scholarly journals Multi-Flexible Body Dynamics Capturing Motion-Induced Stiffness

1991 ◽  
Vol 58 (3) ◽  
pp. 766-775 ◽  
Author(s):  
A. K. Banerjee ◽  
M. E. Lemak
Keyword(s):  
Equations Of Motion ◽  
The Body ◽  
Flexible Body ◽  
Dynamical Equations ◽  
Large Rotation ◽  
Geometric Stiffness ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Inertia Forces ◽  
Modal Coordinates

This paper presents a multi-flexible-body dynamics formulation incorporating a recently developed theory for capturing motion-induced stiffness for an arbitrary structure undergoing large rotation and translation accompanied by small vibrations. In essence, the method consists of correcting dynamical equations for an arbitrary flexible body, unavoidably linearized prematurely in modal coordinates, with generalized active forces due to geometric stiffness corresponding to a system of 12 inertia forces and 9 inertia couples distributed over the body. Computation of geometric stiffness in this way does not require any iterative update. Equations of motion are derived by means of Kane’s method. A treatment is given for handling prescribed motions and calculating interaction forces. Results of simulations of motions of three flexible spacecraft, involving stiffening during spinup motion, dynamic buckling, and a slewing maneuver, demonstrate the validity and generality of the theory.

A Recursive Implementation Method With Implicit Integrator for Multibody Dynamics

2001 ◽  
Author(s):  
H. J. Cho ◽  
H. S. Ryu ◽  
D. S. Bae ◽  
J. H. Choi ◽  
B. Ross
Keyword(s):  
Equations Of Motion ◽  
Flexible Body ◽  
Differential Algebraic Equation ◽  
Dynamic Correction ◽  
Body Dynamics ◽  
Mode Method ◽  
Numerical Integrators ◽  
Flexible Body Dynamics ◽  
Body Concept ◽  
Implementation Method

Abstract A recursive implementation method for the equations of motion and kinematics is presented. Computational structure of the kinematic and dynamic equations is exploited to systematically implement a dynamic analysis program RecurDyn. A differential algebraic equation solution method with implicit numerical integrators is discussed. Virtual body concept is introduced for the flexible body dynamics. The accuracy of the flexible body solutions is estimated by an error measure and is improved by the dynamic correction mode method. Several examples are solved to demonstrate the efficiency of the proposed methods.

Dynamic Analysis of Flexible Multi-Body Systems With Time-Variant Mode Shapes

1991 ◽  
Author(s):  
F. M. L. Amirouche ◽  
M. Xie
Keyword(s):  
Equations Of Motion ◽  
Rate Of Change ◽  
Mode Shapes ◽  
Flexible Body ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Application Problem ◽  
Nodal Coordinates ◽  
Multi Body ◽  
Modal Coordinates

Abstract The paper extends the theory of flexible multi-body systems to include time-variant mode shapes to account for the changes of boundary conditions that a flexible body undergoes while in motion. The method presented herein makes use of finite element methods to discretize the elastic body, then the nodal coordinates are related to the modal coordinates through the mode shapes. The latter are computed separately and their rate of change is accounted for in the dynamical equations of motion. The resulting governing equations of motion are presented in a computer form and a possible application problem is proposed.

A Virtual Body and Joint for Constrained Flexible Multibody Dynamics: A Generalized Recursive Formulation

1999 ◽  
Author(s):  
D. S. Bae ◽  
J. M. Han ◽  
J. H. Choi
Keyword(s):  
Rigid Body ◽  
Reference Frames ◽  
Equations Of Motion ◽  
Recursive Formula ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Flexible Body ◽  
Relative Coordinate ◽  
Body Dynamics ◽  
Flexible Body Dynamics

Abstract This research extends the generalized recursive formulas for the rigid body dynamics to the flexible body dynamics using the backward difference formula (BDF) and the relative generalized coordinate. When a new force or joint module is added to a general purpose program in the relative coordinate formulations, the modules for the rigid bodies are not reusable for the flexible bodies. Since the flexible body dynamics handles more degrees of freedom than the rigid body dynamics does, implementation of the flexible dynamics module is generally complicated and prone to coding mistakes. In order to overcome the implementation difficulties, a virtual rigid body is introduced at every joint and force reference frames. A virtual flexible body joint is introduced between two body reference frames of the virtual and original bodies. Since the multibody system dynamics are formulated by highly nonlinear algebraic and differential equations and there are many different types of joints, a tremendous amount of computer implementation is required to develop a general purpose dynamic analysis program using the relative coordinate formulation. The implementation burden is relieved by the generalized recursive formulas. The notationally compact velocity transformation method is used to derive the equations of motion in the joint space. The terms in the equations of motion which are related to the transformation matrix are classified into several categories each of which recursive formula is developed. Whenever one category of the terms is encountered, the corresponding recursive formula is invoked. Since computation time in a relative coordinate formulation is approximately proportional to the number of the relative coordinates, computational overhead due to the additional virtual bodies and joints is minor. Meanwhile, implementation convenience is dramatically improved.

