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.

Dynamic Analysis of Mechanical Systems With Intermittent Motion

1982 ◽  
Vol 104 (4) ◽  
pp. 778-784 ◽  
Author(s):  
R. A. Wehage ◽  
E. J. Haug
Keyword(s):  
Dynamic Analysis ◽  
Numerical Integration ◽  
Large Scale ◽  
Mechanical Systems ◽  
Integration Algorithm ◽  
Large Scale Systems ◽  
Jump Discontinuities ◽  
Impulsive Forces ◽  
Computer Generation ◽  
Intermittent Motion

A method is presented for dynamic analysis of systems with impulsive forces, impact, discontinuous constraints, and discontinuous velocities. A method of computer generation of the equations of planar motion and impulse-momentum relations that define jump discontinuities in system velocity for large scale systems is presented. An event predictor, working in conjunction with a new numerical integration algorithm, efficiently controls the numerical integration and allows for automatic equation reformulation. A weapon mechanism and a trip plow are simulated using the method to illustrate its capabilities.

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.

Recursive Method for the Dynamic Analysis of Open-Loop Flexible Multibody Systems

2003 ◽  
Author(s):  
Yunn-Lin Hwang
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Recursive Method ◽  
Flexible Bodies ◽  
System Equations ◽  
Generalized Newton ◽  
Time Invariant

The main objective of this paper is to develop a recursive method for the dynamic analysis of open-loop flexible multibody systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve for the equations of motion for open-loop systems consisting of interconnected rigid and flexible bodies is presented in this investigation. This method applies recursive method with the generalized Newton-Euler method for flexible bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the vector or digital computer systems. The algorithms presented in this investigation are illustrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The basic recursive formulations developed in this paper are demonstrated by two numerical examples.

Automated Dynamic Analysis of Chain-Driven Mechanical Systems

1983 ◽  
Vol 105 (3) ◽  
pp. 362-370 ◽  
Author(s):  
Ting W. Lee
Keyword(s):  
Dynamic Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Dynamic Effect ◽  
General Purpose ◽  
Displacement Function ◽  
Analysis And Design ◽  
Driven System ◽  
Chain Dynamic ◽  
System Equations

A general approach to analyze the dynamics of chain-driven systems subjected to transient loads is developed and applied. The method suitable for many automated dynamic analysis techniques involves the simulation of the dynamic effect of chain by a displacement function and the introduction of this function as a kinematic constraint to couple with the system equations of motion. A general purpose dynamic analysis algorithm, the DADS code (Dynamic Analysis and Design Systems), is then employed to generate the set of system equations and to provide a computer-aided dynamic analysis of the overall chain-driven system. Two ways of formulating the chain displacement functions are described. One provides the displacement of the chain based on the pitch circles of chain sprockets; the other includes a consideration of the polygonal effect of the chain which contributes essentially to the dynamics of the chain. The latter involves the use of the principle of kinematic equivalency, i.e., modeling the chain dynamic effect by a four-bar linkage. Using the proposed displacement function, the kinematic motion of the chain can be taken into account. This procedure, therefore, makes the system adaptable to conventional dynamic analysis code in which the chain is usually not included as one of the standard elements. Moreover, pulsation and dynamic load of the chain as well as the system dynamic response due to chain effect may be estimated. A typical large-scale chain-driven system which is an externally powered machine gun is investigated to illustrate the potential usefulness of the approach.

scholarly journals An Equivalent Non-uniform Beam-like Model for Dynamic Analysis of Multi-storey Irregular Buildings

2020 ◽  
Author(s):  
Annalisa Greco ◽  
Ilaria Fiore ◽  
Giuseppe Occhipinti ◽  
Salvatore Caddemi ◽  
Daniele Spina ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Large Scale ◽  
Numerical Models ◽  
Equations Of Motion ◽  
Uniform Beam ◽  
Uniform Shear ◽  
Modes Of Vibration ◽  
Urban Level ◽  
Torsional Beam ◽  
Computational Procedures

Dynamic analyses and seismic assessments of multi-storey buildings at urban level require large-scale simulations and computational procedures based on simplified but accurate numerical models. At this aim the present paper propos-es an equivalent non-uniform beam-like model, suitable for the dynamic analysis of buildings with asymmetric plan and non-uniform vertical distribution of mass and stiffness. The equations of motion of this beam-like model, which pre-sents only shear and torsional deformability, are derived through the application of Hamilton’s principle. The linear dy-namic behaviour is evaluated by discretizing the continuous non-uniform model according to a Rayleigh-Ritz approach based on a suitable number of modal shapes of the uniform shear-torsional beam. In spite of its simplicity, the model is able to reproduce the dynamic behaviour of low- and mid-rise buildings with a significant reduction of the computa-tional burden with respect to that required by more general models. The efficacy of the proposed approach has been tested, by means of comparisons with linear FEM simulations, on three multi-storey buildings characterized by different irregularities. The satisfactory agreement, in terms of natural frequencies, modes of vibration and seismic response, proves the capability of the proposed approach to reproduce the dynamic response of complex spatial multi storey frames.

