scholarly journals Consistent structural linearisation in flexible-body dynamics with large rigid-body motion

2012 ◽  
Vol 110-111 ◽  
pp. 1-14 ◽  
Author(s):  
Henrik Hesse ◽  
Rafael Palacios
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Body ◽  
Body Dynamics ◽  
Flexible Body Dynamics

Development of a New Multi-Flexible Body Dynamics (MFBD) Platform: A Relative Nodal Displacement Method for Finite Element Analysis

2005 ◽  
Author(s):  
Dae Sung Bae
Keyword(s):  
Rigid Body ◽  
Reference Frame ◽  
Large Deformations ◽  
Shape Function ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Body ◽  
Element Analysis ◽  
Body Dynamics ◽  
Flexible Body Dynamics

Recently the analysis of multi flexible body dynamics has been a hot issue in the area of the computational dynamics research. There have been two main streams of research. One is the extension of conventional FEA theory for the multi flexible body systems, using either the total Lagrangian or updated Lagrangian method. The other is the extension of the multi body dynamics theory. The latter is the topic of this research. One essential requirement of a shape function in FEA theory is ability to represent the rigid body motion. This research proposes to use the moving reference frame to represent the rigid body motion. Therefore, the shape function does not need to have ability to represent the rigid body motion. The moving reference frame covers the rigid body. Since the nodal displacements are measured relative to its adjacent moving nodal reference frame, they are still small for a truss structure undergoing large deformations if the element sizes are small. As a consequence, many element formulations developed under small deformation assumptions are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. Several numerical examples are analyzed to demonstrate the efficiency and validity of the proposed method.

A Virtual Body and Joint for Constrained Flexible Multibody Dynamics

1999 ◽  
Author(s):  
D. S. Bae ◽  
J. M. Han ◽  
J. H. Choi
Keyword(s):  
Rigid Body ◽  
Multibody Dynamics ◽  
Reference Frames ◽  
Flexible Multibody Dynamics ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Flexible Body ◽  
Body Dynamics ◽  
Flexible Multibody ◽  
Flexible Body Dynamics

Abstract A convenient implementation method for constrained flexible multibody dynamics is presented by introducing virtual rigid body and joint. The general purpose program for rigid and flexible multibody dynamics consists of three major parts of a set of inertia modules, a set of force modules, and a set of joint modules. Whenever a new force or joint module is added to the general purpose program, the modules for the rigid body dynamics are not reusable for the flexible body dynamics. Consequently, the corresponding modules for the flexible body dynamics must be formulated and programmed again. Since the flexible body dynamics handles more degrees of freedom than the rigid body dynamics does, implementation of the module is generally complicated and prone to coding mistakes. In order to overcome these difficulties, a virtual rigid body is introduced at every joint and force reference frames. New kinematic admissibility conditions are imposed on two body reference frames of the virtual and original bodies by introducing a virtual flexible body joint. There are some computational overheads due to the additional bodies and joints. However, since computation time is mainly depended on the frequency of flexible body dynamics, the computational overhead of the presented method could not be a critical problem, while implementation convenience is dramatically improved.

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.

Numerical and Experimental Approaches on the Motion of a Tethered System With Large Deformation, Rotation and Translation

2005 ◽  
Author(s):  
Shoichiro Takehara ◽  
Yoshiaki Terumichi ◽  
Masahiro Nohmi ◽  
Kiyoshi Sogabe ◽  
Yoshihiro Suda
Keyword(s):  
Rigid Body ◽  
Large Deformation ◽  
Numerical Solutions ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Body ◽  
Numerical Formulation ◽  
Experimental Approaches ◽  
Good Agreement

In this paper, we discuss the motion of a tethered system. In general, a tether is a cable or wire rope, and a tethered system consists of a tether and attached equipment. A tethered subsatellite in space is an example of this system. We consider the tethered system consisting of a very flexible body (the tether) and rigid bodies at one end as our analytical model. A flexible body in planer motion is described using the Absolute Nodal Coordinate Formulation. Using this method, the motion of a flexible body with large deformation, rotation and translation can be expressed with the accuracy of rigid body motion. The combination of flexible body motion and rigid body motion is performed and the interaction between them is discussed. We also performed experiments to investigate the fundamental motion of the tethered system and to evaluate the validity of the numerical formulation. The first experiments were conducted using a steel tether and rubber tether in gravity space. We also conducted experiment of the motion of the tethered system with a rigid body in microgravity space. The numerical solutions using the proposed methods for the modeling and formulation for the tethered system are in good agreement with the experimental results.

