Villanueva Roberto, Epstein Marcelo
Department of Mechanical and Manufacturing Engineering, The University of Calgary, Calgary, Alberta T2N 1N4, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 2):066609. doi: 10.1103/PhysRevE.71.066609. Epub 2005 Jun 21.
A model of a partially deformable Euler disk is presented that allows transverse vibrations to be treated with the techniques of classical analytical mechanics. The model clearly shows that the increasing audible frequency produced during motion can be directly related to the forcing effect of the reaction and the angular velocity of the contact point. The material of the disk seems to play a role in affecting the intensity and quality of the sound, but not its pitch. Moreover, the friction force grows rapidly with the decline of the disk, thus causing the slipping that is partially responsible for the abrupt end of the motion. The model also supports the conjecture [P. Kessler and O. M. O'Reilly, Regul. Chaotic Dyn. 7, 49 (2002)] that the vibrations themselves contribute to this phenomenon by causing a loss of contact with the surface at small angles of inclination.
提出了一种部分可变形的欧拉盘模型，该模型允许使用经典分析力学技术处理横向振动。该模型清楚地表明，运动过程中产生的可听频率增加与接触点的反作用力和角速度的强迫效应直接相关。盘的材料似乎在影响声音的强度和质量方面起作用，但不影响音高。此外，摩擦力随着盘的下降而迅速增加，从而导致打滑，这是运动突然结束的部分原因。该模型还支持这样的推测[P.凯斯勒和O.M.奥赖利，《规则与混沌动力学》7，49（2002）]，即振动本身通过在小倾斜角度下导致与表面失去接触而促成了这一现象。
