Combination Resonances of a Circular Plate With Three-Mode Interaction

1995 ◽  
Vol 62 (4) ◽  
pp. 1015-1022 ◽  
Author(s):  
Won Kyoung Lee ◽  
Cheol Hong Kim
Keyword(s):  
Circular Plate ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Initial Conditions ◽  
Resonance Condition ◽  
Equilibrium Points ◽  
Nonautonomous System ◽  
Mode Interaction ◽  
Resonance Frequencies

A nonlinear analysis is presented for combination resonances in the symmetric responses of a clamped circular plate with the internal resonance, ω3≈ω1+2ω2. The combination resonances occur when the frequency of the excitation are near a combination of the natural frequencies, that is, when Ω≈2ω1+ω2. By means of the internal resonance condition, the frequency of the excitation is also near another combination of the natural frequencies, that is, Ω≈ω1−ω2+ω3. The effect of two near combination resonance frequencies on the response of the plate is examined. The method of multiple scales is used to solve the nonlinear nonautonomous system of equations governing the generalized coordinates in Galerkin’s procedure. For steady-state responses, we determine the equilibrium points of the autonomous system transformed from the nonautonomous system and examine their stability. It has been found that in some cases resonance responses with nonzero-amplitude modes don’t exist, and the amplitudes of the responses decrease with the excitation amplitude. We integrate numerically the nonautonomous system to find the long-term behaviors of the plate and to check the validity of the analytical solution. It is found that there exist multiple stable responses resulting in jumps. In this case the long-term response of the plate depends on the initial condition. In order to visualize total responses depending on the initial conditions, we draw the deflection curves of the plate.

scholarly journals Aircraft Maintenance Check Scheduling Using Reinforcement Learning

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 113
Author(s):  
Pedro Andrade ◽  
Catarina Silva ◽  
Bernardete Ribeiro ◽  
Bruno F. Santos
Keyword(s):  
Reinforcement Learning ◽  
Time Horizon ◽  
Learning Algorithm ◽  
Initial Conditions ◽  
Q Learning ◽  
Scheduling Policy ◽  
Real Scenario ◽  
Maintenance Plan ◽  
Small Disturbances

This paper presents a Reinforcement Learning (RL) approach to optimize the long-term scheduling of maintenance for an aircraft fleet. The problem considers fleet status, maintenance capacity, and other maintenance constraints to schedule hangar checks for a specified time horizon. The checks are scheduled within an interval, and the goal is to, schedule them as close as possible to their due date. In doing so, the number of checks is reduced, and the fleet availability increases. A Deep Q-learning algorithm is used to optimize the scheduling policy. The model is validated in a real scenario using maintenance data from 45 aircraft. The maintenance plan that is generated with our approach is compared with a previous study, which presented a Dynamic Programming (DP) based approach and airline estimations for the same period. The results show a reduction in the number of checks scheduled, which indicates the potential of RL in solving this problem. The adaptability of RL is also tested by introducing small disturbances in the initial conditions. After training the model with these simulated scenarios, the results show the robustness of the RL approach and its ability to generate efficient maintenance plans in only a few seconds.

Upgraded Railway Front Searchlight Design Plastic Deformations by its Vibrations with Resonance Frequencies

2016 ◽  
Vol 684 ◽  
pp. 111-119 ◽  
Author(s):  
Stanislav Rafaelevich Abulkhanov ◽  
Dmitrii Sergeevich Goryainov
Keyword(s):  
Natural Frequencies ◽  
Ansys Software ◽  
Software Environment ◽  
Low Frequencies ◽  
Plastic Deformations ◽  
Vibration Resistance ◽  
First Case ◽  
Resonance Frequencies ◽  
The One ◽  
Electric Lamp

Natural frequencies of the four upgraded front searchlight designs were received in ANSYS software environment. In the first case serial front searchlight incandescent electric lamp was replaced by a LED group which was mounted on the one-piece cylinder backing. The second front searchlight design had the backing which was upgraded by a radial ribs and concentric rigidity ferrules. Analyze of the backing deformation character by vibrations with the natural frequencies established a number of design solutions which make it possible to raise front searchlight vibration resistance. By the front searchlight model were established that the natural frequencies of the searchlight with the one-piece backing appertain to the whole range of the train vibrations. Natural frequencies of the backing with perforation, rigidity ferrules, and radial ribs appertain to the low frequencies of the railway locomotive vibrations spectrum. On basis of devised methodology of analyze of the deformation and natural frequencies of the surface carrying a LED group the vibration-proof searchlight design was introduced and researched.

