# Research Progress on Curved Plates in China: Applications in Architecture
## 3 Acoustic Characteristics of Curved Plates
### Curved Surfaces in Theater Acoustic Design  
The design of theaters has changed gradually with construction capacity. In the beginning, it was only possible to build square concert halls with small spans and simple shapes, but the heights of halls were increased due to the need for ventilation. The narrow and high shape resembled a shoebox, which is where the \"shoe box-type concert hall\" comes from [68]. With the improvement of architectural technology and the deepening of architectural acoustics studies, fan-type concert halls full of modern styles emerged, followed by unique and vineyard-type concert halls. In the process, changes in shape and acoustic requirements were compromised, and surfaces were gradually highlighted. The shoebox-type concert hall is equipped with an acoustic system within a square space. In the evolution from classical to modern, its walls have changed from the original flannel carpets and exquisite reliefs to the modern curved surfaces. From empirical design to theoretical design, the reflection of a curved plate is used to greatly improve the distribution of sound fields. Since the shoe box-type concert hall itself has a great acoustic effect, most of the curved surface applications are as local fine-tuning processing [69]. In China, the most typical cases are the Shanghai Grand Theater and Guilin Grand Theater. The parallel side design provides a great spreading environment for sound reverberation. At the same time, to improve the effect of sound diffusion, a convex-arc reflective surface is adopted in the front sidewall and ceiling of the halls, local sidewalls are serrated diffusers, while balconies and their fence plates are, respectively, wavy lines and serrated (Figure 3a,b). However, compared with the classical design of the Shanghai Grand Theater, Guilin Grand Theater also incorporates local cultural characteristics into the design of the sound diffusion group. The roof adopts the structural form of the top of a cave, and the whole theater adoptsirregular natural streamline modeling, with locally uneven processing. On the side, the appearance of stalactites (Figure 3(b2)) is combined with the structural form of diffusers. The overall shape is irregular and wavy, and the local shape is similar to that of a stalactite. The concave and convex and thick and thin arrangements conform to the morphological rules of QRDs and MLS diffusers, respectively (Figure 3(b3)), meeting the requirements of the disordered arrangement of acoustic diffusers [70]. The fan-type theater conforms to the concept of modern architecture design, but due to its poor acoustic effect, it needs to seek help from the surface to improve the acoustics design in the development process, improve smooth transitions to be more natural, and decrease the sound field darkness. With this series of local changes, the theater can significantly improve the acoustic field distribution and compensate for defects in natural modeling. For example, Guangzhou, Zhuhai Grand Theater (Figure 3c,d), which caters to the \"pearl river stone\" and \"the sun moon scallop\" [76; 77], has a theater building modeled after a fan-type arrangement. To meet the acoustic requirements, the sound diffusion group is arranged in an arc shape at the top of the theater to achieve sound focusing to a certain extent, providing sound reflection to the rear balcony, which in turn provides sound reflection to the bottom pool seats, making up for the weak sound intensity at the back of the theater. Each independent sound diffuser is a convex surface, which locally performs sound diffusion and equalizes the sound energy density in the theater. Combined with the microstructures of surface materials and electroacoustic compensation, indoor acoustic designs can be effectively improved [78]. Compared with the Zhuhai Grand Theater, the side and surrounding walls of the Guangzhou Grand Theater are arranged in a zigzag shape (Figure 3c) to effectively avoid the impact of plane reflection on sound quality [79; 80].