基底厚度小于热渗透深度的石墨烯薄膜热声理论

Thermo-acoustic theory of the graphene film with a substrate thinner than thermal penetration depth

基于热声效应,对基底厚度小于热渗透深度的石墨烯薄膜发声器进行理论和仿真研究。首先,利用石墨烯薄膜发声器的热功率平衡方程与气体中的热弹性耦合线性方程组推导出了石墨烯薄膜发声器的近/远场声压表达式。将理论计算结果与实验测试值进行对比,二者吻合良好,验证了理论模型的正确性。然后,利用仿真软件对石墨烯薄膜的近远场声压值进行了仿真计算,并将仿真值与理论值进行对比,二者有良好的一致性,验证了仿真计算方法的有效性。研究表明,石墨烯薄膜发声器的远声场为球面波,近声场近似为平面波。在远场低频段,声压级随输出声频率的增加而缓慢增大;在近场高频段,声压级几乎不受输出声频率的影响。研究结果为基底厚度小于热渗透深度情形下的热致发声器提供了理论计算和分析方法,对石墨烯薄膜声源器件的实验研究具有指导意义。

Based on thermo-acoustic effect,the graphene film with a substrate thinner than thermal penetration depth is studied both in theory and simulation.Firstly,the expressions of sound pressure in near and far field of graphene film thermophones are derived by using the thermal power balance equation of the thermophone and the thermalelastic coupled linear equations in gas.By comparison,the theoretical calculation results are in good agreement with the experimental results,which verifies the availability of the theoretical model.Then,the sound pressures in near and far field of graphene films are calculated by simulation method,and the results are compared with the theoretical values to show their good consistency,which validates the availability of the simulation calculation method.The analysis results show that the sound wave in far field of the graphene film is spherical,and approximately planar in near field.At low frequencies,the sound pressure level(SPL)in far field increases with frequency;while at high frequencies,the SPL in near field is nearly independent of frequency.The study in this paper presents a calculation and analysis method for the graphene film thermophone with a substrate thinner than the thermal penetration depth,and provides guidance for the experimental research on graphene film thermophones.