Study on the different shapes of ultrasonic horn with a central hole

Based on the analytical method,the property factors and frequency equations of the horn with a cylindrical and a conical hole are derived.Utilizing finite element method,the distribution of stress and vibration of the two kinds of horns are studied along the axial.The results show that under the same resonant frequency and area factor,the amplification of the conical horn with a conical hole is the greatest,then is the conical horn with a cylindrical hole and the last is the solid conical horn.It found that the sum of displacement of node and strain maxima is substantially equivalent to its half wave resonant length.Finally,it is proved that the hollow and solid horns have the same equivalent circuit.