声带计算机仿真的新型数学–力学模型综述

Review on New Mathematical and Mechanical Models for the Computer Simulation of Vocal Cord

摘要: 本文综述了目前声带仿真模型研究的新型数学模型和力学模型。基本模型是一个双质量块非线性振动系统，该系统被认为是一种基本发音过程的力学描述。声带模型不仅可以扩展为三质量块系统、五质量块系统和多质量块系统，也可以扩展为随时间变化而导致参数不同的系统，或者是三维系统。另外，还可以简化成一个具有双向偏转和具有阻尼功能的耦合系统。相应的数学模型对应的二阶微分方程系统，描述了对称和非对称声带的振动。以上这些模型给出了规则和不规则运动的条件，这些运动发生在声带的分叉点，或者是确定性混沌状态。当我们不能从视觉上看出有疾病时，实验得出的结果使得检查声带的病理状态有特殊的意义。根据文中给出的结果，在未来进行这项研究是一个可以实现的目标。

Abstract: A review on new mathematical and mechanical models of the vocal cords is given. The basic model is a two-mass nonlinear oscillator system which is accepted to be the basic one for mechanical de-scription in voice production. The model is not only extended into three, five, and more mass sys-tems, systems with time variable parameters and three-dimensional systems, but also simplified into one-mass system with coupled two-direction deflection and damping functions. The corres-ponding mathematical models are the systems of coupled second-order differential equations which describe the vibrations of the symmetric and asymmetric vocal folds. The models give the conditions for the regular and irregular motions like bifurcation and deterministic chaos in vocal folds. The obtained results are of special interest for detecting the pathology of vocal cords, when there is no visual effect of disease. Based on the results given in the paper, the objectives for future investigation in this matter are given.