Anharmonicity

In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used. In reality all oscillating systems are anharmonic, but most approximate the harmonic oscillator the smaller the amplitude of the oscillation is.

As a result, oscillations with frequencies ${\displaystyle 2\omega }$ and ${\displaystyle 3\omega }$ etc., where ${\displaystyle \omega }$ is the fundamental frequency of the oscillator, appear. Furthermore, the frequency ${\displaystyle \omega }$ deviates from the frequency ${\displaystyle \omega _{0}}$ of the harmonic oscillations. See also intermodulation and combination tones. As a first approximation, the frequency shift ${\displaystyle \Delta \omega =\omega -\omega _{0}}$ is proportional to the square of the oscillation amplitude ${\displaystyle A}$:

${\displaystyle \Delta \omega \propto A^{2}}$

In a system of oscillators with natural frequencies ${\displaystyle \omega _{\alpha }}$, ${\displaystyle \omega _{\beta }}$, ... anharmonicity results in additional oscillations with frequencies ${\displaystyle \omega _{\alpha }\pm \omega _{\beta }}$.

Anharmonicity also modifies the energy profile of the resonance curve, leading to interesting phenomena such as the foldover effect and superharmonic resonance.