Multirate Integration for Multibody Dynamic Analysis With Decomposed Subsystems

1999 ◽  
Author(s):  
Sung-Soo Kim ◽  
Jeffrey S. Freeman
Keyword(s):  
Dynamic Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Inertia Force ◽  
Integration Scheme ◽  
Integration Algorithm ◽  
Multibody Dynamic ◽  
Higher Order Derivative ◽  
Derivative Information

Abstract This paper details a constant stepsize, multirate integration scheme which has been proposed for multibody dynamic analysis. An Adams-Bashforth Moulton integration algorithm has been implemented, using the Nordsieck form to store internal integrator information, for multirate integration. A multibody system has been decomposed into several subsystems, treating inertia coupling effects of subsystem equations of motion as the inertia forces. To each subsystem, different rate Nordsieck form of Adams integrator has been applied to solve subsystem equations of motion. Higher order derivative information from the integrator provides approximation of inertia force computation in the decomposed subsystem equations of motion. To show the effectiveness of the scheme, simulations of a vehicle multibody system that consists of high frequency suspension motion and low frequency chassis motion have been carried out with different tire excitation forces. Efficiency of the proposed scheme has been also investigated.

scholarly journals Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Coupled System ◽  
Weak Form ◽  
Integration Scheme ◽  
Motion Constraints ◽  
Multibody Dynamic ◽  
Time Integration Scheme

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.

A Symbolic Formulation for Linearization of Multibody Equations of Motion

1995 ◽  
Vol 117 (3) ◽  
pp. 441-445 ◽  
Author(s):  
A. G. Lynch ◽  
M. J. Vanderploeg
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Dynamic Systems ◽  
Closed Loop ◽  
Multibody System ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Multibody Dynamic ◽  
Constrained Multibody System ◽  
Symbolic Equations Of Motion

This paper presents a method for obtaining linearized state space representations of open or closed loop multibody dynamic systems. The paper develops a symbolic formulation for multibody dynamic systems which result in an explicit set of symbolic equations of motion. The symbolic equations are then used to perform symbolic linearizations. The resulting symbolic, linear equations are in terms of the system parameters and the equilibrium point, and are valid for any equilibrium point. Finally, a method is developed for reducing a linearized, constrained multibody system consisting of a mixed set of algebraic-differential equations to a reduced set of differential equations in terms of an independent coordinate set. An example is used to demonstrate the technique.

scholarly journals An Approach for Compensation of Geometric Faults in Machine Tools

2005 ◽  
Author(s):  
Christian Rudolf ◽  
Jo¨rg Wauer ◽  
Christian Munzinger ◽  
Ju¨rgen Fleischer
Keyword(s):  
Machine Tools ◽  
Multibody System ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Low Frequency ◽  
Piezoelectric Transducers ◽  
Preliminary Design ◽  
Flexible Multibody System ◽  
Parallel Kinematics

Geometric faults in parts of machine tools with parallel kinematics lead to stresses in the structure and deflections of the tool center point, reducing the quality of the workpiece. Improving the design of machine tools can reduce these influences. In this paper an approach to compensate the influence of geometric faults in parallel kinematics based on the design of an adaptronic strut is introduced. The strut is divided in two halves and two piezoelectric transducers are implemented in between them, used as sensor and actuator, respectively. A preliminary design of the adaptronic strut is presented. The problems of measuring low-frequency signals using piezoelectric transducers are considered in the design. Finally, a primary analytical model of the dynamical behavior of the adaptronic compensation unit is presented. The strut and its connection to the surroundings are regarded as a flexible multibody system, the equations of motion are derived using linear graph theory. Some simulation results are presented.

Implicit Numerical Integration of Constrained Equations of Motion Via Generalized Coordinate Partitioning

1992 ◽  
Vol 114 (2) ◽  
pp. 296-304 ◽  
Author(s):  
E. J. Haug ◽  
Jeng Yen
Keyword(s):  
Numerical Integration ◽  
Equations Of Motion ◽  
Integration Algorithm ◽  
Differentiation Formula ◽  
Generalized Coordinates ◽  
Multibody Dynamic ◽  
Constrained Equations ◽  
Automated Simulation ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

An implicit, stiffly stable numerical integration algorithm is developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, Backward Differentiation Formula (BDF) numerical integration algorithm is used to integrate independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of an example.

Dynamic Modeling of Viscoelastic Body in Multibody System

2011 ◽  
Vol 105-107 ◽  
pp. 587-594
Author(s):  
Da Zhi Cao ◽  
Zhi Hua Zhao ◽  
Ge Xue Ren
Keyword(s):  
Fractional Derivative ◽  
Multibody System ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Time Integration ◽  
Three Dimensional ◽  
Viscoelastic Body ◽  
Integration Scheme ◽  
Large Rotation ◽  
Time Integration Scheme

Dynamic equations of viscoelastic bodies with fractional constitutive are derived base on the principle of virtual work and the theory of continuum mechanics. The three-dimensional fractional derivative viscoelastic constitutive model is implemented into the flexible multibody system (FMBS), using the 3D solid element based on the absolute nodal coordinate formulation (ANCF), which can exactly describe the geometric nonlinearities due to large rotation and large deformation. The BDF time integration scheme in conjunction with the Grünwald approximation of fractional derivative and the Newton-Raphson algorithm are used to solve the equations of motion. Several numerical examples are presented to demonstrate the use of the modeling procedure presented in this investigation and the effects of parameters in the fractional derivative model.

Implicit Numerical Integration of Constrained Equations of Motion via Generalized Coordinate Partitioning

1989 ◽  
Author(s):  
E. J. Haug ◽  
J. Yen
Keyword(s):  
Numerical Integration ◽  
Equations Of Motion ◽  
Integration Algorithm ◽  
Generalized Coordinates ◽  
Multibody Dynamic ◽  
Constraint Set ◽  
Constrained Equations ◽  
Automated Simulation ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract An implicit, stiffly stable numerical integration algorithm is developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, backward difference numerical integration algorithm is applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of a numerical example.

Dynamic Analysis of Constrained System of Rigid and Flexible Bodies With Intermittent Motion

1986 ◽  
Vol 108 (1) ◽  
pp. 38-45 ◽  
Author(s):  
Y. A. Khulief ◽  
A. A. Shabana
Keyword(s):  
Dynamic Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Constrained System ◽  
Integration Algorithm ◽  
Flexible Bodies ◽  
Intermittent Behavior ◽  
Finite Set ◽  
Implicit Integration Algorithm ◽  
Intermittent Motion

A method for dynamic analysis of large-scale constrained system of mixed rigid and flexible bodies with intermittent motion is presented. The system equations of motion are written in the Lagrangian formulation using a finite set of coupled reference position and local elastic generalized coordinates. Equations of motion are computer generated and integrated forward in time using an explicit-implicit integration algorithm. Points in time at which sudden events of the intermittent behavior occur are monitored by an event predictor which controls the integration algorithm and forces a solution for the system impulse-momentum relation at those points. Solutions of impulse-momentum relations define the jump discontinuities in the composite velocity vector as well as the generalized impulses of the reaction forces at different joints of the mechanical system.

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