Radial vibration and ultrasonic field of a long tubular ultrasonic radiator

The radial vibration of a metal long circular tube is studied analytically and its electro-mechanical equivalent circuit is obtained. Based on the equivalent circuit, the radial resonance frequency equation is derived. The theoretical relationship between the radial resonance frequency and the geometrical dimensions is studied. Finite element method is used to simulate the radial vibration and the radiated ultrasonic field and the results are compared with those from the analytical method. It is concluded that the radial resonance frequency for a solid metal rod is larger than that for a metal tube with the same outer radius. The radial resonance frequencies from the analytical method are in good agreement with those from the numerical method. Based on the acoustic field analysis, it is concluded that the long metal tube with small wall thickness is superior to that with large wall thickness in producing radial vibration and ultrasonic radiation. Therefore, it is expected to be used as an effective radial ultrasonic radiator in ultrasonic sewage treatment, ultrasonic antiscale and descaling and other ultrasonic liquid handling applications.