scholarly journals Detection of different dynamics of two coupled oscillators including a time-dependent cubic nonlinearity

2022 ◽  
Author(s):  
A. Labetoulle ◽  
A. Ture Savadkoohi ◽  
E. Gourdon
Keyword(s):  
Coupled Oscillators ◽  
Time Dependent ◽  
Cubic Nonlinearity

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2005 ◽  
Vol 127 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study is motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

scholarly journals Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions

2019 ◽  
Vol 1 (1) ◽  
pp. 82-90 ◽  
Author(s):  
Alejandro R. Urzúa ◽  
Irán Ramos-Prieto ◽  
Manuel Fernández-Guasti ◽  
Héctor M. Moya-Cessa
Keyword(s):  
Coupled Oscillators ◽  
Quantum Physics ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Unitary Operators ◽  
Orthogonal Functions ◽  
Molecular Chemistry ◽  
Coupled Harmonic Oscillators ◽  
Generalized Orthogonal

We show that by using the quantum orthogonal functions invariant, we found a solution to coupled time-dependent harmonic oscillators where all the time-dependent frequencies are arbitrary. This system may be found in many applications such as nonlinear and quantum physics, biophysics, molecular chemistry, and cosmology. We solve the time-dependent coupled harmonic oscillators by transforming the Hamiltonian of the interaction using a set of unitary operators. In passing, we show that N time-dependent and coupled oscillators have a generalized orthogonal functions invariant from which we can write a Ermakov–Lewis invariant.

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2003 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study in motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

A Continuation Approach to the Periodic Boundary Value Problem for a Class of Nonlinear Coupled Oscillators with Potential Depending on Time

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Chao Wang
Keyword(s):  
Coupled Oscillators ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Continuation Theorem ◽  
Coupled Systems ◽  
Time Dependent ◽  
Periodic Boundary Value Problems ◽  
Nonlinear Coupled Oscillators ◽  
Dependent Potential ◽  
Nonlinear Vector

AbstractIn this paper, we prove a new continuation theorem for the solvability of periodic boundary value problems for nonlinear vector equations. By applying the continuation theorem, we prove the existence of a periodic solution for a class of semi-linear weekly-coupled systems with time-dependent potential.

Anisotropic time-dependent coupled oscillators

1990 ◽  
Vol 41 (7) ◽  
pp. 3775-3781 ◽  
Author(s):  
M. Sebawe Abdalla
Keyword(s):  
Coupled Oscillators ◽  
Time Dependent

scholarly journals Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators

2021 ◽  
Vol 3 (4) ◽  
pp. 684-702
Author(s):  
Radouan Hab-arrih ◽  
Ahmed Jellal ◽  
Dionisis Stefanatos ◽  
Abdeldjalil Merdaci
Keyword(s):  
Coupled Oscillators ◽  
Quantum Dynamics ◽  
Quantum Systems ◽  
Time Dependent ◽  
Strongly Correlated ◽  
Classical Analog ◽  
Photon Excitation ◽  
The Stability ◽  
Shed Light ◽  
Photon Excitations

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

QUANTUM TREATMENT OF TIME DEPENDENT COUPLED OSCILLATORS

2002 ◽  
Vol 16 (19) ◽  
pp. 2837-2855 ◽  
Author(s):  
M. SEBAWE ABDALLA
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Invariants ◽  
Quantum Treatment ◽  
Schrödinger Picture

In this paper we consider the most quadratic time dependent Hamiltonian. An exact solution of the wave function in both the Schrödinger picture and coherent states representation is given. Linear and quadratic invariants are discussed. The eigenvalues and the corresponding eigenfunctions are obtained. The expectation values for the energy are also given.

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