Review on Mathematical and Mechanical Models of the Vocal Cord

A review on 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 description in voice production. The model is not only extended into three, five, and more mass systems, 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 corresponding 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 are no visual effects of disease. Based on the results given in the paper, the objectives for future investigation in this matter are given

On the dynamics of bodies with continual mass variation

n this paper the differential equations of the general motion of the rigid body with continual mass variation are considered. The impact force and the impact torque that occur due to addition or separation of the body with velocity and angular velocity which differs from the velocity of mass center and angular velocity of the existing body are introduced. The theoretical consideration is applied for solving a real technical problem when the band winds up on the drum. The plane motion of the drum on which the band winds up is considered. The influence of the velocity of the band on the angular velocity of the drum and the motion of the drum mass center is obtained

O momencie, jako mierze mechanicznego oddziaływania w zasadach dynamiki

In most discussions, the Principles of Dynamics are expressed using the force as a measure of mechanical interaction between the bodies. The intention of the paper is to extend the usual discussion on basic theorems, laws and principles in Dynamics of rigid bodies including the torque as another independent measure of mechanical interaction between the bodies. In D’Alambert’s principle of Dynamics, beside the forces, the active and reaction torques are also included. The torque is introduced in the Euler-Newton equations for general motion of the rigid body. The General Equation of Dynamics is reformulated by including the virtual work of the torques on the virtual rotation. An additional view to Newton’s Laws is also given.W większości rozważań, zasady dynamiki są wyrażane poprzez siły rozumiane jako miary mechanicznych oddziaływań pomiędzy ciałami. Celem tej pracy jest rozszerzenie zwyczajowego podejścia do aksjomatów, praw i zasad dynamiki o pojęcie momentu jako niezależnej miary mechanicznego oddziaływania. Wielkość tę wstawiono do zasady d’Alemberta w postaci momentu czynnego i biernego reakcyjnego. Przedstawiono również momentowe równania Eulera-Newtona dla ogólnego przypadku ruchu bryły sztywnej. Na nowo sformułowano ogólne równanie dynamiki poprzez wstawienie pracy przygotowanej momentu na przemieszczeniu kątowym. Dodatkową dyskusją objęto trzy zasady dynamiki Newtona