Dynamic Instability in Quartering Seas—Part III: Nonlinear Effects on Periodic Motions

1997 ◽  
Vol 41 (03) ◽  
pp. 210-223 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Periodic Motion ◽  
Horizontal Plane ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Nonlinear Effects ◽  
Ship Motions ◽  
Nonlinear Phenomena ◽  
Specific Sequence ◽  
The Stability ◽  
Two Stages

The loss of stability of the horizontal-plane periodic motion of a steered ship in waves is investigated. In earlier reports we referred to the possibility of a broaching mechanism that will be intrinsic to the periodic mode, whereby there will exist no need for the ship to go through the surf-riding stage. However, about this point the discussion was essentially conjectural. In order to provide substance we present here a theoretical approach that is organized in two stages: Initially, we demonstrate the existence of a mechanism of parametric instability of yaw on the basis of a rudimentary, single-degree model of maneuvering motion in waves. Then, with a more elaborate model, we identify the underlying nonlinear phenomena that govern the large-amplitude horizontal ship motions, considering the ship as a multi-degree, nonlinear oscillator. Our analysis brings to light a very specific sequence of phenomena leading to cumulative broaching that involves a change in the stability of the ordinary periodic motion on the horizontal plane, a transition towards subharmonic response and, ultimately, a sudden jump to resonance. Possible means for controlling the onset of such undesirable behavior are also investigated.

scholarly journals EFFECT OF NONCLASSICAL POLARIZATION OF Na+ AND K+ ON THE STABILITY OF SOIL COLLOIDAL PARTICLES IN SUSPENSION

2017 ◽  
Vol 24 (07) ◽  
pp. 1850019
Author(s):  
DING WU-QUAN ◽  
HE JIA-HONG ◽  
WANG LEI ◽  
LIU XIN-MIN ◽  
LI HANG
Keyword(s):  
Negative Pressure ◽  
Colloidal Particles ◽  
Ion Concentration ◽  
Electrostatic Repulsion ◽  
Adjacent Soil ◽  
Net Pressure ◽  
The Stability ◽  
Two Stages ◽  
Soil Colloids ◽  
Total Average

The study of soil colloids is essential because the stability of soil colloidal particles are important processes of interest to researchers in environmental fields. The strong nonclassical polarization of the adsorbed cations (Na[Formula: see text] and K[Formula: see text] decreased the electric field and the electrostatic repulsion between adjacent colloidal particles. The decrease of the absolute values of surface potential was greater for K[Formula: see text] than for Na[Formula: see text]. The lower the concentration of Na[Formula: see text] and K[Formula: see text] in soil colloids, the greater the electrostatic repulsion between adjacent colloidal particles. The net pressure and the electrostatic repulsion was greater for Na[Formula: see text] than for K[Formula: see text] at the same ion concentration. For K[Formula: see text] and Na[Formula: see text] concentrations higher than 50[Formula: see text]mmol L[Formula: see text] or 100 mmol L[Formula: see text], there was a net negative (or attractive) pressure between two adjacent soil particles. The increasing total average aggregation (TAA) rate of soil colloids with increasing Na[Formula: see text] and K[Formula: see text] concentrations exhibited two stages: the growth rates of TAA increased rapidly at first and then increased slowly and eventually almost negligibly. The critical coagulation concentrations of soil colloids in Na[Formula: see text] and K[Formula: see text] were 91.6[Formula: see text]mmol L[Formula: see text] and 47.8[Formula: see text]mmol L[Formula: see text], respectively, and these were similar to the concentrations at the net negative pressure.

scholarly journals Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
V. Kartik ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Parametric Instability ◽  
Primary Resonance ◽  
Free Edge ◽  
Moving Plate ◽  
Torsional Mode ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Axially Moving ◽  
The Stability

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

Some Nonlinear Effects of Magnetic Bearings

1999 ◽  
Author(s):  
Norbert Steinschaden ◽  
Helmut Springer
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Path Following ◽  
Nonlinear Effects ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Amb System ◽  
Large Rotor

Abstract In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used. The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

scholarly journals APPLICATION OF LEARNING REINFORCEMENT METHOD IN ROBOTIZED AND AUTOMATED FORESTRY SYSTEMS

2020 ◽  
Vol 10 (1) ◽  
pp. 256-265
Author(s):  
Andrey Tolstyh ◽  
D Stupnikov ◽  
Sergey Malyukov ◽  
Aleksandr Luk'yanov ◽  
Yuriy Lunev
Keyword(s):  
Physical Environment ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Industrial Robots ◽  
Environment Model ◽  
Random Position ◽  
Learning Reinforcement ◽  
The Stability ◽  
Two Stages ◽  
The Cost

