Radiation coupling between two coaxial disks of different diameter: An exact solution and detailed experimental verification

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Abstract
The impulse response for the acoustic radiation coupling between two disks has been found in a closed analytic form for the case of a transmitter larger in diameter than a coaxially aligned receiver. In order to verify experimentally the derived expression piezoelectric transducers were used as transmitters and receivers. An analysis of piezoelectric transduction is presented in order to account for transduction effects in the experimental system. Discrete time models of the transmitter and receiver processes valid for times less than one reverberation period are formed based on Redwood’s equivalent circuits adapted by z-transform techniques. Recurrence relationships are derived and used in the manner of digital filters to calculate the transducer output due to any type of input. In the case of the transmitter, the force acting on the front face is calculated for any applied electrical waveform, whereas the receiver model calculates the voltage generated across the device due to any force function acting on the receiver face. The transducer models are used in conjunction with the disk to disk impulse response to calculate the voltage generated across the receiver due to any electrical waveform applied to the transmitter. Responses measured experimentally in water are presented and compared with predicted waveforms; receiver amplifier insertion characteristics are included in the model and a correction is made to take into account ultrasonic absorption by water. Good agreement is shown between the predicted and measured waveforms.

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