Coupling Vibration of Tapered Rod

2014 ◽  
Vol 472 ◽  
pp. 69-72
Author(s):  
Shang Wen Hu ◽  
Hong Liang Li ◽  
Yu Meng
Keyword(s):  
Free Vibration ◽  
Rigid Body ◽  
Normal Modes ◽  
Flexible Body ◽  
Coupled Vibration ◽  
Coupling Vibration ◽  
First Order ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Rigid Body Displacement

In rod's free vibration, its easy to obtain normal modes. However, if there is rigid body displacement, the problem will be much more complex. To solve these kinds of problems, single flexible body dynamics is needed. As the first part of the paper, considering rods rigid body displacement, the free vibration of tapered rod is discussed. By solving partial differential equation of rods free vibration, normal frequencies of tapered rod are obtained. As the second part of the paper, coupling vibration is discussed, in which process quasi-variational principle as the most important tool is used. Finally, first-order frequency of coupled vibration of rod is represented.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Computation of Nonlinear Response of Hydraulically Actuated Structures

1997 ◽  
Author(s):  
T. D. Burton ◽  
C. P. Baker ◽  
J. Y. Lew
Keyword(s):  
Rigid Body ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Beam ◽  
Test Bed ◽  
Ode Models ◽  
Hydraulically Actuated ◽  
Pressure Dynamics ◽  
Low Order

Abstract The maneuvering and motion control of large flexible structures are often performed hydraulically. The pressure dynamics of the hydraulic subsystem and the rigid body and vibrational dynamics of the structure are fully coupled. The hydraulic subsystem pressure dynamics are strongly nonlinear, with the servovalve opening x(t) providing a parametric excitation. The rigid body and/or flexible body motions may be nonlinear as well. In order to obtain accurate ODE models of the pressure dynamics, hydraulic fluid compressibility must generally be taken into account, and this results in system ODE models which can be very stiff (even if a low order Galerkin-vibration model is used). In addition, the dependence of the pressure derivatives on the square root of pressure results in a “faster than exponential” behavior as certain limiting pressure values are approached, and this may cause further problems in the numerics, including instability. The purpose of this paper is to present an efficient strategy for numerical simulation of the response of this type of system. The main results are the following: 1) If the system has no rigid body modes and is thus “self-centered,” that is, there exists an inherent stiffening effect which tends to push the motion to a stable static equilibrium, then linearized models of the pressure dynamics work well, even for relatively large pressure excursions. This result, enabling linear system theory to be used, appears of value for design and optimization work; 2) If the system possesses a rigid body mode and is thus “non-centered,” i.e., there is no stiffness element restraining rigid body motion, then typically linearization does not work. We have, however discovered an artifice which can be introduced into the ODE model to alleviate the stiffness/instability problems; 3) in some situations an incompressible model can be used effectively to simulate quasi-steady pressure fluctuations (with care!). In addition to the aforementioned simulation aspects, we will present comparisons of the theoretical behavior with experimental histories of pressures, rigid body motion, and vibrational motion measured for the Battelle dynamics/controls test bed system: a hydraulically actuated system consisting of a long flexible beam with end mass, mounted on a hub which is rotated hydraulically. The low order ODE models predict most aspects of behavior accurately.

Structures of the Phosphazenes [ClC(NPCl3)2]+PCl6 − and [CH3C(NPCl3)2]+SbCl6 − at 90 K

1997 ◽  
Vol 53 (6) ◽  
pp. 953-960 ◽  
Author(s):  
F. Belaj
Keyword(s):  
Rigid Body ◽  
Motion Analysis ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Torsion Angles ◽  
Ionic Compounds ◽  
Intramolecular Motions

The asymmetric units of both ionic compounds [N-(chloroformimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachlorophosphate, [ClC(NPCl3)2]+PCl^{-}_{6} (1), and [N-(acetimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachloroantimonate, [CH3C(NPCl3)2]+SbCl^{-}_{6} (2), contain two formula units with the atoms located on general positions. All the cations show cis–trans conformations with respect to their X—C—N—P torsion angles [X = Cl for (1), C for (2)], but quite different conformations with respect to their C—N—P—Cl torsion angles. Therefore, the two NPCl3 groups of a cation are inequivalent, even though they are equivalent in solution. The very flexible C—N—P angles ranging from 120.6 (3) to 140.9 (3)° can be attributed to the intramolecular Cl...Cl and Cl...N contacts. A widening of the C—N—P angles correlates with a shortening of the P—N distances. The rigid-body motion analysis shows that the non-rigid intramolecular motions in the cations cannot be explained by allowance for intramolecular torsion of the three rigid subunits about specific bonds.

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