# How do engineers reduce vibration of system with multiple known natural frequencies? How do they design the isolation system for specific frequencies?

I have a system that is pretty much a chamber that needs to sit on the ground. I measured the transmissibility of the chamber vs the ground (output/chamber acceleration over input/ground acceleration) with accelerometers and plotted a transmissibility graph (is it also called transfer function plot...?). The steel chamber weighs about 100 kg.

From the graph, I found the natural frequencies (the spiking frequencies). Let's say I would like to reduce the vibration of the 3.2 Hz and 9 Hz vibration, what would be the real world approach to isolate this vibration as an mechanical engineer? Do they buy a specific set of materials online according to the natural frequency and then pad them under the system? Or do they come up with a spring + damper system that target these frequencies?

• So mass of the chamber? That will tell you the energy you need to dissipate which then gives you an idea of suitable systems. If the chamber is a 1m^3 bamboo cube with mosquito netting then it is easy. If it is a steel chanber the same size with a 30cm wall thickness then that’s a different ball game. – Solar Mike May 2 at 21:56
• Thank you for your comment. I do not know the exact weight of the chamber but let's assume it is 100 kg. What would be the next step after knowing what energy I need to dissipate? How do I calculate the energy? Thank you! – Dumb Engineer May 2 at 22:01
• What are the units of the vertical axis? What was used for the excitation, and how was it programmed? (checking that this really is a transfer function) – Pete W May 3 at 2:44

First of all, the two methods you suggested (buying pad materials and spring+damper) are not necessarily different. Usually the different pad materials that can be bought, (mainly) modify the spring constant in the structure.

Additionally, although there are methods of targeting specific frequencies, in most cases they are not very useful. The reason, is that you need to have an excitation that has a very specific frequency. Any deviation from that frequency, will probably have a very adverse effect on the overall dynamic behavior (steady state and transient) of the structure.

Therefore, IMHO, the main option would be to try and reduce the lowest natural frequency of the structure. The result would be that the ratio of the excitation frequency over the natural frequency would increase. However that increase will eventually lead to a reduction of the transmissability ratio.

The reduction of the natural frequency, usually occurs with increasing the mass, or lowering the spring coefficient.

• Thank you. "try and reduce the lowest natural frequency of the structure", do you mean by shifting the natural frequency from 9Hz to like 5 Hz, by adding the weight? How does that reduce the transmissibility at the natural frequency? Would I still experience the awful vibration at the lower natural frequency? – Dumb Engineer May 2 at 23:15
• Frequency is the inverse of the period, f = 1/T, with lower frequency, the period increases with a lower amplitude, thus the transmissibility. – r13 May 2 at 23:34
• Thank you! Would you mind explaining further how increasing the period will lead to lower amplitude? – Dumb Engineer May 2 at 23:40
• Really, this is not answerable unless we understand how the "system" is being excited. For example if it is some sort of boiler and the noise is coming from the combustion which is creating unwanted energy over a wide frequency range, changing the natural vibration frequency will just give you vibration at the new frequency, which might not improve anything. – alephzero May 3 at 1:52
• ... From your description, I guess you put it the device on a shaker table to produce the "ground acceleration" and measured the response curve. But the vibration modes you excited in the test may be completely irrelevant if there is nothing in the system itself when it is operating that can excite them. – alephzero May 3 at 1:58