中文摘要：

耳蜗是人体最为精密的力学元器件,能处理频率从几十到几万赫兹的声信号.实验研究表明,声波进入耳蜗后,沿着基底膜传播,基底膜能够将不同频率的声信号分散到不同的位置,并为位于基底膜上的毛细胞所感知,就像一个天然的Fourier（傅里叶）滤波器.在von Békésy行波理论框架体系下,基于Manoussaki等的三维螺旋基底膜流固耦合耳蜗模型,考虑耳蜗导管高度和基底膜刚度均为纵向梯度变化,推导出基底膜声波传播的频散方程,分别分析了基底膜刚度和耳蜗导管高度对频散特性的影响.发现耳蜗内淋巴液的存在大大提高了耳蜗对低频信号的处理能力,且捕获频率随基底膜刚度和耳蜗导管高度的减小而降低,两者梯度变化在声信号调制中起协同作用.最后,以人、沙鼠和豚鼠的具体耳蜗参数为例,得到3种生物耳蜗频率-点位图,并验证了低频段模型预测的正确性,比较分析了耳蜗频散功能与生物适应性之间的关系.

英文摘要：

The cochlea is the most precise mechanical component in a human body. With frequencies from dozens to thousands of Hertz,acoustic signals can be processed by the cochlea and captured by the sensory hair cells on the basilar membrane（ BM）. Experimental research shows that sound waves of different frequencies are scattered at different positions along the basilar membrane as a natural Fourier filter.Based on Manoussaki＇s 3D fluid-solid coupling model for the spiral cochlear basilar membrane and in addition according to the longitudinal gradients of the cochlear duct height and the BM stiffness,a dispersion equation for the acoustic wave propagation along the basilar membrane was deduced. The influences of the duct height and the BM stiffness on the dispersion characteristics were analyzed. It is found that existence of the cochlear endolymph greatly increases the low-frequency signal processing ability,and the capture frequency reduces with the decreases of both the BM stiffness and the duct height. Finally,3 examples of human,gerbil and guinea pig were empirically studied for verification. 3 frequency-position diagrams corresponding to the 3 animals respectively were obtained to prove the correctness of the proposed dispersion model,and reveal the relationship between the biological adaptability and the function of cochlear dispersion. This study is not only beneficial to understanding of the cochlear function but also promising to lay a theoretical basis for the development and design of sound sensors.