SYNCHRONIZATION OF THE REGULAR AND CHAOTIC STATES OF ELECTROMECHANICAL DEVICES WITH AND WITHOUT DELAY

2004 ◽  
Vol 14 (01) ◽  
pp. 171-181 ◽  
Author(s):  
R. YAMAPI ◽  
J. B. CHABI OROU ◽  
P. WOAFO
Keyword(s):  
Numerical Simulation ◽  
Floquet Theory ◽  
Equations Of Motion ◽  
Stability Boundaries ◽  
Synchronization Process ◽  
Synchronization Time ◽  
Electromechanical Devices

We consider in this paper the problem of stability and duration of the synchronization process between two electromechanical devices, both in their regular and chaotic states. Stability boundaries are derived through Floquet theory. The influence of the precision on the synchronization time is also analyzed using numerical simulation of the equations of motion.

SYNCHRONIZATION OF TWO ELECTROMECHANICAL DEVICES WITH PARAMETRIC COUPLING

2008 ◽  
Vol 18 (11) ◽  
pp. 3473-3484 ◽  
Author(s):  
A. SAMANKEU TCHANA ◽  
P. WOAFO ◽  
R. YAMAPI
Keyword(s):  
Analytical Approach ◽  
Floquet Theory ◽  
Analytical Study ◽  
Complete Synchronization ◽  
Stability Boundaries ◽  
Synchronization Process ◽  
Numerical Investigations ◽  
Parametric Coupling ◽  
Electromechanical Devices

The study of synchronization of two electromechanical devices with parametric coupling, in their regular and chaotic states was investigated. It was observed that an analytical study based on the Floquet theory makes it possible to determine the coefficients of coupling, ensuring a complete synchronization. Emphasis was placed on the analysis of amplitude effects on coupling and stability boundaries of the synchronization process. Numerical investigations are then used to support the accuracy of the analytical approach.

Mulit-Pulse Orbits and Chaotic Motion of Composite Laminated Plates

2008 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Equations Of Motion ◽  
Laminated Plates ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

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.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

Analysis and Verification of a Watt I Six-Bar Furniture Hinge Mechanism

2005 ◽  
Vol 219 (10) ◽  
pp. 1107-1117 ◽  
Author(s):  
F-C Chen
Keyword(s):  
Numerical Simulation ◽  
Equations Of Motion ◽  
Design Requirement ◽  
Differential Algebraic Equation ◽  
Loop Method ◽  
Runge Kutta Method ◽  
Multipliers Method ◽  
Design Requirements ◽  
Further Development ◽  
Coordinate Partitioning

The analysis and verification of a Watt I six-bar furniture hinge mechanism were carried out in this article. Using the characteristics of the topological structure of existing hinge mechanisms and design requirement specification, six hinge designs were synthesized. The most suitable design was selected for kinematic analysis with the vector loop method. The equations of motion of the mechanism were then derived by the Hamilton principle and Lagrange undetermined multipliers method and simplified using coordinate partitioning method. The differential algebraic equation was subsequently solved by using the Runge-Kutta method. From numerical simulation, the dynamic response of the door under various loading conditions was obtained and was found to fulfil the design requirements and constraints. Results obtained from experiments and numerical simulation were comparable, which demonstrated the success of this study. It is anticipated that this research will be beneficial to the further development of hinge designs for use in furniture.

The dynamics and design of a non-linear vibration absorber

1993 ◽  
Vol 207 (6) ◽  
pp. 363-374 ◽  
Author(s):  
D H Gonsalves ◽  
R D Neilson ◽  
A D S Barr
Keyword(s):  
Numerical Simulation ◽  
Equations Of Motion ◽  
Resonance Peak ◽  
Vibration Absorber ◽  
Linear Vibration ◽  
Frequency Range ◽  
Non Linear ◽  
Experimental Rig ◽  
Auxiliary Mass

This paper presents the design of an efficient non-linear vibration absorber. The system comprises a linear absorber with the addition of a spring between the two masses, which contacts the absorber mass when its displacement exceeds a certain value. The addition of this snubber stiffness facilitates a reduction in the amplitude of the second resonance peak of the linear absorber, which therefore enables the system to be operated over a wider frequency range without reaching larger amplitudes. The modification also has the effect of attenuating the response of the auxiliary mass. The equations of motion for the system are presented and optimization is carried out. A description of an experimental rig that was built follows. The results from the rig are compared with those from numerical simulation and show good correlation.

