Development and Application of a Generalized d’Alembert Force for Multifreedom Mechanical Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 317-326 ◽  
Author(s):  
M. A. Chace ◽  
Y. O. Bayazitoglu
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Lagrange Equations ◽  
Second Order Differential Equations ◽  
Dimensional Version ◽  
Mechanical Networks ◽  
Geometric Effects

A set of expressions termed the generalized d’Alembert force is determined for application to two and three-dimensional dynamic analysis of discrete, nonlinear, multifreedom, constrained, mechanical dynamic systems. These expressions greatly simplify the task of developing a correct set of second order differential equations of motion for mechanical systems which are nonlinear because of large deflections or other geometric effects. They apply to both constrained and unconstrained mechanical systems via the method of Lagrange equations with constraint. The two-dimensional version of the expressions has been successfully applied in a type-varient computer program for the dynamic analysis of mechanical networks, and example problems simulated with this program are discussed.

A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1

1977 ◽  
Vol 99 (3) ◽  
pp. 773-779 ◽  
Author(s):  
N. Orlandea ◽  
M. A. Chace ◽  
D. A. Calahan
Keyword(s):  
Computer Simulation ◽  
Dynamic Analysis ◽  
Numerical Solutions ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Front Suspension ◽  
Analysis And Design

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the modal optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

Methods for Automated Dynamic Analysis of Discrete Mechanical Systems

1973 ◽  
Vol 40 (3) ◽  
pp. 809-811 ◽  
Author(s):  
Y. O. Bayazitoglu ◽  
M. A. Chace
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Ordinary Differential Equations ◽  
Mechanical System ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Constrained Systems ◽  
Lower Pair ◽  
Linear And Nonlinear

The equations of motion for any discrete, lower pair mechanical system can be obtained by analyzing a branched, three-dimensional compound pendulum of indefinite length. In this paper, a set of expressions which provides the equations of motion of arbitrary mechanical dynamic systems directly as ordinary differential equations are presented. These expressions and the associated technique is applicable to linear and nonlinear unconstrained dynamic systems, kinematic systems and multidegree-of-freedom constrained systems.

A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 2

1977 ◽  
Vol 99 (3) ◽  
pp. 780-784 ◽  
Author(s):  
N. Orlandea ◽  
D. A. Calahan ◽  
M. A. Chace
Keyword(s):  
Computer Simulation ◽  
Dynamic Analysis ◽  
Numerical Solutions ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Front Suspension ◽  
Analysis And Design

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms, big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the model optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

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.

Analysis and Optimal Design of Spatial Mechanical Systems

1987 ◽  
Author(s):  
H. Ashrafeiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Analysis And Design ◽  
Spatial Systems

Abstract This paper presents a new approach to optimal design of large multibody spatial mechanical systems. This approach uses symbolic computing to generate the necessary equations for dynamic analysis and design sensitivity analysis. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of velocity transformation matrix. Design sensitivity analysis is carried out using the Direct Differentiation method applied to the relative joint coordinate formulation for spatial systems. Symbolic manipulation programs are used to develop subroutines which provide information for dynamic and design sensitivity analysis. These subroutines are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization. An example is presented to demonstrate the efficiency of the approach.

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

Dynamic Analysis of the Ultrasonic Machining Process

1996 ◽  
Vol 118 (3) ◽  
pp. 376-381 ◽  
Author(s):  
Z. Y. Wang ◽  
K. P. Rajurkar
Keyword(s):  
Dynamic Analysis ◽  
Material Removal ◽  
Removal Rate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamic Contact ◽  
Machining Process ◽  
Ultrasonic Machining ◽  
Factors Affecting ◽  
Good Agreement

This paper presents a dynamic analysis of the ultrasonic machining process based on impact mechanics. Equations representing the dynamic contact force and stresses caused by the impinging of abrasive grits on the work, are obtained by solving the three-dimensional equations of motion. The factors affecting the material removal rate have been studied. It is found that the theoretical estimates obtained from the dynamic model are in good agreement with the experimental results.

