In this paper a simplified mathematical model related to human phonation process is presented. Main attention is paid to the treatment of vocal fold vibrations excited by viscous incompressible airflow, which is stopped (chopped) by their periodical contacts. The Hertz impact model is used in the structural part and two new strategies are suggested to treat the contact phenomena in the fluid model. The numerical discretization by finite element (FE) method is described and the model problem is numerically approximated using a penalty approach in the inlet boundary condition for airflow and a thin porous layer in the glottis during the glottal closure. The numerical results are presented and discussed.

本文提出了一种与人类发声过程有关的简化数学模型。主要的注意力集中在粘性不可压缩气流激发的声带振动的治疗上，这种粘性的不可压缩气流通过它们的周期性接触而被阻止（切碎）。在结构部分中使用了赫兹冲击模型，并提出了两种新的策略来处理流体模型中的接触现象。描述了通过有限元（FE）方法进行数值离散化的过程，并且在声门闭合期间使用惩罚方法在气流的入口边界条件和声门中的薄多孔层中对模型问题进行了数值逼近。数值结果进行了介绍和讨论。