Use of the Moving Frame Method in Dynamics to Model Gyroscopic Control of Small Crafts at Sea: Theory — Part 1

2017 ◽  
Author(s):  
Joakim Nyland ◽  
Håkon Teigland ◽  
Thomas J. Impelluso
Keyword(s):  
Numerical Simulation ◽  
Large Scale ◽  
Equations Of Motion ◽  
Companion Paper ◽  
Cross Product ◽  
Moving Frame ◽  
3D Analysis ◽  
Active System ◽  
Moving Frame Method ◽  
Frame Method

This paper presents new method in dynamics — the Moving Frame Method (MFM) — and uses it to address a challenge faceing Norwegian shipping. Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some project locations, the transferring of crew members from vessel to turbine or platform is fraught with safety concerns. These concerns can be alleviated by controlling the motion of the transfer vessel. This research studies an add-on stability system for marine vessels to ease the process of offshore platform maintenance and crew member safety. Specifically, this research concerns an internal active system — an active gyroscopic stabilizer — and a more powerful method of theoretical and computational mechanics. This paper derives the equations of motion of a model system equipped with dual gyroscopic stabilizers, using the MFM. The equations of motion are numerically solved to obtain a numerical simulation. The method exploits a variational principle with a restricted variation of the angular velocity. The MFM simplifies dynamics, enables a consistent notation, from 2D to 3D analysis and exploits matrix algebra in lieu of the vector cross product. Finally, in a companion paper to this one, the mathematical model and the numerical simulation is verified with experiments conducted in a large-scale wave tank.

A Preliminary Investigation of the Dynamic Stability of Flexible Manipulators Performing Repetitive Tasks

1986 ◽  
Vol 108 (3) ◽  
pp. 206-214 ◽  
Author(s):  
D. A. Streit ◽  
C. M. Krousgrill ◽  
A. K. Bajaj
Keyword(s):  
Parametric Excitation ◽  
Floquet Theory ◽  
Equations Of Motion ◽  
Preliminary Investigation ◽  
Zero Solution ◽  
Flexible Manipulator ◽  
Governing Equations ◽  
Repetitive Tasks ◽  
The Stability ◽  
Two Degree Of Freedom

The governing equations of motion for the compliant coordinates describing a flexible manipulator performing repetitive tasks contain parametric excitation terms. The stability of the zero solution to these equations is investigated using Floquet theory. Analytical and numerical results are presented for a two-degree-of-freedom model of a manipulator with one prismatic joint and one revolute joint.

Delayed-Acceleration Feedback for Active-Multimode Vibration Control of Cantilever Beams

2007 ◽  
Author(s):  
Khaled A. Alhazza ◽  
Ali H. Nayfeh ◽  
Mohammed F. Daqaq
Keyword(s):  
Cantilever Beam ◽  
Controller Design ◽  
Equations Of Motion ◽  
Time Integration ◽  
Free Vibrations ◽  
Delayed Feedback Control ◽  
Vibration Modes ◽  
Stability Boundaries ◽  
Single Input Single Output ◽  
The Stability

We present a single-input single-output multimode delayed-feedback control methodology to mitigate the free vibrations of a flexible cantilever beam. For the purpose of controller design and stability analysis, we consider a reduced-order model consisting of the first n vibration modes. The temporal variation of these modes is represented by a set of nonlinearly-coupled ordinary-differential equations that capture the evolving dynamics of the beam. Considering a linearized version of these equations, we derive a set of analytical conditions that are solved numerically to assess the stability of the closed-loop system. To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion. Simulations show excellent agreement between both approaches. We analyze the effect of the size and location of the piezoelectric patch and the location of the sensor on the stability of the response. We show that the stability boundaries are highly dependent on these parameters. Finally, we implement the controller on a cantilever beam for different controller gain-delay combinations and assess the performance using time histories of the beam response. Numerical simulations clearly demonstrate the controller ability to mitigate vibrations emanating from multiple modes simultaneously.

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