Abstract Currently, most large enterprises are actively using industrial robots and other automated solutions. This allows a significant increase in productivity and quality of work performed. This article gave a brief overview of modern industrial robots, their operating principle, basic components and systems. A reinforcement learning algorithm was developed and tested. The task of constructing a learning algorithm with reinforcement was divided into two stages: modeling the environment and description and optimization of the cost function. Since industrial robotic systems operate in the real world, the environment model should reflect basic physical laws. Therefore, the pyBullet library of the physical environment was chosen as the physical environment for testing. After modeling the manipulator in the selected physical medium, it was given the trivial task of touching a given object with the capture of the manipulator. An artificial neural network was used as an agent interacting with the environment. The inputs were the coordinates of the object and the existing angles of rotation of the articulated joints of the robot. Outputs - angle of rotation of joints at this step. This network was trained using the back propagation method, Adam modification. The system was trained for about 12 hours. Success is achieved in 95% of cases when testing the stability of the system (random position of the cylinder). In future, it is planned to test the obtained models on bench samples

scholarly journals Vibroimpact Mobile Robot

2021 ◽  
Vol 17 (4) ◽  
pp. 429-436
Author(s):  
A. P. Ivanov ◽  
Keyword(s):  
Simple Model ◽  
Mobile Robot ◽  
Periodic Motion ◽  
Horizontal Plane ◽  
Coulomb Friction ◽  
Average Velocity ◽  
Moving Mass ◽  
Harmonic Force ◽  
Maximal Average ◽  
The Right

A simple model of a capsule robot is studied. The device moves upon a rough horizontal plane and consists of a capsule with an embedded motor and an internal moving mass. The motor generates a harmonic force acting on the bodies. Capsule propulsion is achieved by collisions of the inner body with the right wall of the shell. There is Coulomb friction between the capsule and the support, it prevents a possibility of reversal motion. A periodic motion is constructed such that the robot gains the maximal average velocity.

scholarly journals Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

2021 ◽  
Author(s):  
Lida Safaei ◽  
Mohsen Hatami ◽  
Mahmood Borhani Zarandi
Keyword(s):  
Communication Systems ◽  
Exact Analytical Solution ◽  
Nonlinear Effects ◽  
High Order ◽  
Order Effects ◽  
Coupled Equations ◽  
Solitary Solutions ◽  
Stability And Instability ◽  
The Stability ◽  
Order Dispersion

Abstract In this paper, we analytically solve the coupled equations of a PT -Symmetric NLDC by considering high-order dispersion and nonlinear effects (Raman Scattering and self-steeping) simultaneously in normal dispersion regime. To the best of knowledge no works has been done in previous studies to decoupled these equations and obtain an exact analytical solution. The new exact bright solitary solutions are derived. In addition, to study the stability and instability of these propagated solitons in a PT -Symmetric NLDC, perturbation theory is used. Numerical methods are applied to find perturbed eigenvalues and eigenfunctions. The Stability of obtained four perturbed eigenvalues and perturbed eigenfunctions for a PT -Symmetric NLDC equations regard to high-order effects are examined. Using these results and simulating the propagation of perturbed temporal bright solitons through PT -Symmetric NLDC show that perturbed solitons are mostly stable. This means that high-order dispersion and nonlinear effects canceled each other and do not affected the propagated solitons. Furthermore, the evolution of perturbed solitons energies match well the previous results and con rmed the stability of these solitons in a PT -Symmetric NLDC. As seen the energies of pulses in bar and cross behave in two manner 1) the exchange of energy is happened in some periods, but the shape of each pulse in bar and cross is preserved. Therefore, the solitons under this eigenfunction perturbation are mostly stable. 2) the evolution of energy in the bar and cross, demonstrate that there is no changes in their energies and they remain constant. It is straightforward to show that in spite of considering high-order effects, the perturbed soliton conserve the shape and it remain stable. The deliverables of this article not only demonstrate a novel approach to ultra-fast pulses, solitons and optical couplers, but more fundamentally, they could give insight for improving the new medical equipments technologies, enabling innovations in nonlinear optics and their usage in designing new communication systems and Photonic devices.

Dynamics and Stability of Partial Immersion Milling Operations

1999 ◽  
Author(s):  
M. X. Zhao ◽  
B. Balachandran ◽  
M. A. Davies ◽  
J. R. Pratt
Keyword(s):  
Hopf Bifurcation ◽  
Time Variation ◽  
Periodic Motion ◽  
Contact Time ◽  
Period Doubling ◽  
Experimental Investigations ◽  
Partial Immersion ◽  
Milling Operations ◽  
Wide Range ◽  
The Stability

Abstract In this paper, numerical and experimental investigations conducted into the dynamics and stability of partial immersion milling operations are presented. A mechanics based model is used for simulations of a wide range of milling operations and instabilities that arise due to regeneration and/or impact effects are studied. Poincaré sections are used to assess the stability of motions. The studies reveal that apart from Hopf bifurcation of a periodic motion, a period-doubling bifurcation of a periodic motion may also lead to chatter in partial immersion milling operations. Issues such as tooth contact time variation and structure of stability charts are also discussed.

The Role of Modal Coupling on the Non-Linear Response of Cylindrical Shells Subjected to Dynamic Axial Loads

2000 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Zenón J. G. N. Del Prado
Keyword(s):  
Dynamic Instability ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Parametric Instability ◽  
Compressive Load ◽  
Basins Of Attraction ◽  
Dynamic Component ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Low Dimensional

Abstract This paper discusses the dynamic instability of circular cylindrical shells subjected to time-dependent axial edge loads of the form P(t) = P0+P1(t), where the dynamic component p1(t) is periodic in time and P0 is a uniform compressive load. In the present paper a low dimensional model, which retains the essential non-linear terms, is used to study the non-linear oscillations and instabilities of the shell. For this, Donnell’s shallow shell equations are used together with the Galerkin method to derive a set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. To study the non-linear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric instability and escape from the pre-buckling potential well. The numerical results obtained from this investigation clarify the conditions, which control whether or not instability may occur. This may help in establishing proper design criteria for these shells under dynamic loads, a topic practically unexplored in literature.

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