scholarly journals Nonlinear interactions in deformable container cranes

2015 ◽  
Vol 230 (1) ◽  
pp. 5-20 ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara ◽  
Matthew P Cartmell
Keyword(s):  
Rigid Body ◽  
Internal Resonance ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Higher Order ◽  
Mode Shapes ◽  
Lagrange Equations ◽  
Internal Resonances ◽  
Container Cranes ◽  
Bending Mode

Nonlinear dynamic interactions in harbour quayside cranes due to a two-to-one internal resonance between the lowest bending mode of the deformable boom and the in-plane pendular mode of the container are investigated. To this end, a three-dimensional model of container cranes accounting for the elastic interaction between the crane boom and the container dynamics is proposed. The container is modelled as a three-dimensional rigid body elastically suspended through hoisting cables from the trolley moving along the crane boom modelled as an Euler-Bernoulli beam. The reduced governing equations of motion are obtained through the Euler-Lagrange equations employing the boom kinetic and stored energies, derived via a Galerkin discretisation based on the mode shapes of the two-span crane boom used as trial functions, and the kinetic and stored energies of the rigid body container and the elastic hoisting cables. First, conditions for the onset of internal resonances between the boom and the container are found. A higher order perturbation treatment of the Taylor expanded equations of motion in the neighbourhood of a two-to-one internal resonance between the lowest boom bending mode and the lowest pendular mode of the container is carried out. Continuation of the fixed points of the modulation equations together with stability analysis yields a rich bifurcation behaviour, which features Hopf bifurcations. It is shown that consideration of higher order terms (cubic nonlinearities) beyond the quadratic geometric and inertia nonlinearities breaks the symmetry of the bifurcation equations, shifts the bifurcation points and the stability ranges, and leads to bifurcations not predicted by the low order analysis.

Penalty Formulations for the Dynamic Analysis of Elastic Mechanisms

1989 ◽  
Vol 111 (3) ◽  
pp. 321-327 ◽  
Author(s):  
E. Bayo ◽  
M. A. Serna
Keyword(s):  
Finite Element Method ◽  
Dynamic Analysis ◽  
Simulation Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Body Motion ◽  
The Finite Element Method ◽  
Floating Frame ◽  
Flexible Mechanisms

A series of penalty methods are presented for the dynamic analysis of flexible mechanisms. The proposed methods formulate the equations of motion with respect to a floating frame that follows the rigid body motion of the links. The constraint conditions are not appended to the Lagrange’s equations in the form of algebraic or differential constraints, but inserted in them by means of a penalty formulation, and therefore the number of equations of the system does not increase. Furthermore, the discretization of the equations using the finite element method leads to a system of ordinary differential equations that can be solved using standard numerical algorithms. The proposed methods are valid for three dimensional analysis and can be very easily implemented in existing codes. Furthermore, they can be used to model any type of constraint conditions, either holonomic or nonholonomic, and with any degree of redundancy. A series of mechanisms composed of elastic members are analyzed. The results demonstrate the capabilities of the proposed methods for simulation analysis.

Dynamics of Flexible Mechanical Systems Using Vibration and Static Correction Modes

1986 ◽  
Vol 108 (3) ◽  
pp. 315-322 ◽  
Author(s):  
W. S. Yoo ◽  
E. J. Haug
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Elastic Deformation ◽  
Large Scale ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonlinear Dynamic Analysis ◽  
Mode Analysis ◽  
Lumped Mass ◽  
Static Correction

A finite-element-based method is developed and applied for geometrically nonlinear dynamic analysis of spatial mechanical systems. Vibration and static correction modes are used to account for linear elastic deformation of components. Boundary conditions for vibration and static correction mode analysis are defined by kinematic constraints between components of a system. Constraint equations between flexible bodies are derived and a Lagrange multiplier formulation is used to generate the coupled large displacement-small deformation equations of motion. A standard, lumped mass finite-element structural analysis code is used to generate deformation modes and deformable body mass and stiffness information. An intermediate-processor is used to calculate time-independent terms in the equations of motion and to generate input data for a large-scale dynamic analysis code that includes coupled effects of geometric nonlinearity and elastic deformation. Two examples are presented and the effects of deformation mode selection on dynamic prediction are analyzed.

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