Ultrasound receiver ringing suppression
In a project some years ago I had this problem (it was a sonar ranging device intended for close quarters- to detect the approach of an irregular heap of material in an unfriendly environment). As background- the problem is that the transmit pulse of a sonar is enormous compared to the return pulse, and if the receive transducer is still ringing from the transmit pulse, you won't be able to reliably detect the return pulse, so objects close to the transducer might not be detectable. 

The coupling of acoustic energy to the output is weak enough that passive damping was simply not possible- even shorting the transducer for a period during the transmit had little effect. I had to pick a transducer that had a lower 'Q' so that the ringing died out more quickly. 

Downside to that is that the return signal level is lower, and there is more noise from frequencies that the transducer is not (mechanically) tuned to. 

You might be able to modify the transducer by adding mechanical damping in the form of a energy-absorbing material as Brian Drummond suggested.