Quarter Car Model: Two Degree of Freedom

General equation of motion for multi-degree of freedom system is:

[M]{Ẋ} + [C]{Ẋ} + [K]{X} + {F(t)}

Where, Ẋ - acceleration; [M] – mass matrix; [C] – damping matrix; [K] – stiffness matrix and F(t) – force.

Natural frequencies (ω) of the vehicle models can be found by using the undamped and free vibration of equations of motions.

The normal mode solution Equation:

{X(t)} = {X} e ^{iwt }

Thus, natural frequencies ω and their corresponding mode shape vectors {X} can be written as:

([K] – ω^{2 }[M]{X}) = 0

The natural frequencies are obtained from the following equation,

det([K] - ω^{2 }[M] = 0

Hope it was helpful to you!

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up