Dynamics of Flexible Body Negotiating a Curve

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Huailong Shi ◽  
Liang Wang ◽  
Ahmed A. Shabana
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Flexible Body ◽  
Motion Trajectory ◽  
Centrifugal Forces ◽  
Coriolis Forces ◽  
Body Dynamics ◽  
Body Reference

When a rigid body negotiates a curve, the centrifugal force takes a simple form which is function of the body mass, forward velocity, and the radius of curvature of the curve. In this simple case of rigid body dynamics, curve negotiation does not lead to Coriolis forces. In the case of a flexible body negotiating a curve, on the other hand, the inertia of the body becomes function of the deformation, curve negotiations lead to Coriolis forces, and the expression for the deformation-dependent centrifugal forces becomes more complex. In this paper, the nonlinear constrained dynamic equations of motion of a flexible body negotiating a circular curve are used to develop a systematic procedure for the calculation of the centrifugal forces during curve negotiations. The floating frame of reference (FFR) formulation is used to describe the body deformation and define the nonlinear centrifugal and Coriolis forces. The algebraic constraint equations which define the motion trajectory along the curve are formulated in terms of the body reference and elastic coordinates. It is shown in this paper how these algebraic motion trajectory constraint equations can be used to define the constraint forces that lead to a systematic definition of the resultant centrifugal force in the case of curve negotiations. The embedding technique is used to eliminate the dependent variables and define the equations of motion in terms of the system degrees of freedom. As demonstrated in this paper, the motion trajectory constraints lead to constant generalized forces associated with the elastic coordinates, and as a consequence, the elastic velocities and accelerations approach zero in the steady state. It is also shown that if the motion trajectory constraints are imposed on the coordinates of a flexible body reference that satisfies the mean-axis conditions, the centrifugal forces take the same form as in the case of rigid body dynamics. The resulting flexible body dynamic equations can be solved numerically in order to obtain the body coordinates and evaluate numerically the constraint and centrifugal forces. The results obtained for a flexible body negotiating a circular curve are compared with the results obtained for the rigid body in order to have a better understanding of the effect of the deformation on the centrifugal forces and the overall dynamics of the body.

On the Geometric Stiffness Matrices in Flexible Multibody Dynamics

1995 ◽  
Vol 117 (4) ◽  
pp. 452-461 ◽  
Author(s):  
S. S. K. Tadikonda ◽  
H. T. Chang
Keyword(s):  
Multibody Systems ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Joint Simulation ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
Body Dynamics ◽  
Geometric Stiffening ◽  
Flexible Body Dynamics ◽  
Self Motion

A flexible branch body in a multibody chain undergoing large overall motions experiences geometric stiffening effects due to its own motions and interbody forces arising from bodies outboard of it. The self-motion effects are modelled through the use of 21 geometric stiffness matrices, in the literature, for an arbitrarily shaped flexible body. In this paper, the effect of interbody forces on the flexible body dynamics is modelled using up to 6 additional geometric stiffness matrices per outboard joint. Simulation results presented indicate that for a flexible body consisting of outboard bodies one may consider only the interbody force effects, without loss of accuracy, and thus significantly reduce the computational burden. This approach is especially suitable for multibody systems such as the Shuttle Remote Manipulator System, where the long boom masses are of similar magnitude, or when the payloads are several orders of magnitude larger than the link masses.

scholarly journals Coupled simulation of elastohydrodynamics and multi-flexible body dynamics in piston-lubrication system

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989585 ◽  
Author(s):  
Seongsu Kim ◽  
Juhwan Choi ◽  
Jin-Gyun Kim ◽  
Ryo Hatakeyama ◽  
Hiroshi Kuribara ◽  
...  
Keyword(s):  
Cylinder Block ◽  
Flexible Body ◽  
Asperity Contact ◽  
Lubrication System ◽  
Film Pressure ◽  
Oil Film ◽  
Piston Skirt ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Oil Film Pressure

In this work, we propose a robust modeling and analysis technique of the piston-lubrication system considering fluid–structure interaction. The proposed schemes are based on combining the elastohydrodynamic analysis and multi-flexible body dynamics. In particular, multi-flexible body dynamics analysis can offer highly precise numerical results regarding nonlinear deformation of the piston skirt and cylinder bore, which can lead to more accurate results of film thickness for gaps filled with lubricant and of relative velocity of facing surfaces between the piston skirt and the cylinder block. These dynamic analysis results are also used in the elastohydrodynamic analysis to compute the oil film pressure and asperity contact pressure that are used as external forces to evaluate the dynamic motions of the flexible bodies. A series of processes are repeated to accurately predict the lubrication characteristics such as the clearance and oil film pressure. In addition, the Craig–Bampton modal reduction, which is a standard type of component mode synthesis, is employed to accelerate the computational speed. The performance of the proposed modeling schemes implemented in the RecurDyn™ multi-flexible body dynamics environment is demonstrated using a well-established numerical example, and the proposed simulation methods are also verified with the experimental results in a motor cycle engine (gasoline) which has a four cycle, single cylinder, overhead camshaft (OHC), air cooled.

