非线性减振器（Nonlinear Shock Absorber）

dongfu

Nonlinear Shock Absorber
Background:
You have seen in lecture and exercises how to model a forced spring-mass system with damping. One application for the model is an automobile suspension system, where the forcing term is the road roughed perhaps by frost heaves.
Mathematicians and engineers at Renault have studied a new type of shock absorber which controls the damping coefficient. Their new shock absorber can increase the damping coefficient whenever the mass (i.e., the car) is returning toward equilibrium. In the mathematical model, the damping coefficient is now a function of the solution.
In this project, you will study the behavior of the solution with different forcing terms. Recognize that once you allow the damping coefficient to depend on the solution, the equation is no longer linear and most analytic solution methods (such as characteristic equations and undetermined coefficients) are useless. You have no choice but to study the system through numerical experiments.
1.To start, describe the limiting behavior of the solution for constant damping when the forcing term is a periodic function. How does the amplitude of the limiting solution depend on?
2.Now work with Renault's controlled shock absorber. In particular, look at a damping coefficient that takes one value when the system is moving away from equilibrium and another value ,when the system is moving toward equilibrium. Explain how to turn this second-order model into a first-order system suitable for numerical analysis. Explain in detail how you program the damping coefficient in your equation.
3.Experiment numerically with Renault's shock absorber. Take for the forcing coefficient. Describe the limiting behavior of the solution for a range of values.
4.Do some numerical experiments with roads (forcing terms) which are more realistic than a or function.
5.Can you explain the behavior that you observe? Does the new shock absorber give a ``smoother'' ride than the original shock absorber? Do you think that Renault should pursue its development of this new shock absorber?

xxg111

楼主要是能翻译一下就好了.

纽基

各位各位，其实楼主说了半天，就是说的我们现在都已经常见的一种弹簧 —— 不等经不等距弹簧。
一大堆的英语，吓唬人啊。。。