Abstract: The traditional theoretical model of the radiated sound power of plate structure is usually calculated by numerical integration method. Many models don’t consider the coupling between modes to shorten the calculation time. The study of the influence of the coupling between modes on the sound power can provide an important reference for accurately predicting and controlling the sound radiation characteristics of the plate structure. In order to efficiently calculate the coupling terms between modes, a matrix form analytic solution model based on the power series form analytic solution model of mode radiation efficiency is proposed and established. Numerical examples show that the model is correct. The acoustic vibration characteristics of plate structure under uniform thermal environment are studied and the influence of the coupling of vibration modes on the acoustic power under fixed-point excitation and random excitation in different temperatures is analyzed. The results show that the thermal stress caused by the internal temperature change reduces the equivalent stiffness of the structure, the natural frequency of each order decreases, and the peak value of the sound power curve shifts to the low frequency. The coupling between modes must be considered in the calculation of sound power, especially at low and medium frequencies, although the coupling term has little influence on the sound power of the structure under some conditions, the influence of the coupling terms will increase when the ambient temperature or the position of external excitation changes.

Key words: simply supported plate, radiation efficiency, sound power, temperature load, vibration