A study to the resonant frequency of ultrasonic horns with large rectangular cross-section

Ultrasonic horns are an important part in transducer vibrational systems,in this paper we studied the coupled vibration of the ultrasonic horns with large rectangular cross section on the basis of the apparent elasticity method,and derived out the resonant frequency equation of horns with single rectangular cross section (exponential,conical,catenoidal and stepped horns).Experiments show that measured frequencies of horns with large rectangular cross section agree well with calculated results.As compared with the results from the one-dimensional vibrational theory,the frequencies from the coupled vibrational theory in this paper are nearer to the measured results.The coupled vibrational theory will find wide applications in the analyses and calculations of large horns with rectangular cross-section and other large-dimensional ultrasonic horns.