VIBRATION |T.O.M.| MECHANICAL ENGINEERING

VIBRATION

Introduction :

When elastic bodies such as a spring, a beam and a shaft are displaced from the equilibrium position by the application of external forces, and then released, they execute a vibratory motion. This is due to the reason that,

when a body is displaced, the internal forces in the form of elastic or strain energy are present in the body. At release, these forces bring the body to its original position. When the body reaches the equilibrium position, the whole of the elastic or strain energy is converted into kinetic energy due to which

the body continues to move in the opposite direction. The whole of the kinetic energy is again converted into strain energy due to which the body again returns to the equilib-

rium position. In this way, the vibratory motion is repeated indefinitely.

Terms Used in Vibratory Motion:-

1. Period of vibration or time period:-

It is the time interval after which the motion is.Repeated itself. The period of vibration is usually expressed in seconds.

2. Cycle:-

It is the motion completed during one time period.

3. Frequency. :-

It is the number of cycles described in one second. In S.I. units, the fre- quency is expressed in hertz (briefly written as Hz) which is equal to one cycle per second.

Types of Vibratory Motion

The following types of vibratory motion are important from the subject point of view :

1. Free or natural vibrations.:-

When no external force acts on the body, after giving it an initial displacement, then the body is said to be under free or natural vibrations. The frequency of the free vibrations is called free or natural frequency.

2. Forced vibrations. :-

When the body vibrates under the influence of external force, then the body is said to be under forced vibrations. The external force applied to the body is a periodic disturbing force created by unbalance. The vibrations have the same frequency as the applied force.

Note : When the frequency of the external force is same as that of the natural vibrations, resonance takes place.

3. Damped vibrations:+

When there is a reduction in amplitude over every cycle of vibration, the motion is said to be damped vibration. This is due to the fact that a certain amount of energy possessed by the vibrating system is always dissipated in overcoming frictional resistances to the motion.

Types of Free Vibrations:-

The following three types of free vibrations are important from the subject point of view :

1. Longitudinal vibrations,

2. Transverse vibrations, and

3. Torsional vibrations.

Consider a weightless constraint (spring or shaft) whose one end is fixed and the other end carrying a heavy disc, as shownin fig. . This system may execute one of the three above mentioned types of vibrations.

. Types of free vibrations.:-

1. Longitudinal vibrations.:-

When the particles of the shaft or disc moves parallel to the axis of the shaft, as shown in Fig. 23.1 (a), then the vibrations are known as longitudinal vibrations.In this case, the shaft is elongated and shortened alternately and thus the tensile and compressive stresses are induced alternately in the shaft.

2. Transverse vibrations.

When the particles of the shaft or disc move approximately perpendicular to the axis of the shaft, as shown in Fig. 23.1 (b), then the vibrations are known as transverse vibrations. In this case, the shaft is straight and bent alternately and bending stresses are induced in the shaft.

3. Torsional vibrations*.

When the particles of the shaft or disc move in a circle about the axis of the shaft, as shown in Fig. 23.1 (c), then the vibrations are known as torsional vibrations. In this case, the shaft is twisted and untwisted alternately and the torsional shear stresses are induced in the shaft.