Study Of Finite Difference Time Domain Method For Acoustic Characteristics Of Ancient Stage Components

Chinese ancient stage is an important type of Chinese traditional architecture.In the history of the world's ancient theater,the Chinese theater has a unique style.Chinese traditional opera,with its performance characteristics of comprehensiveness,virtuality and formality,has fascinated audiences all over the world.China has a vast territory,and each region has formed its local culture in the long-term historical development.There are more than 300 different kinds of local opera in China.The south area of Shanxi Province is known as the cradle of Chinese opera art,and its theater architecture is also the treasure of Chinese ancient architecture art.Since the last century,there have been many scholars carrying out investigations and studies on Shanxi's opera stage.However,the investigations mainly from the perspectives of architecture form,history of cultural relics,opera culture,protection and repair.The study on the theatre's acoustics is less.Chinese courtyard-style traditional theatre belongs to open space,therefore it's not enough to use the classical acoustics research method.It is necessary to explore the research method and subjective and objective sound quality index suitable for Chinese traditional theatre.The essence of sound transmission is a fluctuating process.The most reasonable way to discuss a certain acoustic phenomenon is to start from the most essential mode of sound transmission.Therefore,this paper will apply the finite-difference time-domain acoustic wave equation to investigate the sound quality of ancient stage.After collecting a certain amount of literature,it was found that there were many ancient theatres with caves as the backstage in Shanxi Province.Combining with Shanxi's architectural elements,the ancients set the backstage as a cave,which became a cave-style stage.In order to explore this kind of particular ancient acoustic architecture,in this thesis,five representative cave-style stages in Shanxi Province have been investigated,the architectural features have been described in detail and some acoustic measurements have been made.By comparing the measured and simulated results,the finite-difference time-domain method is proved to be correct in the acoustic research of the traditional theatres.Besides,it is also found that there are splayed walls in the mouth of the stages of Qing Dynasty in Shanxi Province.In this thesis,the acoustic wave equation is used to study theacostical characteristics of cave-style stage and splayed walls.At the beginning of the study,in order to facilitate programming,the sound field of the stage with flat roof in cave dwelling has been discussed.Five stage models have been constructed based on the representative prototype stage of Chaoshan Temple in Xiaohu Village of Pingyao County.The impulse response of several receiving points was obtained through finite-difference time-domain method,which has been done the frequency analysis later.The results show that horizontal caves can enhance the reverberation sense more than vertical ones,and the larger the space inside the cave,the more frequencies can be amplified and the more harmonious the sound effect will be.It is a key problem to solve the curved boundary of arch structure when using the finite-difference time-domain method to simulate the cave-style stage.Rectangular grids are commonly used in the finite-difference time-domain equations.The curved boundary is usually solved by the traditional step approximation method.However,the step approximation method has some error.This paper introduce the local conformal grid technology into sound wave propagation equations from the electromagnetic field research.Combining the absorption boundary of perfectly matched layer?PML?to derive the equations suitable for topless courtyart.In order to verify the accuracy of conformal FDTD equation of sound wave,the sound field of two-dimensional elliptic room has been simulated.The results show that the conformal technique is more accurate than the step approximation method,and the calculation is more convenient.Hence,the conformal technique will be used to solve the curved boundary in this paper.The semi-dome is the commonly used roof structure of existing caves,and the semi-dome equation is a regular equation,which is convenient for programming calculation,for these reasons,the situation of semi-dome is discussed in this paper firstly.For the 3D conformal grid,the conformal area and volume of the grid are the core issues.Since the cave structure is simple and symmetrical,the conformal area and volume can be obtained quickly by the projection method.After obtaining the impulse responses of all receiving points of five models,analyze their loudness,reverberation time T₃₀,early decay time EDT,and other objective acoustic parameters.It is found that,for the traditional courtyard stage in China,the early decay time EDT is better than the reverberation time T₃₀ to explain the reverberation of headless stage.In order to further verify the relationship between objective parameters and the actual sense of hearing,the paired comparison method was used to design a hearing test.After correcting the obtained impulse response,convolved them with three kinds of dry signals respectively to generate the test audio signals.Finally,the Matlab GUI interface has been used to enable the subjects to complete the listening test independently.The result of the test shows that the backstage with cave can bring more spaciousness and fullness.From the hearing test result,the conclusion that early sound energy decay time EDT is better than reverberation time T₃₀ to explain the reverberation of a headless stage.Finally,the models of 2D and 3D splayed walls are established referring to the construction,size and other parameters of the splayed walls in various stages in Shanxi Province.The influence of the splayed walls on sound quality of the theater was discussed by conformal FDTD method.After analyzing the sound field intensity,early sound energy and lateral energy factor in the audience area,it is found that stages with splayed walls can enhance the sound intensity of the audience area more than the stage without splayed walls.The splayed walls can strengthen the early lateral reflection sound and early sound,which makes the spaciousness in the front area of splayed walls better.The structure of the splayed walls is similar to the sound reflection boards on both sides of the stage mouth in modern theater.It beautifies the stage shape and improves the sound quality of the theater,which has great research significance.Moreover,a high order precision algorithm for FDTD equations is proposed to improve the computation speed and accuracy in large space acoustic field.In this paper,the accuracy of high order algorithm is analyzed from the stability and numerical dispersion.Combining the high order precision algorithm with impedance boundary conditions and PML boundary conditions,relevant simulation calculation is carried out and its high efficiency is verified.The research work of this thesis promote the application of FDTD in architectural acoustics,makes up for the lack of research on the acoustic effects of two special architectural components in Shanxi Province:the cave-style stage and the splayed walls in front of the stage.Moreover,the measured and simulated results are significant to the protection of ancient acoustic buildings and the sound quality design of national performance buildings.