scholarly journals Simulation of MASPn Experiments in MISTRA Test Facility with COCOSYS Code

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Mantas Povilaitis ◽  
Egidijus Urbonavičius
Keyword(s):  
Boundary Conditions ◽  
Nuclear Power ◽  
Power Plants ◽  
Volume Fraction ◽  
Characteristic Length ◽  
Initial Conditions ◽  
Test Facility ◽  
Work Package ◽  
Acceptable Agreement

An issue of the stratified atmospheres in the containments of nuclear power plants is still unresolved; different experiments are performed in the test facilities like TOSQAN and MISTRA. MASPn experiments belong to the spray benchmark, initiated in the containment atmosphere mixing work package of the SARNET network. The benchmark consisted of MASP0, MASP1 and MASP2 experiments. Only the measured depressurisation rates during MASPn were available for the comparison with calculations. When the analysis was performed, the boundary conditions were not clearly defined therefore most of the attention was concentrated on MASP0 simulation in order to develop the nodalisation scheme and define the initial and boundary conditions. After achieving acceptable agreement with measured depressurisation rate, simulations of MASP1 and MASP2 experiments were performed to check the influence of sprays. The paper presents developed nodalisation scheme of MISTRA for the COCOSYS code and the results of analyses. In the performed analyses, several parameters were considered: initial conditions, loss coefficient of the junctions, initial gradients of temperature and steam volume fraction, and characteristic length of structures. Parametric analysis shows that in the simulation the heat losses through the external walls behind the lower condenser installed in the MISTRA facility determine the long-term depressurisation rate.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

scholarly journals Soft-wired long-term memory in a natural recurrent neuronal network

2020 ◽  
Author(s):  
Miguel A. Casal ◽  
Santiago Galella ◽  
Oscar Vilarroya ◽  
Jordi Garcia-Ojalvo
Keyword(s):  
Neuronal Network ◽  
Neuronal Networks ◽  
Initial Conditions ◽  
Permutation Entropy ◽  
Long Term Memory ◽  
Term Memory ◽  
C Elegans ◽  
Living Organisms ◽  
Recurrent Connections

Neuronal networks provide living organisms with the ability to process information. They are also characterized by abundant recurrent connections, which give rise to strong feed-back that dictates their dynamics and endows them with fading (short-term) memory. The role of recurrence in long-term memory, on the other hand, is still unclear. Here we use the neuronal network of the roundworm C. elegans to show that recurrent architectures in living organisms can exhibit long-term memory without relying on specific hard-wired modules. A genetic algorithm reveals that the experimentally observed dynamics of the worm’s neuronal network exhibits maximal complexity (as measured by permutation entropy). In that complex regime, the response of the system to repeated presentations of a time-varying stimulus reveals a consistent behavior that can be interpreted as soft-wired long-term memory.A common manifestation of our ability to remember the past is the consistence of our responses to repeated presentations of stimuli across time. Complex chaotic dynamics is known to produce such reliable responses in spite of its characteristic sensitive dependence on initial conditions. In neuronal networks, complex behavior is known to result from a combination of (i) recurrent connections and (ii) a balance between excitation and inhibition. Here we show that those features concur in the neuronal network of a living organism, namely C. elegans. This enables long-term memory to arise in an on-line manner, without having to be hard-wired in the brain.

scholarly journals Assessment of Substrate and TBC Damage Effects on Resonance Frequencies for Blade Health Monitoring

2022 ◽  
Vol 12 (1) ◽  
pp. 1-19
Author(s):  
Jason van Dyke ◽  
Michel Nganbe
Keyword(s):  
Natural Frequencies ◽  
Hot Spot ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Early Assessment ◽  
Element Simulation ◽  
Resonance Frequencies ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Local Plastic Deformation

