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An impedance head combines a force transducer and an accelerometer in one housing for a driving-point vibration test. It measures applied force and acceleration at nearly the same location and along the intended excitation direction. The raw channels yield mechanical accelerance or its reciprocal mechanical dynamic mass; deriving mechanical driving-point mobility or mechanical driving-point impedance additionally requires the acceleration-to-velocity conversion.^[ref]

In the manufacturer's Types8000/8001 example, a piezoelectric acceleration sensor sits above a force gauge in a stiff housing, with separate electrical outputs. The arrangement aims to preserve the phase relation needed for a complex response ratio. This solves a practical apparatus problem: a separate exciter and response sensor can otherwise occupy different points, particularly on a small structure.

An impedance-head mass correction accounts for moving material between the force-sensing plane and the specimen. In a rigid lumped approximation, choose a common positive axis and let that material have effective mass $m_h$ and acceleration complex amplitude $A$. Then Newton's second law givesFor an original in-phase example, let $m_h=0.020\mathrm{kg}$, $A=10m/{\mathrm{s}}^2$ and gauge force $1\mathrm{N}$. Specimen force is $0.80\mathrm{N}$, so specimen accelerance is $12.5\mathrm{k}{\mathrm{g}}^{-1}$ rather than the uncorrected value10. With general signals the correction is a complex subtraction, not subtraction of unsigned amplitudes.

This force-plane correction does not undo every effect of attaching the instrument: added mass and mounting stiffness can change the specimen's actual vibration. The test must also state mounting, calibration, usable frequency range and the motion of any second terminal. Manufacturer guidance distinguishes measurements requiring mass compensation and cases where separate force/acceleration sensors are preferable.^[ref]

An impedance-head mass correction removes the inertial force required to accelerate material between an impedance head's force-sensing plane and the specimen. The manufacturer's construction places the acceleration sensor above the force gauge and makes the connection to the driving point stiff. Its guidance recommends compensation when the specimen's mechanical dynamic mass is comparable to the mass below the gauge.^[ref]

Choose a common positive axis and assume a rigid intervening mass $m_h$ shares specimen acceleration $A$. Newton's second law givesHere $F_g,F_s,A$ are synchronized complex amplitudes at the same angular frequency. Hence the corrected mechanical dynamic mass is $F_s/A=F_g/A-m_h$, and corrected mechanical accelerance is $A/(F_g-m_{h}A)$. The effective intervening mass must include the applicable mounting hardware; it is not automatically the entire sensor mass.

For an original example, take $m_h=0.020\mathrm{kg}$, $A=10m/{\mathrm{s}}^2$ real, and $F_g=(0.60+0.80i)\mathrm{N}$. Then $F_s=(0.40+0.80i)\mathrm{N}$, with magnitude $\sqrt{0.80}\approx 0.8944\mathrm{N}$. Subtracting unsigned amplitudes would instead give $1-0.20=0.80\mathrm{N}$ and lose the correct phase. The corrected mechanical dynamic mass is $(0.040+0.080i)\mathrm{kg}$.

The model requires synchronized channels, appropriate measurement calibration and sufficiently rigid motion below the force gauge. If that assembly flexes, its motion cannot be represented by one frequency-independent $m_h$. Subtracting inertia also does not recover the unattached specimen's response: the attached head can still change its natural frequencies and mode shapes. A useful apparatus check is a rigid test mass, for which the force/acceleration ratio should agree with the total moving mass in the chosen force plane within the tested range.

Mechanical dynamic mass is the complex force-to-acceleration ratio $M_{\mathrm{dyn}}(s)=F(s)/A(s)$ for a stated mechanical excitation and response. It is the scalar reciprocal of mechanical accelerance where that response is nonzero. Its units are kilograms, but a supported structure need not have a real, positive or constant dynamic ratio. An impedance head supplies separate force and acceleration channels from which this response can be estimated.^[ref]

For $m\ddot{x}+c\dot{x}+kx=F$ with zero initial conditions,Equivalently, mechanical dynamic stiffness equals $s^2{M}_{\mathrm{dyn}}$. A freely translating ideal mass gives $M_{\mathrm{dyn}}=m$; a spring-supported mass includes the elastic and dissipative terms. With $m=2\mathrm{kg}$, $k=200N/m$ and $c=4\mathrm{N}s/m$, at $\omega =5rad/s$ the result is $(-6-0.8i)\mathrm{kg}$. At $10rad/s$ it is $-0.4i\mathrm{kg}$. The negative real part in the first case describes a restoring-force contribution relative to acceleration; it is not a negative quantity of material.

An impedance-head mass correction subtracts the effective moving mass below the force-sensing plane from the measured scalar dynamic ratio, provided that material shares the measured acceleration. This is a force-plane correction, not removal of the sensor's physical influence on the structure. At an antiresonance, a small response can produce a very large reciprocal ratio; dividing by a channel near its noise floor makes that estimate unreliable. With coupled measurement coordinates, exchanging complete force/acceleration descriptions requires a matrix inverse, rather than the reciprocal of each transfer entry.