Vibration- Pitch plane analysis

Question 1

What is the main differences between the quarter car model and the pitch plane model?

Answer 1

The unsprung mass is omitted, and now you have to consider the pitch inertia I.

Question 2

How can you get the mode shapes of pitch vibration?

Answer 2

By using newton’s 2nd law (F=ma) in the bounce and pitch directions, the equations of motion can be derived in matrix form. Them this can be put into matrix vector form, with the mass, stiffness and damping matrices etc.
Natural modes of vibration can be found by looking at the undamped case (free vibration), taking Laplace transforms and setting s= jω. The solutions are the eigenvalues (natural frequencies squared) and eigenvectors (mode shapes) of M^-1 * K

Question 3

What do the eigenvalues of M^-1 * K represent?

Answer 3

The natural frequencies squared

Question 4

What do the eigenvectors of M^-1 * K represent?

Answer 4

The mode shapes

Question 5

What fact about the inputs makes the analysis of the pitch plane easier? and express this as an equation

Answer 5

The input at the rear axle is just a time delayed version of the input at the front axle 
Zr2(t) = Zr1 (t - (a+b)/V)
a+b = wheelbase 
V=velocity of vehicle
1=front axle 
2=rear axle

Question 6

What is the Laplace transform of a time delay

Answer 6

δ(t-τ) = e^ -sτ (in maths data book)

Question 7

How can you express the input to the pitch plane as a single input?

Answer 7

By creating a vector L that includes the time delay for the second input, then just multiply the transfer function by this, now you have a single input.

Question 8

What is the phenomenon which causes many peaks to appear in the transfer functions for pitch plane analysis?

Answer 8

Wheelbase filtering

The delay between the road input at the front and rear axles

Question 9

In the transfer functions for vertical acceleration and pitch angle acceleration, does increasing speed make the peaks closer or further away?

Answer 9

Further away

Question 10

Why is it important to consider a range of speeds when choosing suspension values?

Answer 10

As the response depends on speed (and natural modes)

Question 11

What is generally considered more uncomfortable, pitch or bounce?

Answer 11

Pitch

Question 12

How many DOF does the pitch plane model have?

Answer 12

2