Quarter car model

A quarter car model is presented below to consider a simplified representation of the dynamic behavior of the vertical suspension for various input excitations:

Figure 6: Quarter car model

3 types of element are included in the system:

• Purely inertial elements (mass)

• Capacitive elements (spring)

• Resistive elements

We consider 2 input excitations that will engender 2 different simplifications from the initial quarter car model:

• 1st excitation at 10 rad/s (1.59 Hz)

• 2nd excitation at 100 rad/s (15.9 Hz)

The process of observing the Activity Index results for the 1st excitation of 10 rad/s is presented below. It makes it possible to reduce the original model to a new reduced model valid for such an excitation. Some comparisons of the dynamic behavior are show in the frequency-domain to demonstrate that the model reduction process was actually successful.

Figure 7: Activity Index results obtained with the 10 rad/s excitation

Figure 8: Reduced model for the 10 rad/s excitation

Figure 9: Transfer function comparison of the initial model vs. reduced model (considering Activity Index analysis with a 10 rad/s excitation)

We will now achieve the same process for the 100 rad/s input excitation:

Figure 10: Activity Index results obtained with the 100 rad/s excitation

Figure 11: Reduced model for the 100 rad/s excitation

Figure 12: Transfer function comparison of the initial model vs. reduced model (considering Activity Index analysis with a 100 rad/s excitation)