Vibrations - Understanding the basics

You turn your cellphone to vibration mode in a class or a meeting. What are these vibrations?

How do vibrations take place? Do we always need vibrations? Are vibrations a boon or a menace?

Vibration isn't a term unheard of in today's time, owing to one of the cellphone modes we turn on. However, vibrations are much more than that. Every object that has mass and elasticity is prone to vibration. When an external force tries to displace an object from its initial position, the internal elastic forces present in the object try to bring it back to the original position. While doing so, the elastic energy of the object gets converted to kinetic energy. This kinetic energy now allows the body to move in the opposite direction beyond the equilibrium position, and the cycle keeps repeating. This is how the vibratory motion is initiated, and the exchange of energy takes place at infinite times. This brings us to the definition of vibration - A motion repeating itself after a fixed interval of time is called a vibration.

Vibrations - Boon or Curse?

Most musical instruments work on the phenomenon of vibration. Vibration is also a very useful concept in the design of vibratory conveyors, tuning fork experiments, and compactors and finds its use in various industries. The sound itself propagates using vibrations. We can also extract energy from these vibrations.

However, there are cases where vibrations are undesirable. For example, excessive and unwanted vibration in the automotive may cause wear and tear. It may also loosen some of the parts and cause a complete breakdown. Bridges and buildings are prone to vibrations and collapse when the frequency of excitation matches with one of the natural frequencies of these systems. Thus, excessive vibrations are dangerous, and it is very important to design a system to minimize the vibrations. Vibrations can be reduced using shock absorbers, dynamic absorbers and vibration isolators.

Key definitions in the vibration

Since we will also discuss vibrations in future blogs, it's important to get versed with the frequent terminologies encountered while studying vibrations.

Time Period: Time taken for completion of one complete vibration.
Frequency: Number of vibrations per second
Amplitude: The maximum displacement from the mean/equilibrium position
Degree of freedom: Minimum number of independent coordinates specifying the system's motion at any instant. The degree of freedom (DoF) can vary from zero to infinity.
Simple Harmonic Motion (SHM): To and fro motion about a fixed point is called SHM
Damping: Resistance offered to the motion of vibration of the body
Resonance: The synchronization of external excitation frequency with the vibration body's natural frequency, thereby resulting in large amplitudes.

Components of a vibrating system

Any vibratory system should have three elements - mass, spring and a damper. A simple schematic is shown below.

On application of an external force, energy is stored as kinetic energy in the mass, as spring potential energy in the spring and dissipated in the damper.

Types of Vibrations

Free and Forced vibration

Free vibration: When the system vibrates on its own after an initial excitation, this type of vibration is called free vibration.

Forced vibration: Vibration occurring for continuous external force is called forced vibration.

Linear and Non-Linear Vibration

Linear vibration: All the vibratory components, mass, spring and damper, follow a linear behaviour.

Nonlinear vibration: If any of the vibratory components follows a non-linear behaviour, we term such behaviour as nonlinear vibration.

Damped and Undamped vibration

Damped vibration: In the presence of a damper, the amplitude of oscillations reduces after each cycle; such vibrations are termed damped vibrations

Undamped vibration: When the damper is absent, the oscillation amplitude remains constant for each cycle; such vibrations are termed undamped vibrations.

Beats

The superposition of two harmonic motions with slightly different frequencies travelling in the same straight line in the same direction is called beats. When the two waves remain in the same phase, the resultant amplitude of vibration is maximum, whereas when the two waves are not in phase, the resultant amplitude of vibration is minimal.

History

The history of vibrations can be dated back to the use of the first musical instruments. The Greek mathematician and philosopher Pythagoras was the first to deduce scientific findings through musical sounds. Pythagoras performed his experiments on a monochord (similar to the present-day sonometer) which was a simple string kept under tension placed on two knife edges with a movable knife-edge between the two. He observed that on striking the string kept under the same tension but at different lengths using the movable knife-edge, the shorter length emits a higher note. In fact, he observed if the shorter string was precisely half of the longer ones, the shorter string emitted an octave above the other note produced by the longer string.

Summary

The study of vibrations is vital in designing systems. Any undesirable, unwanted vibrations should be damped out.
There are only three essential components of any vibratory system - Mass, spring and damper.
Beats are the superposition of two waves with slightly different frequencies.