What is Damping and Resonance?

In this blog we shall explore some of the fundamental concepts of vibration, with the aim of gaining an overall appreciation and understanding of resonance and damping without any mathematical treatment.

All structures are flexible to some extent. Vibration is the inevitable consequence of a structure due to its flexible nature, which results in an oscillatory motion.

Vibration may be totally unnoticeable to the human user of a structure or machine, or it may become a problem to health with excessive vibration of power tools for instance, where occupational diseases such as vibration white finger are common.

The vibration may become a problem to the structural integrity of a structure and ultimately can result in catastrophic failure.

The famous Tacoma Narrows Bridge failure can be seen here, offering an extreme example of where structures can catastrophically fail if vibration is not well understood:

Resonance

Below is what happens when we excite a structure (a wine glass in this demonstration) at the same frequency as it’s resonance frequency:

Natural Frequency

All structures have a so-called ‘natural frequency’; this is the frequency at which the structure vibrates with a very high amplitude if excited at that same frequency. In fact, all real structures have an infinite number of these natural frequencies. However, for practical purposes, we are usually only interested in those frequencies that are in the range at which we would typically excite the structure at.

For instance, let us take a typical motor car with an internal combustion engine that operates within the engine speed range of 1000-6000 RPM. This corresponds to an excitation frequency range of:

f₁ = 1000 / 60 = 16.6Hz

f₂ = 6000 / 60 = 100Hz

If the vehicle has a 4-stroke cycle with 4 cylinders, then this equates to 2 firing events every cycle of the engine crank.

In other words, the engine will excite the structure of the car chassis and body with a frequency in the range of 33.2Hz (2 x 16.6 Hz) to  200Hz (2 x 100Hz). If we ignore harmonics, then it is reasonable to conclude that the vehicle is not going to be excited at any of the resonant frequencies that exist above 200Hz. 

Resonance occurs when the frequency of the structure is excited at or near to one if it’s resonant frequencies.

Damping

From the above discussion, it can be concluded that there are natural frequencies that are inherent within structures and these frequencies, if excited, will cause an uncontrolled large amplitude response, which could potentially have catastrophic consequences.

However, the energy of these large amplitude responses at resonance can be counteracted by the inclusion of damping. Damping is any mechanism that serves to absorb the energy of resonance and hence reduce the amplitude of response.

The energy of the high amplitude response is converted to heat. Below we see the time response of a single-degree of freedom lumped parameter model exhibiting a damped response.

Consider, once more, a typical motor vehicle, which will have a damping element attached to each suspension system. At a simple level, this consists of a cylinder containing oil, and this is indeed one of the most common forms of damping known as viscous damping.

Interestingly, such dampers are also commonly employed in tall skyscrapers to minimise vibration response to earthquake and wind loads. Observe the difference below of the multi-story building model with and without damping as an example.

So in conclusion, we can say that damping is introduced into a structure to reduce the amplitude of the response.

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