Modal Analysis - Shake, Rattle and Roll!

There are lots of engineering scenarios that cause a structure or components to sway, shake, rattle and roll. It could be induced by an earthquake, a rotating shaft, the pistons of an engine, the meshing of gears and so on. All show themselves as either movement or vibration.

Modal analysis is often married to dynamic analysis and like any good marriage, they need each other. It is the backbone of Harmonic Response, Transient Response, Random Vibration and Response Spectrum Analysis (RSA).

The relationship between modal and dynamic analysis is a fragile one since modal analysis is quite a sensitive soul. It is affected by location of mass and stiffness of both components and connections. In general, the stiffer the structure, the higher the frequency of the first mode as shown in figure 1.

Figure 1 – First Mode Frequency Comparison

The stiffness of a steelwork structure is sensitive to how it is held in place. Rigid connections are often modelled in Finite Element Analysis (FEA) as fixed and flexible connections as pinned. In reality, most bolted connections are in fact someway between fixed and pinned.?Connection stiffness and the assumptions made in the FE Model can influence the modal frequencies and dynamic analysis results considerably.?

The first mode of a simple column as shown in figure 2 shows a swaying motion. There is high mass participation, or in other words, most of the mass is swaying back and forth at a low frequency.?

Figure 2 – Mode Shape Comparison

The third mode has much lower mass participation at a higher frequency, or in other words, not much mass is moving but it's moving faster. Higher modes give?more of a ripple effect which is vibration.

Earthquakes are typically in the low frequency range of under 40 Hz and a rotating shaft on a turbocharger is very high frequency at around 3000 Hz.

No structure or component is free to sway or vibrate forever because of damping. The energy loss from the material or assembly will always decay the movement until it returns to its original state.

Modal Analysis may not be very exciting to some people but some modes can get very excited if they happen to be at the same frequency as the input frequency from sources such as?seismic ground shaking or the meshing of gears. This is called resonance and the consequences of such can cause bridges to collapse or less dramatically produce some unwanted vibration in a gear box.

It is advisable to avoid resonance and this can be achieved by stiffening the structure or component in the right places to shift the modal frequencies away from the input frequency. If the first modal frequency is greater than the input frequency, then the structure or component will not get excited.

Well that’s enough excitement for one day!

This article can also be found on the Value Design Ltd FEA Blog at www.valuedes.co.uk