= Mechanical impedance measurement
A <mechanical impedance measurement> determines the amplitude and phase of driving <force> relative to motion at a specified port. With the convention $Z=F/V$, a driving-point test measures the <force> and <velocity> at the same location and in the same direction. Both terminal motions must be included if the second terminal moves. Ole Døssing's manufacturer guide describes this need for coincident excitation/response measurements and the use of an <impedance head> combining force and acceleration sensing.<Structural Testing Part I: Mechanical Mobility Measurements by Ole Døssing>[“Response Measurements”, printed pp.30–32, driving-point transducer arrangement]{ref}
A typical apparatus uses a vibration exciter or instrumented impact to drive the structure, a force transducer in the excitation path, an <accelerometer> near the driving point, and synchronized acquisition of both signals. The <measurement calibration>, mounting, excitation range and fixture motion belong in the test description. A transfer response at a remote point is useful but answers a different question from driving-point <mechanical impedance>.
For a steady sinusoid with convention $e^{i\omega t}$, acceleration <complex amplitude> $A$ gives $V=A/(i\omega)$, hence
$$
Z(i\omega)=i\omega\frac{F}{A}.
$$
For example, at $\omega=100\,\mathrm{rad/s}$ let the applied <force> amplitude be $1\,\mathrm N$ and acceleration amplitude be $10\,\mathrm{m/s^2}$ in phase with the force. Then $|V|=0.10\,\mathrm{m/s}$ and $Z=i10\,\mathrm{N\,s/m}$. This is the response of a pure $0.10\,\mathrm{kg}$ mass: force leads velocity by a quarter cycle. Reporting only the two amplitudes would lose that distinction from a dissipative response.
For broadband excitation, estimate the relevant <frequency response> from the synchronized force and response records, with suitable error analysis. A response peak alone can come from a peak in the applied force, so the response spectrum by itself does not establish structural resonance. Transducer mass can modify a small structure, and fixture inertia can contribute measured force; both require an explicit measurement model. Repeating at another excitation amplitude tests the assumed linear regime rather than treating a changed response ratio as the same invariant system property.<Structural Testing Part I: Mechanical Mobility Measurements by Ole Døssing>[“The Frequency Response Function”, p.14; “Errors”, pp.23–25; “Response Measurements”, pp.30–32; “Calibration”, p.43]{ref}
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