Modelling for a new mechanical passive damper and its mathematical analysis

To improve ride comfort, an oil damper should restrain its damping force in a high-velocity range. A lot of dampers with such properties were developed. For example, the one controlling the flux of oil by a leaf valve is widely adapted and reasonable. However, it is difficult to represent its dynamics with a simple mathematical model, and the cost of a computational fluid dynamics is too expensive. To overcome the disadvantages, the first author in [15] developed the other mechanical oil damper with sub-pistons instead of the leaf valve, which enabled us to propose a simple mathematical model with linear ordinary differential equations, thanks to the simple mechanism to control the oil flow. In this article, we give a more detailed mathematical model for the damper taking the dynamic pressure resistance into account, which is represented by nonlinear ordinary differential equations. In addition, a numerical scheme for the model is also proposed and its mathematical analysis such as the validity of the numerical solutions is shown.