Dynamics question - Need fast answer

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Use a simplified 2 DOF free vibration ¼ car model for bounce, to estimate the natural frequencies and mode shapes. Include the tyres in this model and state any other assumptions used.
Dec 18th, 2014

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] – ω2 [M]{X}) = 0 

The natural frequencies are obtained from the following equation, 

det([K] - ω2 [M] = 0 

Hope it was helpful to you!

Dec 19th, 2014

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