The complex-mode vibration of ultrasonic vibration systems.

The longitudinal-flexural and torsional-flexural vibrations are studied for the ultrasonic solid horn and the ultrasonic vibration system comprised of a sandwich transducer and a solid horn. The discussed solid horn is of arbitrary non-uniform cross-section. The analysis on flexural-mode vibration is based on Timoshenko theory. The theoretical results are verified by experiment.