Mechanical impedance

Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the force applied at a point to the resulting velocity at that point.

Mechanical impedance is the inverse of mechanical admittance or mobility. The mechanical impedance is a function of the frequency ${\displaystyle \omega }$ of the applied force and can vary greatly over frequency. At resonance frequencies, the mechanical impedance will be lower, meaning less force is needed to cause a structure to move at a given velocity. The simplest example of this is pushing a child on a swing. For the greatest swing amplitude, the frequency of the pushes must be near the resonant frequency of the system.

${\displaystyle \mathbf {F} (\omega )=\mathbf {Z} (\omega )\mathbf {v} (\omega )}$

Where, ${\displaystyle \mathbf {F} }$ is the force vector, ${\displaystyle \mathbf {v} }$ is the velocity vector, ${\displaystyle \mathbf {Z} }$ is the impedance matrix and ${\displaystyle \omega }$ is the angular frequency.

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