Mechanical Vibration

Web Book

Chapter 1


Learning objectives

  1. Recognize phenomena and applications of vibration in practice.
  2. Model a vibrating system with mass, spring and damper elements.
  3. Understand the concept of amplitude, frequency and phase.


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1.1  Why study vibration?

In June 29, 1995 people in Seoul, South Korea were mourned with the deadliest disaster of a building collapse which killed 502 people and 937 were injured. The structural failure was caused by vibration from the air-conditioned chiller installed on the roof, which provided energy load by four times the design limit of the roof structure (Figure 1.1).

On April 24, 2013 similar tragedy took place in Bangladesh, where an eight-storey building collapsed leaving 1,129 people died and 2,515 were injured. The building which was designed for shops and offices, was later used as a garment factory. The structure unfortunately could not sustain the vibration energy coming from heavy machineries. Figure 1.2 shows the scene when the disaster happened.

Figure 1.1 Building structural damage due to machine vibration and load in South Korea.

The two examples reveal the capacity of vibration to the damage and destruction; which gives similar result of damage due to ’natural’ vibration energy from an earthquake (scary, isn’t it?).

The receiving structure should have an allowable level of vibration energy injected by vibrating machines. For this purpose vibration isolators are used at the contact points between the machine and the structure to block some of the vibration input power from the machine.

Figure 1.2 Building collapse in Dhaka, Bangladesh due to vibration impact excitation from machineries.

Not only to the receiving structures, the machinery system itself can also suffer mechanical failure due to the internal vibration. Rotating machineries which are commonly found in oil and gas industry; electric motors, compressors, centrifugal pump, gas turbine, must be maintained properly to ensure the system runs smoothly for production.

Any failure due to vibration from mass unbalance and misalignment, for example, can damage bearings and shafts and results in shutting down the operation unexpectedly for machine replacement and unscheduled maintenance
(see Figure 1.3).

The company can lose millions of dollar a day, besides bad image of company to customers due to late delivery. If you are the engineer in charge, you could straight away get fired!

Figure 1.3 Possible faults in rotating machines which can be indicated by high level of vibration.


Other negative effects from vibration are discomfort and disturbance. Apart for structural safety, cars, trains and airplanes are also designed to have minimum transmitted vibration which can create discomfort to the passengers. The car engine, for example, is mounted on vibration-isolated mountings to minimise transfer of vibration waves across the car structure. The car floor is usually treated with damping layer to reduce vibration and noise radiation into the cabin.

Vibration can damage bearings and shaft in a rotating machine.

Railway track should be properly treated in order to reduce the ground-borne vibration transmission to nearby dwelling which can vibrate the walls, ceilings and floors of houses and finally radiates an annoying low frequency noise causing sleep disturbance (Figure 1.4).

Figure1.4 Transfer of vibration energy not only creates noise in the train cabin, but also to the environment.


Direct exposure to vibration has also been known to affect human health. In vehicles, frequent experience to low frequency vibration is found to cause back pain to the driver. This is found especially for a tractor operator working in an agriculture sector. A regulation is thus enforced by a government for the tractor manufacturer to comply with minimum level of vibration.

A worker with a prolonged use of vibrating hand-held tools such as pneumatic jack hammers, drills or grinders could suffer had-arm vibration syndrome and vibration induced white finger. The latter causes a person to end up with the fingers becoming numb due to poor blood circulation.

Figure 1.5 Tractor’s operator can be susceptible to vibration exposure to the back of the body.


In this book, the content is aimed at providing the fundamental concepts of vibration. In practice, a vibration engineer tasks are:

  • to design a mechanical system to avoid high vibration amplitude in an engineering structure, and
  • to perform analysis and troubleshoot to eliminate vibration in a rotating machine or in a structure. 

Here, both math and physics are used as the tools for the deep analysis to understand the concept. You will find in certain chapters that you have to deal with a rather ‘abstract system’ which is sometimes difficult to be related in a real situation. This is not merely the mathematical exercise, but to help improve the cognitive skill, strengthening the concept of mass, spring and damper elements, and also the amplitude and frequency.

Later in industry, you will use a sophisticated numerical software to design or to solve vibration problems. However if the fundamental concept is not strong, the software becomes just a black-box, and accurate engineering solution is difficult to obtain.