Nonlinear Effects in Dynamic Analysis of Flexible Multibody Systems

2001 ◽  
Author(s):  
Y. C. Mbono Samba ◽  
M. Pascal
Keyword(s):  
Rigid Body ◽  
Standard Method ◽  
Multibody Systems ◽  
Nonlinear Effects ◽  
Elastic Deformations ◽  
Dynamics Of Multibody Systems ◽  
Flexible Parts ◽  
Order Of Magnitude ◽  
Rigid Body Motions ◽  
Crank Mechanism

Abstract The work is concerned with the dynamics of multibody systems with flexible parts undergoing large rigid body motions and small elastic deformations. The standard method used in most cases leads to keep only linear terms with respect to the deformations. However, for large rates or large accelerations, this linearisation is sometimes too premature. In this work, a non dimensional analysis of the system is performed, with some estimate about the order of magnitude of the different parameters occuring in the dynamical model obtained by Kane’s method [1]. A flexible slider crank mechanism is used as a test example, together with AUTOLEV [2] software for numerical results.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

The Use of Vector Techniques in Variational Problems

1986 ◽  
Vol 108 (2) ◽  
pp. 141-145 ◽  
Author(s):  
L. J. Everett ◽  
M. McDermott
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Double Pendulum ◽  
Coordinate Transformations ◽  
Elastic Deformations ◽  
Variational Techniques ◽  
Convenient Means ◽  
Moving Coordinate ◽  
Rigid Body Motions

A convenient means for applying vector mathematics to variational problems is presented. The total and relative variations of a vector are defined and results which follow from these definitions are developed and proved. These results are then used to express the variation of a functional using vector techniques rather than the classical scalar or matrix techniques. The simple problems of deriving equations of motion for a rigid body and for a rigid double pendulum are presented as examples of the technique. The key advantages of the method are that (1) it allows the investigator who is familiar and proficient with vector techniques to apply these skills to variational problems and (2) it greatly simplifies the application of variational techniques to problems which include both rigid body motions and elastic deformations. This is accomplished by providing the techniques necessary for computing the variation of a vector defined in a moving coordinate system without using coordinate transformations.

A Variational Principle for the Elastodynamic Motion of Planar Linkages

1976 ◽  
Vol 98 (4) ◽  
pp. 1306-1312 ◽  
Author(s):  
B. S. Thompson ◽  
A. D. S. Barr
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Problem Definition ◽  
Compatibility Conditions ◽  
Elastic Deformations ◽  
Rigid Body Motions ◽  
Planar Linkages ◽  
Crank Mechanism ◽  
Approximate Equations ◽  
Motion Boundary

A variational principle is presented that may be used for setting up the equations describing the elastodynamic motion of planar linkages in which all the members are considered to be flexible. These systems are modeled as a set of continua in which elastic deformations are superimposed on gross rigid-body motions. Displacement continuity at pin joints, or any other special constraints that are peculiar to the linkage being analyzed, are incorporated by the use of Lagrange multipliers. By permitting independent variations of the stress, strain, displacement, and velocity parameters for each link approximate equations of motion, boundary and compatibility conditions for the complete mechanism may be systematically constructed. As an illustrative example, the derivation of the problem definition for a flexible slider-crank mechanism is given.

Dynamic Response of Composite Pressure Vessels to Inertia Loads

1991 ◽  
Vol 113 (1) ◽  
pp. 86-91
Author(s):  
J. C. Prucz ◽  
J. D’Acquisto ◽  
J. E. Smith
Keyword(s):  
Rigid Body ◽  
Combustion Engine ◽  
Pressure Vessels ◽  
Body Motion ◽  
Connecting Rod ◽  
Filament Wound ◽  
Potential Benefits ◽  
Rigid Body Motions ◽  
Crank Mechanism ◽  
Selection Of

A new analytical model has been developed in order to investigate the potential benefits of using fiber-reinforced composites in pressure vessels that undergo rigid-body motions. The model consists of a quasi-static lamination analysis of a cylindrical, filament-wound, pressure vessel, combined with an elastodynamic analysis that accounts for the coupling effects between its rigid-body motion and its elastic deformations. The particular type of motion investigated in this paper is that of an oil-pressurized, tubular connecting rod in a slider-crank mechanism of an internal combustion engine. A comprehensive parametric study has been focused on the maximum wall stresses induced in such a rod by the combined effect of internal pressure and inertia loads associated with its motion. The numerical results illustrate potential ways to reduce these stresses by appropriate selection of material systems, lay-up configurations and geometric parameters.

scholarly journals On the relations between kinetic energy and linear momentum, angular momentum of the particle and of the rigid body

2001 ◽  
Vol 23 (2) ◽  
pp. 110-115
Author(s):  
Nguyen Van Khang
Keyword(s):  
Angular Momentum ◽  
Kinetic Energy ◽  
Rigid Body ◽  
Partial Derivative ◽  
Multibody Systems ◽  
Linear Momentum ◽  
Dynamics Of Multibody Systems

Using the definition for the partial derivative of a scalar in respect to the vector, this paper presents the relations between kinetic energy and linear momentum, angular momentum of the particle and of the rigid body. The obtained results are useful for the investigation of the dynamics of multibody systems

Modeling a Robot With Flexible Joints and Decoupling its Equations of Motion

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Flexible Joints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Recent Advances ◽  
Dynamics Of Multibody Systems ◽  
Two Degree Of Freedom

Abstract Recent advances in the study of dynamics of multibody systems indicate the need for decoupling of the equations of motion. In this paper, our efforts are focused on this issue, and we have tried to expand the existing methods for multi-rigid body systems to include systems with some kind of flexibility. In this regard, the equations of motion for a planar two-degree-of-freedom robot with flexible joints is carried out using Lagrange’s equations and Kane’s equations with congruency transformations. The method of decoupling the equations of motion using Kane’s equations with congruency transformations is presented. Finally, the results obtained from both methods are compared.

Effects of Hull Flexibility on the Structural Dynamics of a TLP Floating Wind Turbine

2018 ◽  
Author(s):  
Carlos Eduardo Silva de Souza ◽  
Erin E. Bachynski
Keyword(s):  
Rigid Body ◽  
Wind Turbine ◽  
Fatigue Damage ◽  
Flexible Structures ◽  
Structural Response ◽  
Secondary Importance ◽  
Fatigue Damage Accumulation ◽  
Fatigue Damage Analysis ◽  
Order Of Magnitude ◽  
Rigid Body Motions

Structural analysis of floating wind turbines is normally carried out with the hull considered as a rigid body. This paper explores the consequences of modeling the pontoons of a tension leg platform (TLP) wind turbine as flexible structures. The analysis is based on numerical simulations of free decays, structural response to wave excitation and short-term fatigue damage accumulation at chosen points of the platform. In addition, the importance of considering hydroelasticity effects is evaluated. It is observed that pontoon flexibility can change the platform natural periods significantly, as well as the intensity and peak frequencies of internal structural loads. The adoption of a fully rigid-body is shown to be non-conservative for the fatigue damage analysis. Loads due to hydroelasticity have order of magnitude comparable to those related to rigid-body motions, but still lower enough to be considered of secondary importance.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

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