Parallel Algorithm for Modeling Constrained Multi-Flexible Body System Dynamics

2013 ◽  
Author(s):  
Rudranarayan Mukherjee ◽  
Jeremy Laflin
Keyword(s):  
Parallel Implementation ◽  
Equations Of Motion ◽  
Small Deformation ◽  
The Body ◽  
Deformation Field ◽  
Flexible Body ◽  
Disassembly Process ◽  
Joint Constraints ◽  
Kinematic Loop ◽  
Kinematic Joint

This paper presents an algorithm for modeling the dynamics of multi-flexible body systems in closed kinematic loop configurations where the component bodies are modeled using the large displacement small deformation formulation. The algorithm uses a hierarchic assembly disassembly process in parallel implementation and a recursive assembly disassembly process in serial implementation to achieve highly efficient simulation turn-around times. The operational inertias arising from the rigid body modes of motion at the joint locations on a component body are modified to account for the nonlinear inertial effects and body forces arising from the body based deformations. Traditional issues, such as motion induced stiffness and temporal invariance of deformation field related inertia terms, are robustly addressed in this algorithm. The algorithm uses a mixed set of coordinates viz. (i) absolute coordinates for expressing the equations of motion of a body fixed reference frame, (ii) relative or internal coordinates to express the kinematic joint constraints and (iii) body fixed coordinates to account for the body’s deformation field. The kinematic joint constraints and the closed loop constraints are treated alike through the formalism of relative coordinates, joint motion spaces and their orthogonal complements. Verification of the algorithm is demonstrated using the planar fourbar mechanism problem that has been traditionally used in literature.

Anguilliform body dynamics: modelling the interaction between muscle activation and body curvature

1991 ◽  
Vol 334 (1271) ◽  
pp. 385-390 ◽  
Keyword(s):  
Muscle Activation ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Travelling Wave ◽  
The Body ◽  
Linear Functions ◽  
Careful Examination ◽  
Body Tissues ◽  
Body Dynamics ◽  
Dynamics Modelling

A simple two-dimensional rod and pivot model is proposed for the mechanical structure of the lamprey, each pivot being controlled by a muscle segment attached via perpendicular extensions to the two rods. The elastic and viscous properties of the body tissues (including muscle) are described as linear functions of the relative displacement and angular velocity of the rods at each pivot. The contractile properties of the muscle are introduced as time-dependent forcing torques at the pivots, which are generated by a travelling wave of activation. The angles between the rods at each pivot are used as adapted coordinates, and the equations of motion are linearized by assuming low curvature dynamics, corresponding to slow swimming speeds. Investigation of these equations with varying viscous and elastic parameters leads to a reconstruction of a lamprey viewed in motion on a smooth flat surface out of water. The most striking feature is of an apparently standing wave motion, which is indeed observed in the real animal but which on careful examination in the model corresponds to a travelling wave of varying amplitude.

Generalized Constraint and Joint Reaction Forces in the Inverse Dynamics of Spatial Flexible Mechanical Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 777-784 ◽  
Author(s):  
D. C. Chen ◽  
A. A. Shabana ◽  
J. Rismantab-Sany
Keyword(s):  
Inverse Dynamics ◽  
Mechanical Systems ◽  
Flexible Body ◽  
Body Dynamics ◽  
Joint Reaction Forces ◽  
Flexible Body Dynamics ◽  
Reaction Forces ◽  
Applied Forces ◽  
Generalized Constraint ◽  
Joint Reaction

In both the augmented and recursive formulations of the dynamic equations of flexible mechanical systems, the inerita, constraints, and applied forces must be properly defined. The inverse dynamics is a commonly used approach for the force analysis of mechanical systems. In this approach, the system is kinematically driven using specified motion trajectories, and the objective is to determine the driving forces and torques. In flexible body dynamics, however, a force that acts at a point on the deformable body is equipollent to a system, defined at another point, that consists of the same force, a moment that depends on the relative deformation between the two points, and a set of generalized forces associated with the elastic coordinates. Furthermore, a moment in flexible body dynamics is no longer a free vector. It is defined by the location of its line of action as well as its magnitude and direction. The joint reaction and generalized constraint forces represent equipollent systems of forces. Both systems in flexible body dynamics are function of the deformation. In this investigation, a procedure is developed for the determination of the joint reaction forces in spatial flexible mechanical systems. The mathematical formulation of some mechanical joints that are often encountered in the analysis of constrained flexible mechanical systems is discussed. Expressions for the generalized reaction forces in terms of the constraint Jacobian matrices of the joints are presented. The effect of the elastic deformation on the reaction forces is also examined numerically using the spatial flexible multibody RSSR mechanism that consists of a set of interconnected rigid and elastic bodies. The procedure described in this investigation can also be used to determine the joint torques and actuator forces in kinematically driven spatial elastic mechanism and manipulator systems.

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