Performance of implicit A-stable time integration methods for multibody system dynamics

Zhang, Huimin; Zhang, Runsen; Zanoni, Andrea; Masarati, Pierangelo

doi:10.1007/s11044-021-09806-9

Cited by 7 publications

(4 citation statements)

References 35 publications

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“…For the ad-hoc formulation, Matlab's ode23() implementation of the explicit Runge-Kutta scheme proposed by Bogacki and Shampine [44] was used. With MBDyn, a second-order accurate, implicit A-stable multistep scheme with tunable algorithmic dissipation and asymptotic spectral radius ρ ∞ = 0.6 [45] was used.…”

Section: Loss Of Isotropy: One Damper Inoperativementioning

confidence: 99%

Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics

Cassoni

Zanoni

Tamer

et al. 2023

Journal of Computational and Nonlinear Dynamics

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The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.

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Section: Loss Of Isotropy: One Damper Inoperativementioning

confidence: 99%

Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics

Cassoni

Zanoni

Tamer

et al. 2023

Journal of Computational and Nonlinear Dynamics

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“…where A represents the amplification matrix, and its elements refer to Appendix C. Then, the characteristic polynomial of A can be derived from Equation (28), as…”

Section: Spectral Characteristicsmentioning

confidence: 99%

“…To our knowledge, there are many excellent implicit methods for structural dynamics, such as the single-step parameters methods [21,22], energy momentum methods [23][24][25], linear multistep methods [26][27][28][29], and composite methods [30][31][32][33][34][35][36][37][38][39][40]. Using them to simulate multibody systems seems natural.…”

Section: Introductionmentioning

confidence: 99%

New Insights into a Three-Sub-Step Composite Method and Its Performance on Multibody Systems

Zhang

Xing

2022

Mathematics

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This paper develops a new implicit solution procedure for multibody systems based on a three-sub-step composite method, named TTBIF (trapezoidal–trapezoidal backward interpolation formula). The TTBIF is second-order accurate, and the effective stiffness matrices of the first two sub-steps are the same. In this work, the algorithmic parameters of the TTBIF are further optimized to minimize its local truncation error. Theoretical analysis shows that for both undamped and damped systems, this optimized TTBIF is unconditionally stable, controllably dissipative, third-order accurate, and has no overshoots. Additionally, the effective stiffness matrices of all three sub-steps are the same, leading to the effective stiffness matrix being factorized only once in a step for linear systems. Then, the implementation procedure of the present optimized TTBIF for multibody systems is presented, in which the position constraint equation is strictly satisfied. The advantages in accuracy, stability, and energy conservation of the optimized TTBIF are validated by some benchmark multibody dynamic problems.

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“…The smooth subsystem consisting of bodies S i is modeled as a generic multibody system, which can be formulated as a set of DAEs using the physical coordinates q 1 as in [34,35]:…”

Section: Formulation Of Smooth Subsystemsmentioning

confidence: 99%

Explicit smooth/nonsmooth cosimulation using kinematic constraints

Zhang

Zhang²,

Zanoni

et al. 2022

Multibody Syst Dyn

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An explicit cosimulation scheme is developed to study the coupling of smooth and nonsmooth systems using kinematic constraints. Using the force-displacement decomposition, the coupling constraints are formulated at the velocity level, to preserve consistency with the impulse-momentum equations for frictional contacts in the nonsmooth solver, which however potentially leads to instability of the explicit cosimulation. To improve the stability of the cosimulation without affecting the format of the coupling constraints, guidelines for the modification of the prescribed motion are developed following the spirit of Baumgarte’s stabilization technique and the characteristics of the proposed integration scheme, which prescribes a combination of position, velocity, and acceleration to the constrained bodies. Using modified inputs, the stability of the cosimulation is tested using a rigidly connected two-mass oscillator model, which shows clear improvement compared to that with unaltered inputs. The performances of the cosimulation with modified inputs are further illustrated using a double-pendulum system and a complex flexible multibody system coupled with a particle damper. It follows that cosimulation results well agree with those obtained using monolithic simulation or simplified models, verifying the explicit smooth/nonsmooth cosimulation. The results also show a higher efficiency of the explicit cosimulation scheme, which requires much less computational time to obtain similar results, compared to the implicit smooth/nonsmooth cosimulation.

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Performance of implicit A-stable time integration methods for multibody system dynamics

Cited by 7 publications

References 35 publications

Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics

Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics

New Insights into a Three-Sub-Step Composite Method and Its Performance on Multibody Systems

Explicit smooth/nonsmooth cosimulation using kinematic constraints

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