vibration and stiffness

Hi. I am an intern working for general motors. My supervisor asked me to find
out about the stiffness of the piece connecting the 2 sides of a bushing engine mount. In other
words, the question is whether or not the stiffness of the metal would change if it was preloaded
ahead of time. For all practical purposes he told me to model the piece as a simple cylinder in
one case with a horizontal force(preload) and without a horizontal distributed force. Does
anyone know if the stiffness would change from case to case. I was under the impression that
stiffness was a material property, and not subject to change based on loading condition. His
colleagues seem to think that it is based on the equation natural freq = sq root of (stiffness /
mass). They claim that as the load increases the natural frequency will change, therefore
changing the stiffness. I am especially interested in how the stiffness will change in the vertical direction and if buckling will play a role.

 

[wimvandendobbelsteen]

Mr. Bucklebran,

I think you are right in saying that the stiffness is a material and geometrical related property.
The axial stiffness for instance can be defined as k;
where k=(E*A)/L; E for elastic modulus;Area;L length
or Torsional stiffness;
k=(G*Ip)/L, G is shear modulus of eleasticity;Ip polair moment of inertia.
When you calculate the natural circular frequency of a one sided clamped pipe , the formula is:
omega=1.875^2*square{(E*Ip)/m*L^4)}, where m is mass.
Here you see that changing the L, the unsupported length, or the horizontal force your boss is refering to, will change the natural frequency of the cilinder, but not the stiffness.
Hope this will help.
Wim

 

[tomirvine]

There are some special cases.....

For example, the load could become so high that either the elastic modulus or the shear modulus becomes nonlinear. In this cases, loading would effect the natural frequency.

Furthermore...

When an axial tensile or compressive load acts on a beam, the natural bending frequencies are different from those for the same beam without such loading.
(Reference: Harris, Shock and Vibration Handbook).

Sincerely, Tom Irvine

http://www.vibrationdata.com

 

[GregLocock]

What you say is true, Tom, but in the case of engine mount brackets on passenger cars it does not affect the result, since they are nowadays so stiff that the loads are completely insignificant.

Roughly speaking the modes of the engine mount pedestal and brackets should be a margin above the firing excitation of the engine, which is ncyl*redlinerpm/60/2 for a 4 stroke engine.

If you measure the modes on a good car, say a BMW 528, you will find that this margin is anything up to 100%.

The effect of load on the stiffness of structures is (to the limits of my reasonably good knowledge) not considered practically significant in the passenger automotive business, except for crash. Interestingly we are currently developing a component that has a nasty tendency to buckle elastically, and I am sure that we will have to consider this.

Another handy rule is that the stiffness of the brackets should be a multiple of the stiffness of the bush mounted on them. Desirable values of that number can be calculated using impedance mismatch theory. Clue: 1 is a very bad choice!

Bucklebran should talk to his Noise&Vibration department for a less cryptic set of numbers on this.
Cheers

Greg Locock