Modeling And Analysis Of Thermo-acoustic Emission From Graphene Films

The thermo-acoustic effect(TA)of graphene films was discovered by researchers in 2011.Since then,the phenomenon of TA emission from graphene films has attracted many researchers’ attention.Compared with traditional electro-acoustic(EA)transducers that generate sound by mechanical vibration,graphene film TA transducers show a lot of attractive merits----no vibration parts,small in size,light in weight and flexible,which can improve the situation in the vehicles where the loudspeakers are too big in size to be installed flexibly.They can also be used as secondary sound sources for active noise control(ANC)in vehicle cabins.Up to now,most study on the graphene film loudspeakers has focused on the experimental investigations of the TA characteristics,theoretical studies are very few.Recently,with the development of advanced manufacturing technology,the thickness of the substrate of the graphene film can be reduced to a few nanometers.The theoretical studies of the graphene on a substrate thinner than the thermal penetration depth is very few.And the corresponding characterization parameters and selection principles of substrates and gases have not been reported publicly.This paper is under the background of the project of National Natural Science Foundation of China(Study on Thermo-Acoustic Mechanism of Graphene Films).In this paper,the TA theory models for graphene both on a substrate thinner than the thermal penetration depth and on a substrate thicker than the thermal penetration depth are established by using thermal-mechanical coupling analysis and acoustic radiation from the piston-like sound source,respectively.The analytical solutions of sound pressure are derived and the influences of different substrates and different gas on the output sound pressure of graphene film TA emitters are analyzed.The selection principle of substrates and gases are provided.Then,the numerical solutions of output sound pressure at different power,different distance,different frequency and in different gases are calculated to analyze and compare with the analytical solutions.Finally,and the experimental tests of the sound pressure at different power,different distance,different frequency are conducted to analyze and verify the analytical solutions and the numerical solutions.The main contents and conclusions of this paper are as follows:(1)Firstly,from the perspective of the thermo-mechanical coupling,the TA models for graphene on a substrate thinner than the thermal penetration depth and on a substrate thicker than the thermal penetration depth are established respectively,and the analytical solutions of output sound pressure of graphene film in near-and far-field are derived.The validity of the analytical solutions is verified by the published experimental results,and the characterization parameters and selection principles of substrates are analyzed.As the study shows,when the thickness of the substrate is less than the thermal penetration depth,the TA performance of the substrate is characterized by the heat capacity per unit area(HCPUA)of the substrate.The smaller the HCPUA of the substrate,the larger the sound pressure(SP)of the graphene film;when the thickness of the substrate exceeds the thermal penetration depth,the TA performance of the substrate is characterized by the thermal effusivity of the substrate.The smaller the thermal effusivity of the substrate is,the larger the SP of the film is.(2)Next,in order to further understand the principle of TA emission,the thermal piston models for graphene on a substrate thinner than the thermal penetration depth and on a substrate thicker than the thermal penetration depth are established.The analytical solutions of output sound pressure of the graphene films are derived.And accordingly,the limit of the sound pressure in full-space and half-space are obtained.By comparing the solutions of the sound pressure derived by the coupled thermo-mechanical model with the thermal piston model,the solutions are firstly found to be identical in the ideal gas medium for the two different models in this paper.After comparing the SP of graphene films in different gases,the characterization parameters and selection principles of gases are analyzed.As the study shows,when the thickness of the substrate is less or larger than the thermal penetration depth,the TA performance of the gas is characterized by the specific heat and the thermal effusivity.A lower specific heat with a higher thermal effusivity is favorable to a high SPL of the film.(3)Then,the output sound pressure of graphene film at different power,different distance,different frequency and in different gas mediums is numerically calculated by simulation software.Compared the numerical results with the analytical results,the relationships between output SPL of graphene film and power,distance,frequency and gas mediums are analyzed.As the study shows,the numerical values are in good agreement with the theoretical ones.the output SPL of the graphene film in far-field increases with the increase of frequency and tends to be stable with the increase of frequency,while the output SPL in near-field shows little fluctuation with the change of frequency.The output sound pressures(SP)of the film in far-and near-field are proportional to the input power.The output SP of the film in far-field is inversely proportional to the distance.For air,helium,argon and xenon,the SPL is the highest when in xenon and is the lowest when in helium.(4)Finally,a sound pressure test system is established to test and analyze the relationship between the output SP and power,the SP and distance,and the SPL and frequency for graphene films with different substrates,where the theoretical model is further verified.