Small Vibrations Superimposed on Non-Linear Rigid Body Motion

1997 ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rigid Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Connecting Rod ◽  
Non Linear ◽  
Linear Differential

Abstract In the case of small elastic deformations in a flexible multi-body system, the periodic motion of the system can be modelled as a superposition of a small linear vibration and a non-linear rigid body motion. For the small deformations this analysis results in a set of linear differential equations with periodic coefficients. These equations give more insight in the vibration phenomena and are computationally more efficient than a direct non-linear analysis by numeric integration. The realization of the method in a program for flexible multibody systems is discussed which requires, besides the determination of the periodic rigid motion, the determination of the linearized equations of motion. The periodic solutions for the linear equations are determined with a harmonic balance method, while transient solutions are obtained by averaging. The stability of the periodic solution is considered. The method is applied to a pendulum with a circular motion of its support point and a slider-crank mechanism with flexible connecting rod. A comparison is made with previous non-linear results.

Seismic Analysis of Structures With Coulomb Friction

1983 ◽  
Vol 105 (2) ◽  
pp. 171-178 ◽  
Author(s):  
V. N. Shah ◽  
C. B. Gilmore
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Seismic Event ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Superposition Method ◽  
Modal Superposition Method

A modal superposition method for the dynamic analysis of a structure with Coulomb friction is presented. The finite element method is used to derive the equations of motion, and the nonlinearities due to friction are represented by pseudo-force vector. A structure standing freely on the ground may slide during a seismic event. The relative displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. Three single degree-of-freedom problems are solved to verify this method. In a fourth problem, the dynamic response of a platform standing freely on the ground is analyzed during a seismic event.

scholarly journals An Efficient Modelling of Flexible Airships

2006 ◽  
Author(s):  
Selima Bennaceur ◽  
Naoufel Azouz ◽  
Djaber Boukraa
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
General System ◽  
Rigid Body Motion ◽  
The Body ◽  
Body Motion ◽  
Modal Synthesis ◽  
Stiffness Matrices ◽  
Updated Lagrangian ◽  
Convenient Technique

This paper presents an efficient modelling of airships with small deformations moving in an ideal fluid. The formalism is based on the Updated Lagrangian Method (U.L.M.). This formalism proposes to take into account the coupling between the rigid body motion and the deformation as well as the interaction with the surrounding fluid. The resolution of the equations of motion is incremental. The behaviour of the airship is defined relatively to a virtual non-deformed reference configuration moving with the body. The flexibility is represented by a deformation modes issued from a Finite Elements Method analysis. The increment of rigid body motion is represented similarly by rigid modes. A modal synthesis is used to solve the general system equations of motion. Time constant matrices appears (i.e. mass and structural stiffness matrices), and we show a convenient technique to actualise the time dependant matrices.

A Variationally Consistent Approach to Constrained Motion

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
John T. Foster
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
A Priori ◽  
Nonholonomic Systems ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Constrained Motion ◽  
Consistent Approach ◽  
Holonomic And Nonholonomic Systems ◽  
D'alembert's Principle

A variationally consistent approach to constrained rigid-body motion is presented that extends D'Alembert's principle in a way that has a form similar to Kane's equations. The method results in minimal equations of motion for both holonomic and nonholonomic systems without a priori consideration of preferential coordinates.

Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints

1990 ◽  
Vol 112 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Ye-Chen Pan ◽  
R. A. Scott ◽  
A. Galip Ulsoy
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Differential Algebraic Equations ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Integration Scheme ◽  
System Response ◽  
Constraint Equations ◽  
Prismatic Joints

A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into the equations of motion by Lagrange multipliers. The small displacements due to the flexibility of the links are then discretized by a displacement based finite element method. Equations of motion are derived for the cases of prescribed rigid body motion as well as prescribed joint torques/forces through application of Lagrange’s equations. The equations of motion and the constraint equations result in a set of differential algebraic equations. A numerical procedure combining a constraint stabilization method and a Newmark direct integration scheme is then applied to obtain the system response. An example, previously treated in the literature, is presented to validate the modeling and solution methods used in this study.

Calculations of non-linear waves generated by complex body motion

2000 ◽  
Vol 214 (6) ◽  
pp. 771-780 ◽  
Author(s):  
T Chen ◽  
A T Chwang
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Grid Method ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Promising Alternative ◽  
Potential Flows ◽  
Linear Waves ◽  
Non Linear ◽  
Marine Engineering

A structured and unstructured hybrid overlapping grid method is developed for simulating free-surface waves generated by submerged arbitrary bodies undergoing rigid body motion in multi-degrees of freedom. Exact boundary conditions are applied to the transient free and body surfaces. The accuracy, efficiency and generality of the present two-dimensional code for potential flows are validated by comparisons with available theories and experiments. Numerical experiments are reported in this paper to investigate the non-linear behaviour of waves due to the complex rigid body motion, in terms of wave patterns and the pressure distribution. Combining the best features of both grid systems for finite elements and finite differences, the present method provides a promising alternative in computational fluid dynamics for the design and analysis in marine engineering.

Equations of Motion of an Aircraft Wing Modeled As a Composite Plate-Beam Model Including the Rigid-Body Motion

2001 ◽  
Author(s):  
Samir A. Emam ◽  
Ali H. Nayfeh ◽  
Scott L. Hendricks
Keyword(s):  
Boundary Conditions ◽  
Rigid Body ◽  
Composite Beam ◽  
Composite Plate ◽  
Equations Of Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Beam Model ◽  
Aircraft Wing ◽  
Hamilton Principle

Abstract The equations of motion of an aircraft wing modeled as a composite beam are presented. The contribution of the rigid-body motion is taken into account; it affects the response of the wing, especially in maneuvers. The Hamilton principle is used to derive the equations of motion and the corresponding boundary conditions.

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