Dynamic stress from frequency response analysis

[rameng123]

Hi
I am doing frequency response analysis of cantilever beam with L-section by using 20g acceleration(Inertia load). Also obtained the first five natural frequencies from modal analysis. First mode shape is bending on x-direction and second mode shape is bending on XY direction.

Method 1: By applying the 20g load in x, the stress is maximum at first natural frequency and thereafter, the stress decreases for second and further natural frequencies. As the component is most likely to excite at first natural frequency, I believe the frequency response is correct.
Method 2: But if the load is applied in XY direction, the maximum stress occurs at second natural frequency and second mode shape. (though the stress is less than the one obtained from method 1).

The actual applied load on the structure is considered to be in XY direction but the response of the structure is not what I am expecting.
My question is:
1) Should I consider the second method results as it resembles the actual load XY direction ? If yes, how to validate this? Is it always necessary that stress must be highest at first natural frequency?
2) Or else, conservatively should I consider the method 1 which giving the expected frequency response and highest stress at first natural frequency?

I need suggestions from all of you to understand these results. Thanks in advance for your time and help.

 

[rameng123]

In frequency response analysis, Could anyone suggest me is it necessary to have maximum stress and displacement at first natural frequency and first mode shape?
Thanks

 

[structSU10]

I think it would depend on the frequency of your loading condition. If the frequency of the load is close to the 1st harmonic, you would expect resonance and therfore a larger response.

 

[WARose]

If I understand your situation correctly, it sounds like your “inertia” load is [the equivalent of] support excitation (of the cantilever). In such a situation, you would have a model of your beam (with its mass represented as multiple (lumped) points along its length)…….based on that model, you would do a modal analysis to determine the participation factors for each mode. [To answer your question: you should consider whatever direction your structure is dynamically sensitive if it will be accelerated in that direction.] You would then need to manipulate the equation of motion to obtain your maximum displacements. (From which you could figure your maximum stresses, forces, etc……and place a safety factor/Dynamic load factor [DLF] on top of.) [See ‘Structural Dynamics’ 2nd edition, by: Mario Paz, p.215-219 for a example with a structure with 2 levels of mass but just one degree of freedom.]

This solution is based upon the modes of vibration being fairly simple and it just one or two directions. If your dynamic response is more complicated than that (and you really don’t care about accuracy) you should be able to figure a maximum based on a (simple) conservation of energy principle and put a DLF on that.