities of the system and the sensitivities of the accelerations and of the velocities integrated in time using a multi-step multi-order integration algorithm. Then, the optimal design of the flexible multibody system is formulated to minimize the deformation energy of the system subjected to a set of technological and functional constraints. The methodologies proposed are first discussed for a simple demonstrative example and applied after to the optimization of a complex flexible multibody system, represented by a satellite antenna that is unfolded from its launching configuration to its functional state.

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Dynamics of Flexible Mechanical Systems Using Vibration and Static Correction Modes

Cited by 104 publications

References 0 publications

Static modes switching for more efficient flexible multibody simulation

Static modes switching for more efficient flexible multibody simulation

Sensitivity analysis of flexible multibody systems using composite materials components

Optimization of a complex flexible multibody systems with composite materials

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