Overlap of natural frequencies

[patelam]

I have a 6.5ft long vertical cantilever channel, its top end has fixed support(fully restrained to displace rotate in all 3 directions). At the bottom free end, 1ft(b) x 1ft(d) x 5ft(height) of steel sheet box is attached. The box is attached at its mid-height to the vertical channel.

How do I find the amplification factor resulting from the overlap between natural frequencies of vertical channel and steel box? I just want to understand the process to determine the amplification factor.

 

[GregLocock]

In physics, as opposed to structural engineering, you add the complex response function for each mode at each location. For this you need to know the damping of each mode, which is critical for accuracy.

https://engcourses-uofa.ca/books/vi...ibrations-of-two-degree-of-freedom-systems-2/

seems to cover it.

Cheers

Greg Locock


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[TLHS]

What is the exciting load that you're talking about? Is this a vibration issue? Seismic? Do you have a diagram that you could share? What are you trying to accomplish with it?

There are ways to approximate resonance amplification, but a lot of vibration and seismic issues are a lot better solved by a design change. The analysis approximations for restraint and stiffness make the accuracy you need for this sort of thing pretty hard to get. Your error bars become unreasonably large and it's better to do something that removes it as a problem.

If you're talking about a combined vibration mechanism, it's going to be a lot better to just model your items somehow and do a frequency analysis or a time history analysis of the combined system so you can see how the various modes act.