The analysis for the influence of the plate thickness on acoustic radiation characteristics of an unbaffled thin plate

The influence of the thickness of the plate on the Green function is usually neglected and a double layer potential is adopted to calculate the sound radiation characteristics of an unbaffled thin plate. Considering the acoustic radiation impedance caused by the thickness, the sound pressure is calculated by using the mixed layer potential and the influence of the thickness on the acoustic radiation parameters is analyzed. According to compatibility conditions at the interface, the pressure and velocity of the plate surfaces are denoted by boundary integral equations and the same items in the expressions are merged. The structural dynamic equation is substituted into the velocity equations with the forms of mixed layer potential, and the pressure jump and the plate displacement are developed in series of the vibration modes to obtain radiation impedance of double integral form. So the coefficients of vibration modes are solved and the radiation characteristic parameters are determined. Sound radiation parameters are calculated and compared with the example of a simply supported rectangular plate and the sensitivity to the thickness is discussed. The result shows that the acoustic radiation impedance caused by the thickness has little effect on the magnitude of the parameters, but with the increase of the frequency, the resonance frequency is shifted more distinct; In the range of the same order resonant frequency, the greater the thickness of the plate is, the larger the parameter error calculated with the double layer potential is.