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A Special Case of Rolling Tire Vibrationsстатья
- Автор: Kozhevnikov I.F.
- Журнал: Nelineinaya Dinamika
- Том: 15
- Номер: 1
- Год издания: 2019
- Первая страница: 67
- Последняя страница: 78
- DOI: 10.20537/nd190107
- Аннотация: We investigate a special case of vibrations of a loaded tire rolling at constant speed withoutslipping in the contact area. A previously proposed analytical model of a radial tire is considered.The surface of the tire is a flexible tread combined with elastic sidewalls. In the undeformed state,the sidewalls are represented by parts of two tori and consist of incompressible rubber describedby the Mooney – Rivlin model. In the undeformed state, the tread is a circular cylinder. Thetread is reinforced with inextensible cords. The tread deformations are considered taking intoaccount the exact nonlinear conditions of inextensibility of reinforcing cords. Due to nonlineargeometric constraints in the deformed state, the tread retains its cylindrical shape, which is notcircular for a typical configuration. The contact between the wheel and the ground plane occursby a part of the tread. The previously obtained partial differential equation which describes thetire radial in-plane vibrations about the steady-state regime of rolling is investigated. Analyzingthe discriminant of the quartic polynomial, which is the function of the frequency of the tenthdegree and the function of the angular velocity of sixth degree, the rare case of two pairs ofmultiple roots is discovered. If the geometry of the tire and the internal tire pressure are known,then the angular velocity of rotation, the tire speed and the natural frequency, correspondingto this case, are determined analytically. The mode shape of vibration in the neighborhood ofthe singular point is determined analytically.
- Добавил в систему: Кожевников Иван Федорович