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.

Design Sensitivity Analysis of Large-Scale Constrained Dynamic Mechanical Systems

1984 ◽  
Vol 106 (2) ◽  
pp. 156-162 ◽  
Author(s):  
E. J. Haug ◽  
R. A. Wehage ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Adjoint Equations ◽  
Design Sensitivity Analysis ◽  
Integration Algorithm ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

A method for computer-aided design sensitivity analysis of large-scale constrained dynamic systems is presented. A generalized coordinate partitioning method is used for assembling and solving sets of mixed differential-algebraic equations of motion and adjoint equations required for calculation of derivatives of dynamic response measures with respect to design variables. The reduction in dimension of the equations of motion and associated adjoint equations obtained through use of generalized coordinate partitioning significantly reduces the computational burden, as compared to methods previously employed. Use of predictor-corrector numerical integration algorithms, rather than an implicit integration algorithm used in the past is shown to greatly simplify the equations that must be formulated and solved. Two examples are presented to illustrate accuracy of the design sensitivity analysis method developed.

Dynamic Analysis of Flexible Gear Trains/Transmissions: An Automated Approach

1991 ◽  
Author(s):  
F. M. L. Amirouche ◽  
N. H. Shareef ◽  
M. Xie
Keyword(s):  
Dynamic Analysis ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Elastic Behavior ◽  
Flexible Bodies ◽  
Gear Teeth ◽  
Six Degrees Of Freedom ◽  
Contact Information ◽  
Gear Trains

Abstract In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of inter-connected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of 3-D isoparametric elements having six degrees of freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions together with the equations of motion using Kane’s method, strain energy concepts are presented in a matrix form suitable for computer implementation. The constraint jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.

scholarly journals Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages

2005 ◽  
Vol 46 (4) ◽  
pp. 575-589
Author(s):  
Hazem Ali Attia
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Constraint Forces ◽  
Constrained System ◽  
Open Chain ◽  
Closed Chain ◽  
Efficient Integration ◽  
Planar Linkages

AbstractThis paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

scholarly journals An Equivalent Non-Uniform Beam-Like Model for Dynamic Analysis of Multi-Storey Irregular Buildings

2020 ◽  
Vol 10 (9) ◽  
pp. 3212 ◽  
Author(s):  
Annalisa Greco ◽  
Ilaria Fiore ◽  
Giuseppe Occhipinti ◽  
Salvatore Caddemi ◽  
Daniele Spina ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Large Scale ◽  
Dynamic Behaviour ◽  
Numerical Models ◽  
Equations Of Motion ◽  
Element Model ◽  
Uniform Beam ◽  
Uniform Shear ◽  
Modes Of Vibration ◽  
Computational Procedures

Dynamic analyses and seismic assessments of multi-storey buildings at the urban level require large-scale simulations and computational procedures based on simplified but accurate numerical models. For this aim, the present paper proposes an equivalent non-uniform beam-like model, suitable for the dynamic analysis of buildings with an asymmetric plan and non-uniform vertical distribution of mass and stiffness. The equations of motion of this beam-like model, which presents only shear and torsional deformability, were derived through the application of Hamilton’s principle. The linear dynamic behaviour was evaluated by discretizing the continuous non-uniform model according to a Rayleigh–Ritz approach based on a suitable number of modal shapes of the uniform shear-torsional beam. In spite of its simplicity, the model is able to reproduce the dynamic behaviour of low- and mid-rise buildings with a significant reduction of the computational burden with respect to that required by more general models. The efficacy of the proposed approach was tested, by means of comparisons with linear Finite Element Model (FEM) simulations, on three multi-storey buildings characterized by different irregularities. The satisfactory agreement, in terms of natural frequencies, modes of vibration and seismic response, proves the capability of the proposed approach to reproduce the dynamic response of complex spatial multi-storey frames.

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