Application of modified local parametrization method for the constrained multibody dynamic systems

1998 ◽  
Vol 12 (1) ◽  
pp. 22-30
Author(s):  
Dong-Chan Lee ◽  
Sang-Ho Lee ◽  
Chang-Soo Han
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.


2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.


2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.


Author(s):  
Corina Sandu ◽  
Adrian Sandu ◽  
Brendan J. Chan ◽  
Mehdi Ahmadian

This study addresses the critical need for computational tools to model complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. Polynomial chaos has been used extensively to model uncertainties in structural mechanics and in fluids, but to our knowledge they have yet to be applied to multibody dynamic simulations. We show that the method can be applied to quantify uncertainties in time domain and frequency domain.


Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact truth models and linearized large-articulation models are developed in a companion paper. The purpose of the truth models is to aid in evaluating the use of various types of component body assumed modes in the large-articulation models. The assumed mode models are analytically evaluated from the perspectives of both structural dynamics and multibody dynamics. In this paper, component body assumed modes are tested in a linearized large-articulation model. The numerical behavior of the model and its performance in the presence of parameter variation is investigated and explained. The results show that high accuracy, high simulation efficiency, and numerical robustness cannot be simultaneously achieved. However, in many cases, satisfactory levels of all three are achievable. Guidelines are proposed for modeling the flexible bodies in controlled-articulation flexible multibody dynamic systems.


2005 ◽  
Author(s):  
C. Sandu ◽  
A. Sandu ◽  
B. J. Chan ◽  
Mehdi Ahmadian

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