Mechanical Input Admittance of Ultrasonic Delay Lines Operating in Torsional or Shear Modes

Abstract

The mechanical input admittance at the end face of an ultrasonic delay line operating in torsional modes for a rod or shear modes for a plate is analyzed. The analysis is based on the facts that SH waves in a plate constitute a Fourier series and torsional waves in a rod constitute a Dini series, and consequently any stress distribution on the end face can be expanded in terms of these waves. It is shown that modes below cutoff contribute to the susceptance, and modes above cutoff contribute to the conductance. Three transducer configurations are discussed: namely, a single transducer for exciting symmetric modes in a plate, two push-pull transducers for exciting antisymmetric modes in a plate, and a hollow coaxial transducer for exciting torsional modes in a rod. Modes below cutoff decay exponentially along the direction of propagation. The distance from the end face at which these modes have significant effects is discussed. As the frequency becomes successively higher than cutoff frequencies, successively more modes become propagating. The amplitude distribution among these propagating modes is also discussed. A transducer which covers the whole cross section can excite the fundamental nondispersive mode in plates and rods without generating higher modes. Hence, this configuration is recommended for delay line design in order to avoid possible complications due to higher modes in the delay line characteristics.