How can I limit the ringing time and amplitude of an ultrasonic receiver that has just been hit by an incoming wave? [Note - just adding a resistor in parallel does not work well]. Any known techniques?
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.
The sharpness of the passband of the transducer, its Q, and how long it "rings" are directly related. Any one of these tells you the others without having to know anything about how the transducer actually works.
You therefore need a lower Q receiver. Many receivers are deliberately tuned to a narrow band to reduce noise. Often this is desirable, but it also leads to longer ringing. In your case you want a lower Q receiver. Look around. Talk to the manufacturer of the one you are using as a start. But, be prepared for the additional off-frequency noise such a receiver will pick up, and reduced sensitivity at your frequency. Basically, you are looking more for a microphone that works at ultrasonic frequencies than a ultrasound receiver tuned to your specific frequency.
This is similar to a radio CTCSS tone squelch ringing issue. what is done in a Radio CTCSS transmit circuit is to do one half cycle of Tone that is 180 degrees out of phase from the initial drive signal. this electronically dampens the ringing. In a radio the CTCSS signal is low frequency but the same principle would apply to a high frequency. you may have to experiment with either just 1/2 wave or more to see what works best.