Keywords: 2D vibration, wave equations, vehicle vibration, bending vibration, vertical vibration, horizontal vibration, bending vibration, step shafting, stress equations, strain equations, spinning shafts, total dynamic response
Analytical and experimental study on bending vibration of internal combustion engines shafting system based on wave equations
This paper proposes a new analytical approach to study the bending vibration of N step shafting system. Changes of the shaft step properties under rotary condition are governed by two–dimensional wave equations. The source of the bending vibration is first analysed. Then strain and stress equations of the spinning shaft are established. After Hamilton principle is applied, a two–dimensional wave equation is established. After that, the calculation formula of one dimensional bending vibration response is obtained where a sinusoidal excitation force is applied on an arbitrary concentrated mass. By using this formula, the total dynamic response can be obtained based on the principle of the linear superposition. The calculated results were compared with measured results. It was found they agree with each other in the vertical direction but not in the horizontal direction. At the end of paper, the reason of difference was analysed.