Mechanical Vibration

Mechanical Vibration

1. The study of vibrations is concerned with the oscillating motion of elastic bodies and the force associated with them.

   • Linear systems
     • The principle of superposition holds.
       • Free vibration takes place when a system oscillates under the action of forces inherent in the system itself due to initial disturbance, and when the externally applied forces are absent. The system under free vibration will vibrate at one or more of its natural frequencies, which are properties of the dynamical system, established by its mass and stiffness distribution.
   • Nonlinear systems
     • The principle of superposition doesn't hold.
       • The vibration that takes place under the excitation of external forces is called forced vibration. If excitation is harmonic, the system is forced to vibrate at excitation frequency . If the frequency of excitation coincide with one of the natural frequencies of the system, a condition of resonance is encountered and dangerously large oscillations may result, which results in failure of major structures

2. Degrees of Freedom

   • The number of independent co-ordinates required to describe the motion of a system is termed as degrees of freedom.

3. Oscillatory Motion

   • Repeat itself regularly for example pendulum of a wall clock

4. Periodic Motion

   • This motion repeats at equal interval of time T.

5. Period of Oscillatory

   • The time taken for one repetition is called period.

6. Harmonic motion