Maximum Resonant Impedance of a piezo disc
Piezoelectric transducers have several major issues from the driving circuits point of view:


Capacitance. Piezoelectric transducers have large capacitive values compared to other transducers. Those for audio and low frequency ultra-sound have a capacitance of about 150nF. These disc are about 1"/25mm in diameter.
Those for 1MHZ to 10MHZ ultra-sound are small rectangles epoxied to a resonant plate.
Often the driver is custom made for a certain type of Piezoelectric crystal. This protects both the driver and the crystal from non-resonate frequencies and DC offset currents that can warp the crystal.
The resonant frequency consumes the least amount of current and produces the highest output level possible. Damage would occur if the intensity of the signal was too strong, and/or the crystal gets too hot due to a lack of a heat sink or high ambient temperatures.
The anti-resonant frequency consumes the most amount of current and produces the lowest output level possible. Damage would occur if the intensity of the signal was too strong, and/or the crystal gets too hot due to a lack of a heat sink or high ambient temperatures.
It is a basic law of physics that the larger the crystal, the lower the resonate frequency. For a given resonate frequency a small variation in frequency is allowed, with less output as you move further away from the center point of peak resonate output. Most crystals will allow +/-20% at most.
I could not find the term "average resonant impedance", at least during the searches I did. However the term "Fundamental Radial Resonance" refers to the center point between the peak resonant frequency and the peak anti-resonant frequency. This is equivalent to the "average resonant impedance". They are not including lower sub-harmonics which emit out the side of the crystal, and the driver amplifier is designed not to allow these out-of-band frequencies.
If you can find the source of certain 'terms' used to describe piezoelectric crystal behaviour then we can try to interpret them for you.


The following article covers some basics of impedance vs. resonate frequency.


  The electrical impedance is a distinguishing characteristic for
  piezoelectric elements. It differs substantially from the impedance of
  non-piezoelectric dielectric elements when driven at high-enough
  frequencies. The difference stems from the coupling of electrical
  energy input to mechanical motion output. Recall that the electrical
  impedance is defined as the voltage drop across an element divided by
  the current through the element. For a (simple geometry) piezoelectric
  element, the electrical impedance over a given frequency range will
  appear similar to that
  shown here:


Impedance Plot:


  The impedance for a non-piezoelectric element (of the same shape and
  dielectrical properties) is also shown in blue. The presence of
  electrical resonances and anti-resonances make the piezoelectric
  impedance unique. The resonances result from the electrical input
  signal exciting a mechanical resonance in the piezo element. For each
  mechanical resonance in the piezo element, a resonance/anti-resonance
  pair will exist in the impedance.


The following link and PDF goes into much more detail, including materials and shapes vs. resonate properties, thermal limits,
 etc: http://www.piezotechnologies.com/knowledge-desk/overview-piezo-materials