Nonlinear resonance

foldover effectnon-linear resonanceNonlinear Resonancesnonlinear resonant
In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system.wikipedia
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Resonance

resonantresonant frequencyresonance frequency
In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. Nonlinear effects may significantly modify the shape of the resonance curves of harmonic oscillators. In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

Anharmonicity

anharmonicanharmonic oscillatoranharmonic oscillators
Nonlinear effects may significantly modify the shape of the resonance curves of harmonic oscillators.
Anharmonicity also modifies the energy profile of the resonance curve, leading to interesting phenomena such as the foldover effect and superharmonic resonance.

Wave turbulence

turbulenceturbulentweak wave turbulence
A graphical representation of a resonant cluster of wave components is given by the corresponding NR-diagram (nonlinear resonance diagram).

Physics

physicistphysicalphysicists
In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system.

Nonlinear system

nonlinearnon-linearnonlinear dynamics
In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system.

Amplitude

peak-to-peakintensityvolume
In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

Oscillation

oscillatorvibrationoscillators
In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

Linear system

linearlinear systemslinear theory
In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

Force

forcesattractiveelastic force
From the physical point of view, they are defined by whether or not external force coincides with the eigen-frequency of the system (linear and nonlinear resonance correspondingly).

Natural frequency

natural frequencieseigen-frequencyeigenfrequency
From the physical point of view, they are defined by whether or not external force coincides with the eigen-frequency of the system (linear and nonlinear resonance correspondingly).

Partial differential equation

partial differential equationsPDEPDEs
with possibly different being eigen-frequencies of the linear part of some nonlinear partial differential equation.

Vector (mathematics and physics)

vectorvectorsvectorial
Here is a vector with the integer subscripts i being indexes into Fourier harmonics – or eigenmodes – see Fourier series.

Normal mode

modesnormal modesmode
In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude. Here is a vector with the integer subscripts i being indexes into Fourier harmonics – or eigenmodes – see Fourier series.

Fourier series

Fourier coefficientFourier expansionFourier coefficients
Here is a vector with the integer subscripts i being indexes into Fourier harmonics – or eigenmodes – see Fourier series.

Diophantine equation

Diophantine equationsDiophantine analysisDiophantine
Accordingly, the frequency resonance condition is equivalent to a Diophantine equation with many unknowns.

Hilbert's tenth problem

Hilbert's 10th problem10th10th Hilbert problem
The problem of finding their solutions is equivalent to the Hilbert's tenth problem that is proven to be algorithmically unsolvable.

Harmonic oscillator

harmonic oscillatorsharmonic oscillationdamped harmonic oscillator
Nonlinear effects may significantly modify the shape of the resonance curves of harmonic oscillators.

Harmonic

harmonicsflageoletharmonic frequencies
These functions reveal resonance ridges, harmonic, inter modulation, and energy transfer effects in a way that allows the user to relate these terms from complex nonlinear discrete and continuous time models to the frequency domain and vice versa.