Define vibration?

After motion that repeats itself after a interval of time is called as vibration. There vibration is periodic motion

At mean position, strain or potential energy ----------- kinetic energy

At extreme positions, kinetic energy ------------- strain or potential energy.

Mention the causes of vibration?

UNBALANCED FORCES IN THE MACHINE: These forces are produced from within the machine itself. To avoid vibrations, these forces must be balanced.

DRY FRICTION between the two mating surfaces.

EXTERNAL EXCITATION: These excitations may be periodic or random.

WIND: this may produce vibrations on telephone lines and power transmitting lines.

EARTHQUAKES: This is the main cause for the failure of many buildings, dams, etc.

Define the following terms:

TIME PERIOD (OR) PERIOD OF VIBRATION: It is the time taken the vibrating body to repeat the motion itself. Time period id usually represented in seconds.

AMPLITUDE: The maximum displacement of the vibrating body from the mean position. It is usually expressed in millimeters (mm).

FRQUENCY: The number of cycles completed in one second is called as frequency. In the S.I. units, the frequency is expressed in hertz or cycles per second.

DAMPING: Any resistance to the motion of the vibrating body is called as damping.

(E.G) In the simple pendulum air acts as damping medium.

What are the types of vibration?

There are two types of vibration they are.

Free vibrations

Forced vibrations

Define free vibration?

When a body is allowed to vibrate on its own, after giving it an initial displacement, then ensuring vibration is known as free or natural vibration. No external force is applied on the body. The frequency of the free vibrations is called as free or natural frequency and is denoted as f.

EG. Tuning fork vibrations, guitar string vibrations.

Define forced vibrations?

When a body vibrates under the influence of the external forces, then the ensuring vibration is called as forced vibrations. When an external force is applied, the body doesn’t vibrate with its own natural frequency but vibrate with the same frequency of the applied external force. The external force is a periodic disturbing force created by unbalance.

What is meant by resonance?

When the frequency of the external force coincides with the natural frequency of the vibrating system, then the vibrating takes place with very high amplitude. This phenomenon is called as resonance.

Define damped vibrations?

When the amplitude of the vibrations reduces in cycle then the vibration is known as damped vibrations. This is because some amount of energy possessed by the vibrating system is dissipated in overcoming the frictional resistances to the motion. Damping is provided by connecting ‘dash pot’. When the dash pot is connected with the free vibrating body to control vibrations, then it is called free damped vibrations and when is connected with forced vibrating body to control vibrations, then it is called as forced damped vibrations. The frequency of damped vibrations is called as damped natural frequency.

What are the different types of vibrations?

There are three different types of vibration. They are

Longitudinal vibrations

Transverse vibrations

Torsional vibrations

Define degrees of freedom?

The number of independent coordinates required to specify completely the configuration of a system at any instant is called as degree of freedom.

Define longitudinal vibrations?

When the particles of the shaft or disc move parallel to the axis of the shaft, then ensuring the vibrations are known as longitudinal vibrations.

Give the representation of free damped longitudinal vibration?

Free longitudinal is represented as shown

K = stiffness of the constraint.

m = mass of the body suspended from the constraint

c = damping coefficient.

Define stiffness of the spring?

It is defined as the force required to produce unit displacement in the direction of the vibration. It is expressed in N/m.

Mention the governing equation of the free undamped longitudinal vibration?

Mention the formula for the natural frequency of free longitudinal vibration (I) by neglecting the effect of inertia of the constraint (ii) by considering the effect of inertia of the constraint?

Natural frequency (neglecting the effect of inertia of the constraint)

Natural frequency of vibration (considering the effect of inertia of the constraint)

Define damping and mention its types?

Any resistance to the motion of the vibrating body is called as damping. In damping vibrations the amplitude of the damping decreases over every cycle with respect to the amount of damping.

Generally there are four types of damping

Viscous damping

Dry friction or coulomb damping

Solid damping or structural damping or hysteresis damping

Slip or interfacial damping

Define hysteresis damping?

The damping due to the internal friction of the molecules is called solid or structural damping. This damping occurs in all vibrating systems subjected to elastic restoring forces. The amount of damping is small.

Define interfacial damping?

The damping due to the microscopic slip is called as slip or interfacial damping. Energy of vibration is dissipated by microscopic slip on the interfaces of machine parts in contact under fluctuating loads. Microscopic slip occurs at the joints of the machine elements.

What is the advantage of damping?

In mechanical systems damping is provided to control the amplitude of vibration so that failure due to the reference can be avoided.

Define degrees of dampness?

The ratio of is called as degree of dampness.

Define damping coefficient?

The damping force per unit velocity is known as damping coefficient. It is given by

C=

Define damping factor?

Damping factor can be defined as the ratio of actual damping coefficient to critical damping coefficient.

Define logarithmic decrement?

It is defined as the natural logarithm of the ratio of any two successive amplitudes of an under damped system. It is represented as and it is a dimensionless quantity.

Give the expression for natural frequency of a simple pendulum?

The natural frequency of a simple pendulum is given by,

Give the expression for natural frequency of a compound pendulum?