Design flexural vibrating stepped thin plate and calculating its acoustic performances

The flexural vibrating stepped thin plate,which is improved by the thin plate,seems to be a very useful type of transducer for the generation of ultrasounds in fluids.However,due to the existence of step,the frequency equation can be derived according to the continuity of deflection,slope,shear force and radial bending moment at its vibrating nodal lines,as well as its boundary conditions.More one vibrating nodal line will increase four equations. More variables,and more complex equation coefficients,make difficult to solve the frequency equations.In this paper, taking a flexural vibrating stepped thin plate with a single nodal line as an example,a feasible numerical method is presented,and a computer program is developed.It is shown that the tested results are in good agreement with the theoretical ones.Furthermore,the acoustic field distribution and the radiation impedance of the stepped thin plate can be obtained.This study can provide an effective method for designing and calculation acoustic performances of the flexural vibrating stepped thin plate.