# Analysis of the Effect of Temperature on the Sound Transmission Loss of a Curved Plate
## 1 Introduction
[25] derived the thermoacoustic response of a rectangular simply supported flat plate in a thermal environment, verified the accuracy of the model using the finite element method, and studied the effects of the temperature difference and thermal convection on the STL and modal frequency based on the theoretical model. [PERSON] et al. [26] established the vibration control equations of a thin shell with a functional gradient under thermal load excitation based on the thin-shell theoretical model developed by [PERSON], which was solved using the Galerkin method, and analyzed the effect of temperature on the natural frequency. The results showed that an increase in temperature decreased the natural frequency, but at a certain value of temperature, the natural frequency changed abruptly, which was mainly due to the temperature changing the wave number of the lowest natural frequency. [PERSON] et al. [27] established a model for the STL of a double-layered rectangular sandwich panel in a thermal environment and calculated the thickness ratio of the incident- and transmitted-side rectangular panels based on the theoretical model. The results showed that the average STL under a 2 \({}^{\circ}\)C temperature gradient was largest when the thickness ratio of the rectangular panels on the two sides was 1.9. The literature shows that few studies have been conducted on the performance of curved plates under temperature effects. In particular, most current research relies on the traditional elastic mechanics model to directly calculate the deflection in the dynamic equations of curved plates. The reason is that the complexity of the equation is difficult to solve. Therefore, this limitation is overcome in this study by simplifying dynamical equations by neglecting the shear force, plane displacement, and plane inertia according to the Donnell theory. In addition, the effect of temperature is considered, and the vibroacoustic performance of the curved plate is directly focused on through the solution of the modal superposition method. In this study, based on the fluctuation and heat conduction theories, a theoretical model of the STL of a curved plate under simply supported boundary conditions when subjected to temperature and acoustic loads was established, considering the effect of temperature/thermal stress. The modal superposition method was used to solve the theoretical model, and the effects of the opening angle, radius of curvature, temperature, and acoustic incidence angle on the modal frequency and STL were analyzed. This paper is organized as follows. The next section discusses the development of the theoretical model of the STL of curved plates in a thermal environment. In the Section 3, the theoretical results of modal frequencies and the STL are compared with the results of the finite element method to validate the model. Furthermore, based on the theoretical model, the effects of temperature on the modal frequency and STL are analyzed, as well as the effects of the pitch angle, azimuth angle, radius of curvature, opening angle, and loss factor on the STL. Finally, the conclusions are presented.