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.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.[1][2]
Mechanical impedance is the inverse of mechanical admittance or mobility. The mechanical impedance is a function of the frequency {\displaystyle \omega } \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. A simple 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 )} \mathbf {F} (\omega )=\mathbf {Z} (\omega )\mathbf {v} (\omega )
Where, {\displaystyle \mathbf {F} } \mathbf {F} is the force vector, {\displaystyle \mathbf {v} } \mathbf {v} is the velocity vector, {\displaystyle \mathbf {Z} } \mathbf {Z} is the impedance matrix and {\displaystyle \omega } \omega is the angular frequency.