Computational method for dynamic analysis of constrained mechanical systems using partial velocity matrix transformation

2000 ◽  
Vol 14 (2) ◽  
pp. 159-167 ◽  
Author(s):  
Jung Hun Park ◽  
Hong Hee Yoo ◽  
Yoha Hwang
Keyword(s):  
Dynamic Analysis ◽  
Mechanical Systems ◽  
Computational Method ◽  
Matrix Transformation ◽  
Constrained Mechanical Systems ◽  
Partial Velocity

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems

1985 ◽  
Vol 107 (4) ◽  
pp. 488-492 ◽  
Author(s):  
C. O. Chang ◽  
P. E. Nikravesh
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
General Purpose ◽  
Adaptive Mechanism ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Transient Dynamic Analysis ◽  
Constrained Mechanical Systems ◽  
Feedback Control Theory

The transient dynamic analysis of equations of motion for constrained mechanical systems requires the solution of a mixed set of algebraic and differential equations. A constraint violation stabilization method, based on feedback control theory of linear systems, has been suggested by some researchers for solving these equations. However, since the value of damping parameters for this method are uncertain, the method is to some extent unattractive for general-purpose use. This paper presents an adaptive mechanism for determining the damping parameters. The results of the simulation for two examples illustrate the improvement in reducing the constraint violations when using this method.

Dynamic Analysis of Constrained Mechanical Systems Considering Their Statistical Properties

2004 ◽  
Author(s):  
Dong Hwan Choi ◽  
Se Jung Lee ◽  
Hong Hee Yoo
Keyword(s):  
Monte Carlo ◽  
Dynamic Analysis ◽  
Mechanical Systems ◽  
Tolerance Analysis ◽  
Statistical Properties ◽  
Dynamic Responses ◽  
Statistical Characteristics ◽  
Analytic Method ◽  
Constrained Mechanical Systems ◽  
The Monte Carlo Method

A method of dynamic analysis and reliability analysis of constrained mechanical systems considering their statistical properties is presented in this paper. Statistical properties, which result from manufacturing tolerances, can be represented by means or variances and standard deviations. The statistical characteristics of dynamic responses of mechanical systems with tolerances are obtained by two ways: the analytic method and the Monte Carlo method. The former necessitates sensitivity information. In this paper, a direct differentiation method is used to find the sensitivities of mechanical systems. The first order variance is considered in tolerance analysis. To verify the accuracy of the proposed method, three numerical examples are solved and the results obtained by using the proposed analytic method are compared to those obtained by the Monte Carlo simulation.

A Differentiable Null Space Method for Constrained Dynamic Analysis

1987 ◽  
Vol 109 (3) ◽  
pp. 405-411 ◽  
Author(s):  
C. G. Liang ◽  
George M. Lance
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Null Space ◽  
Mechanical Systems ◽  
Geometric Approach ◽  
Constraint Violation ◽  
Constrained Mechanical Systems ◽  
Tangent Hyperplane ◽  
Space Method ◽  
Constraint Surface

A geometric approach to the solution of the dynamic response of constrained mechanical systems is proposed. A continuous and differentiable basis of the constraint null space is automatically generated using the Gram-Schmidt process. The independent coordinates are obtained by transforming the physical velocity coordinates to the tangent hyperplane of the constraint surface. As a result the independent coordinates lie on the constraint surface and no constraint violation control is necessary.

scholarly journals Mobility Method Applied to Calculate the Lubrication Properties of Bearing under Dynamic Loads

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Tao He ◽  
Xiqun Lu ◽  
Jingzhi Zhu
Keyword(s):  
Dynamic Analysis ◽  
Mechanical Systems ◽  
Journal Bearings ◽  
Numerical Results ◽  
Dynamic Loads ◽  
Analysis Program ◽  
Computational Program ◽  
Dynamically Loaded ◽  
Mobility Method ◽  
Lubrication Properties

The analytical mobility method for dynamically loaded journal bearings was presented, with the intent to include it in a general computational program, such as the dynamic analysis program, that has been developed for the dynamic analysis of general mechanical systems. An illustrative example and numerical results were presented, with the efficiency of the method being discussed in the process of their presentation.

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