fundamentals of mechanical vibration

7/29/2019 Fundamentals of Mechanical Vibration

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Fundamentals of

Mechanical Vibration

Lecture - 1


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Purposely kept as blank


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What is Vibration?

1. In its simplest form, vibration can be considered to be the oscillation or

repetitive motion of an object around an equilibrium position.

2. The equilibrium position is the position the object will attain when the force

acting on it is zero.

Vibration is occasionally "desirable". For example the motion of a tuning fork, the

reed in a woodwind instrument or harmonica, or the cone of a loudspeaker is

desirable vibration, necessary for the correct functioning of the various devices.


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More often, vibration is undesirable, wasting energy and creating unwanted sound

noise.

For example, the vibrational motions of engines, electric motors, or any mechanical

device in operation are typically unwanted.

The main reasons of vibrations are

1. Unbalance centrifugal force in the system. This is caused because of non-uniform

material distribution in the rotating machine parts.

2. Elastic nature of the system.

3. External excitation applied on the system.


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Importance of vibration study in engineering

1. Due to faulty design and poor manufacture there is unbalance in the engines

which causes excessive and unpleasant stresses in the rotating system

because of vibration

2. The vibration causes rapid wear of machine parts such as bearings and gears.

3. Many building s, structures and bridges falls because of vibration.

4. Because of heavy vibration proper readings of instruments cannot be taken.


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Parts of vibrating system

1. Mass : Energy is stored by mass in the

form of K.E

2. Spring : Energy is stored by mass in theform of P.E

3. Damper: Dissipate the energy in the form

of heat


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Parts of vibrating system

Vibrating System

K Spring

x

M Mass

C Damper


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Basic Concepts of Vibration

All the bodies having mass and elasticity are capable of vibration .The mass is inherent of the body.

Elasticity causes relative motion among its parts.


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When body particles are displaced by the application of external force , the

internal forces in the form of elastic energy are presented in the body . These

forces try to bring the body to its original position. At equilibrium position, the

hole of the elastic energy is converted in to kinetic energy and body continues tomove in the opposite direction because of it. The whole of the kinetic energy is

again converted into elastic or strain energy due to which the body returns to the

equilibrium position. In this way vibratory motion is repeated.


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Types of vibration

Free vibration and forced vibration

When the motion is maintained by the restoring forces only, the

vibration is described asfree vibration. When a periodic force is

applied to the system, the motion is described asforced vibration.

Damped undampedvibration

When the frictional dissipation of energy is neglected, the motion

is said to be undamped. Actually, all vibrations are dampedto

some degree.


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Methods of reducing vibration

1. Removing external excitation if possible.

2. Use shock absorber.

3. Dynamic absorber.

4. Resting the system on proper vibration isolators.


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Methods of Vibration Analysis

Energy Method :Sum of the energies associated with the system is constant.

Rayleighs Method: This method is the extension of energy method. The method is

based on the principle that the total energy of a vibrating system is equal to the

maximum potential energy

Equilibrium Method : Algebraic sum of the forces and moments acting on the

system must be zero.


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The simplest vibratory system can be described by a single mass connected to a spring

(and possibly a dashpot). The mass is allowed to travel only along the spring elongation

direction. Such systems are called Single Degree-of-Freedom (SDOF) systems and are shown in

the following figure,

SDOF vibration can be analyzed by Newton's second law of motion, F= m*a. The analysis

can be easily visualized with the aid of a free body diagram,


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The resulting equation of motion is a

1. second order,

2. non-homogeneous,

3. ordinary differential equation.

with the initial conditions,The solution to the general SDOF equation of motion is shown inthe damped SDOF discussion.


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Continued.

fundamentals of mechanical vibration

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