The reliability of critical aircraft components continues to shift towards onboard monitoring to optimize maintenance scheduling, economy efficiency and safety. Therefore, the present study investigates changes in dynamic behavior of turbine blades for the detection of defects, with focus on substrate cracks and TBC spallation as they relate to vibration modes 1 to 6. Two‐dimensional and three-dimensional finite element simulation is used. The results indicate that TBC spallation reduces natural frequencies due to the ensuing hot spot and overall increase in temperature, leading to drops in blade stiffness and strength. Cracks cause even larger frequency shifts due to local plastic deformation at the crack that changes the energy dissipation behavior. Mode 1 vibration shows the largest shifts in natural frequencies that best correlate to the size of defects and their position. As such, it may be most appropriate for the early assessment of the severity and location of defects.

scholarly journals Complexity In Psychological Self-Ratings: Implications for research and practice

2020 ◽  
Author(s):  
Merlijn Olthof ◽  
Fred Hasselman ◽  
Anna Lichtwarck-Aschoff
Keyword(s):  
Complex Systems ◽  
Systems Approach ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Regime Shifts ◽  
Fundamental Aspect ◽  
Time Varying ◽  
Term Prediction ◽  
Sensitive Dependence

Background: Psychopathology research is changing focus from group-based ‘disease models’ to a personalized approach inspired by complex systems theories. This approach, which has already produced novel and valuable insights into the complex nature of psychopathology, often relies on repeated self-ratings of individual patients. So far it has been unknown whether such self-ratings, the presumed observables of the individual patient as a complex system, actually display complex dynamics. We examine this basic assumption of a complex systems approach to psychopathology by testing repeated self-ratings for three markers of complexity: memory, the presence of (time-varying) short- and long-range temporal correlations, regime shifts, transitions between different dynamic regimes, and, sensitive dependence on initial conditions, also known as the ‘butterfly effect’, the divergence of initially similar trajectories.Methods: We analysed repeated self-ratings (1476 time points) from a single patient for the three markers of complexity using Bartels rank test, (partial) autocorrelation functions, time-varying autoregression, a non-stationarity test, change point analysis and the Sugihara-May algorithm.Results: Self-ratings concerning psychological states (e.g., the item ‘I feel down’) exhibited all complexity markers: time-varying short- and long-term memory, multiple regime shifts and sensitive dependence on initial conditions. Unexpectedly, self-ratings concerning physical sensations (e.g., the item ‘I am hungry’) exhibited less complex dynamics and their behaviour was more similar to random variables. Conclusions: Psychological self-ratings display complex dynamics. The presence of complexity in repeated self-ratings means that we have to acknowledge that (1) repeated self-ratings yield a complex pattern of data and not a set of (nearly) independent data points, (2) humans are ‘moving targets’ whose self-ratings display non-stationary change processes including regime shifts, and (3) long-term prediction of individual trajectories may be fundamentally impossible. These findings point to a limitation of popular statistical time series models whose assumptions are violated by the presence of these complexity markers. We conclude that a complex systems approach to mental health should appreciate complexity as a fundamental aspect of psychopathology research by adopting the models and methods of complexity science. Promising first steps in this direction, such as research on real-time process-monitoring, short-term prediction, and just-in-time interventions, are discussed.

Parametrically Excited Vibrations and Auto-Parametric Resonance in Cylindrical Shells

2000 ◽  
Author(s):  
A. A. Popov ◽  
J. M. T. Thompson ◽  
F. A. McRobie
Keyword(s):  
Internal Resonance ◽  
Cylindrical Shells ◽  
Mode Interaction ◽  
Geometric Description ◽  
Modal Interactions ◽  
Structural Behaviour ◽  
Parametrically Excited ◽  
Parametric Resonances ◽  
Shell Vibration ◽  
Low Dimensional

Abstract Vibrations of cylindrical shells parametrically excited by external axial forcing or by internal auto-parametric resonances are considered. A Rayleigh-Ritz discretization of the von Kármán-Donnell equations through symbolic computations leads to low dimensional models of shell vibration. After applying methods and ideas of modern dynamical systems theory, complete bifurcation diagrams are constructed and analyzed with an emphasis on modal interactions and their relevance to structural behaviour. In the case of free shell vibrations, the Hamiltonian and a transformation into action-angle coordinates followed by averaging provides readily a geometric description of the interaction between concertina and chequerboard modes. It was established that the interaction should be most pronounced when there are slightly less than 2 N square chequerboard panels circumferentially, where N is the ratio of shell radius to thickness. The two mode interaction leads to preferred vibration patterns with larger deflection inwards than outwards, and at internal resonance, significant energy transfer occurs between the modes. The regular and chaotic features of this interaction are studied analytically and numerically.

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