### INTRODUCTION

#### The study of vibration

A body is said to vibrate if it has periodic motion. Mechanical vibration is the study of oscillatory motions of bodies. Vibrations are harmful for engineering systems. Some times vibrations can be useful. For example, vibratory compactors are used for compacting concrete during construction work. Excessive vibration causes discomfort to human beings, damage to machines and buildings and wear of machine parts such as bearings and gears. The study of vibrations is important to aeronautical, mechanical and civil engineers. It is necessary for a design engineer to have a sound knowledge of vibrations. The object of the sixth semester course on mechanical vibrations is to discuss the basic concepts of vibration with their applications. The syllabus covers fundamentals of vibration, un-damped and damped single degree of freedom systems, multi degrees of freedom systems and continuous systems.

**Examples of vibration**

1.Beating of heart

2. Lungs oscillate in the process of breathing

3. Walking- Oscillation of legs and hands

4. Shivering- Oscillation of body in extreme cold

5. Speaking – Ear receives Vibrations to transmit message to brain

6. Vibration of atoms

7. Mechanical Vibrations

One method of classifying mechanical vibrations is based on degrees of freedom. The number of degrees of freedom for a system is the number of kinematically independent variables necessary to completely describe the motion of every particle in the system. Based on degrees of freedom, we can classify mechanical vibrations as follows:

1.Single Degree of freedom Systems

2.Two Degrees of freedom Systems

3.Multi degree of freedom Systems

4.Continuous Systems or systems with infinite degrees of freedom

**Another broad classification of vibrations is:**

1. Free and forced vibrations

2. Damped and un-damped vibrations.

**Sometime vibration problems are classified as:**

1.Linear vibrations

2. Non-linear vibrations

3. Random vibrations

4.Transient vibrations

A system is linear if its motion is governed by linear differential equations. A system is nonlinear if its motion is governed by nonlinear differential equations. If the excitation force is known at all times, the excitation is said to be deterministic. If the excitation force is unknown, but averages and standard derivations are known,the excitation is said to be random. In this case the resulting vibrations are also random. Some times systems are subjected to short duration non-periodic forces. The resulting vibrations are called transient vibrations. One example of a non-periodic short duration excitation is the ground motion in an earthquake

**The main causes of vibrations are:**

1. Bad design

2. Unbalanced inertia forces

3. Poor quality of manufacture

4. Improper bearings (Due to wear & tear or bad quality)

5. Worn out gear teeth

6. External excitation applied on the system

**The effects of vibrations are as follows:**

1. Unwanted noise

2. Early failure due to cyclical stress(fatigue failure)

3. Increased wear

4. Poor quality product

5. Difficult to sell a product

6. Vibrations in machine tools can lead to improper machining of parts