Nonlinear Dynamics of a Flexible Multirod (Multibeam) System

1998 ◽  
Vol 120 (2) ◽  
pp. 224-231 ◽  
Author(s):  
E. Edelstein ◽  
A. Rosen
Keyword(s):  
Equations Of Motion ◽  
Rigid Bodies ◽  
Elastic Model ◽  
Axial Motion ◽  
Lagrange Method ◽  
Flexible Rods ◽  
Rigid Body Motions ◽  
New Formulation ◽  
Nonlinear Numerical Model ◽  
Good Agreement

The paper presents a general nonlinear numerical model for the dynamic analysis of a spatial structure that includes chains of flexible rods, with rigid bodies between them, and different kinds of connections between all these components. Such a system is denoted a multirod or multibeam system. The model is derived using a multibody system approach. The motion of each rod includes elastic deformations that are superimposed on finite rigid body motions. The elastic model of each rod is nonlinear and includes bending in two perpendicular directions, torsion, axial motion, and warping. Any distribution of the rod properties can be considered. Finite elements are used to describe the deformations. Although the elastic derivation is confined to moderate deformations, any level of nonlinearity can be addressed by dividing each rod into sub-rods. The joints between the rods are general and may include springs and dampers. A new formulation of Lagrange method is used in order to derive the equations of motion. It offers various advantages concerning the accuracy, stability of the constraints, and the modeling of constraints. The model is validated by comparing its results with new experimental results. Good agreement is shown between the experimental and numerical results.

Effects of steady-state axial deformation on bending frequency of rotating cantilever beam

2016 ◽  
Vol 231 (24) ◽  
pp. 4521-4527
Author(s):  
Guowei Zhao ◽  
Zhigang Wu
Keyword(s):  
Steady State ◽  
Cantilever Beam ◽  
Present Model ◽  
Equations Of Motion ◽  
Considerable Effect ◽  
Axial Motion ◽  
Axial Deformation ◽  
Transverse Bending ◽  
Coupling Dynamic ◽  
Good Agreement

A coupling dynamic model of a rotating cantilever beam is established by considering the effect of steady-state axial deformation on transverse bending deformation. The present method uses fully nonlinear Green strain–displacement relationship to derive the coupling terms in the equations of motion. The steady-state axial deformation is derived by analysing the equation of axial motion. An expression of the rotational speed limit is also obtained. The numerical results indicate that the steady-state axial deformation has a considerable effect on the transverse bending frequencies. A comparison of the present model with the absolute nodal coordinate formulation indicates that the two models are in good agreement, which proves the effectiveness and rationality of the present model.

A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations

1986 ◽  
Vol 108 (2) ◽  
pp. 176-182 ◽  
Author(s):  
S. S. Kim ◽  
M. J. Vanderploeg
Keyword(s):  
Equations Of Motion ◽  
General Purpose ◽  
Rigid Bodies ◽  
Transformation Matrix ◽  
Cartesian Coordinates ◽  
Velocity Transformation ◽  
Joint Coordinates ◽  
Relative Coordinates ◽  
General Purpose Computer ◽  
New Formulation

This paper presents a new formulation for the equations of motion of interconnected rigid bodies. This formulation initially uses Cartesian coordinates to define the position of the system, the kinematic joints between bodies, and forcing functions on and between bodies. This makes initial system definition straightforward. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates relative coordinates to Cartesian coordinates. It is derived using kinematic relationships for each joint type and graph theory for identifying the system topology. By using relative coordinates, the equations of motion are efficiently integrated. Use of both Cartesian and relative coordinates produces an efficient set of equations without loss of generality. The algorithm just described is implemented in a general purpose computer program. Examples are used to demonstrate the generality and efficiency of the algorithms.

Dynamics of Systems That Include Wings in Autorotation

1999 ◽  
Vol 121 (2) ◽  
pp. 248-254 ◽  
Author(s):  
D. Seter ◽  
A. Rosen
Keyword(s):  
Equations Of Motion ◽  
Rigid Bodies ◽  
General Nature ◽  
Aerodynamic Loads ◽  
Multibody Model ◽  
Euler Approach ◽  
Theoretical Results ◽  
Rotor Model ◽  
Good Agreement ◽  
Blade Element

A general multibody model, appropriate for investigating the autorotation of various systems of rigid bodies, is presented. Using the Newton-Euler approach, a generic modular matrix form of the equations of motion is obtained. The general nature of this detailed, nonlinear model allows the description of a large variety of autorotating systems. The calculations of the aerodynamic loads that act on the blades include the use of empirical data combined with an extended blade element/momentum analysis. The model is first validated by comparing its results with analytical results for simple cases. Then the use of the model to investigate the autorotation of a rotor model in a wind tunnel is presented. Good agreement between the experimental and theoretical results is shown.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

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.

Investigation of Sinkage and Trim by Ships in Shallow Water Based on Overset Grid

2015 ◽  
Vol 713-715 ◽  
pp. 2126-2132
Author(s):  
Da Ming Sun ◽  
Ji Yong Liu ◽  
Qing Wen Kong
Keyword(s):  
Shallow Water ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Overset Grid ◽  
Ship Hulls ◽  
Surface Ship ◽  
Solving Equations ◽  
Sinkage And Trim ◽  
Volume Method ◽  
Good Agreement

A study on the navigation behavior for ships in shallow water had been carried out on CFD. The problem of surface ship hulls free of sinkage and trim in shallow water is analyzed numerically by simultaneously solving equations of the Reynolds averaged Navier-Stokes (RANS). The computations, based on the single-phase level set and overset grid, are discretized by finite volume method (FVM). An earth-based reference system is used for the solution to the fluid flow, while a ship-based reference is used to compute the rigid-body equations of motion. A S60 CB=0.6 ship model is taken as an example to the numerical simulation. Numerical results of the sinkage and trim of the seven Froude Numbers (Fn=0.5~0.8) are compared against experimental data, which have a good agreement.

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

Investigation of the Stability of Axially Moving Beams With Discrete Masses

2021 ◽  
Author(s):  
Konstantina Ntarladima ◽  
Michael Pieber ◽  
Johannes Gerstmayr
Keyword(s):  
Large Deformations ◽  
Equations Of Motion ◽  
Arbitrary Lagrangian Eulerian ◽  
Axial Motion ◽  
Multibody Modeling ◽  
Conveyor Belts ◽  
Axially Moving Beams ◽  
Concentrated Masses ◽  
Axially Moving ◽  
The Stability

Abstract The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

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