Use some multi body simukation (Adams or Simpack). Analytically you will not solve it
Good day, Ali.
The quarter car can be represented by three differential equations (if not considering such things as self-aligning torque and lateral force).
These should be: the equation for the revolution speed, the eqn for longitudinal velocity, eqn for vertical acceleration.
These amount to the following:
You might want to take a look at some books on the subject such as Theory of Ground Vehicles by J. Y. Wong
Thank Pavel for your notes, also I have this book.But I look for a nonlinear model of quarter car.
This model is indeed nonlinear. This is so because the behavior of the horizontal force depends non-linearly on the system's state which is the velocity and revolution frequency. It is often convenient to consider the horizontal force as a function of a coefficient multiplied by the vertical load where the coefficient depends on slip which is in turn a nonlinear function of the velocity and revolution frequency. For a particular function, you might want to take a look at "M. Schreiber and H. Kutzbach. Comparison of different zero-slip definitions and a proposal to standardize tire traction performance". Also, there is the famous Pacejka formula. Regards
Many thanks Pavel, I need more information about "M. Schreiber and H. Kutzbach"
Kinds
Your question is not specific as which type of analysis you expect? But you have used the term quarter-car it might be the vertical vibration response to the ground excitation.
Again which type of non-linearity and in which element (Suspension and tire stiffnes, damping) is to be considered?
For a quarter-car vehicle model at least two-dof are required for complete specification of the vertical vibration response. It is difficult to solve analytically the multi-dof non-linear vibration problems the only way is to linearize the model about equilibrium point and then solve it analytically.
Usually the analytical solution is aimed for parameter identification and this can be done with help of linearized model.
Why you want to solve it analytically?
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