15 February 2018

Introduction to mechanical vibration

A body is said to vibrate if it has a to and fro motion. A pendulum swinging on either side of a mean position does so under the action of gravity. When the pendulum swings through the mid position, its centre of mass is at the lowest point and it possesses only kinetic energy. At each extremity of its swing, it has only potential energy. In the absence of any friction, the motion continues indefinitely. It can be shown that if the swings on either side of the mean position are very small, it approximates to simple harmonic motion. 

Usually, vibrations are due to elastic forces. Work is done on the elastic constraints of the forces on the body when a body is displaced from its equilibrium position and is stored as strain energy. Now, if the body is released, the internal forces cause the body to move towards its equilibrium position. If the motion is frictionless, the strain energy stored in the body is converted into kinetic energy during the period the body reaches the equilibrium position at which it has maximum kinetic energy. The body passes through the mean position, the kinetic energy is utilized to overcome the elastic forces and is stored in the form of strain energy. 

The vibration is mainly three types :

  1. Longitudinal vibrations
  2. Transverse vibrations
  3. Torsional vibrations 
Terms related to vibration :
  1. Free vibration 
  2. Damped vibration 
  3. Forced vibration 
  4. Period
  5. Cycle
  6. Frequency 
  7. Resonance 
All the terms are used in vibrations are explain below :

Free vibration is also called natural vibration. Elastic vibration in which there are no friction and external forces after the initial release of the body is known as free vibration.

Damped vibrations are when the energy of a vibrating system is gradually dissipated by friction and other resistances is called damping. The vibrations gradually cease and the system rests in its equilibrium position.

Forced vibration is when a repeated force continuously acts on a system. The vibration is said to be forced. The frequency of the vibrations is that of the applied force and is independent of their own natural frequency of vibrations. 

The period is the time taken by a motion to repeat itself and is measured in seconds. 

The cycle is the motion completed during one time period. 

Frequency is the number of cycles of motion completed in one second. It is expressed in hertz ( Hz ) and is equal to one cycle per second. 

Resonance is the frequency of the external forces is the same as that of the natural frequency of the system. 
A state of resonance is said to have been reached. 

It results in large amplitudes of vibrations and this may be dangerous. 

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