MECHANICAL VIBRATION - PART 1

MECHANICAL TIPS AND STUDY MATERIAL

Due to the application of external forces when an elastic body such as, a spring, a beam and a shaft are displaced from the equilibrium position , and then released, they witness a vibratory motion, because of strain energy present in the body. After reaching the equilibrium position, the whole of the stain energy is converted into kinetic energy due to which the body continues to move in the opposite direction. 

Complete kinetic energy is converted into strain energy due to which the body again returns to the equilibrium position and the vibratory motion is repeated continuously.


When the body moves back and forth continuously across the equilibrium position then it is said to have Oscillatory motion. The repeating pattern may not have specified repeating pattern.


HARMONIC MOTION






Harmonic motion is a type of motion where the pattern of motion is prescribed by either a sine or cosine. This motion is also called as simple harmonic motion. This S.H.M is described in terms of frequency. Frequency term expressed in the units radians per seconds (rad/sec). The

relationship between the frequency in Hz (cps) and the frequency in rad/sec is simply the
relationship. 2 rad/sec.

PERIODIC MOTION


Periodic motion is a kind of motion where the  pattern of the motion repeats itself with a

uniform time interval. This uniform time interval is referred to as the period and has units of seconds
per cycle. The reciprocal of the period is referred to as the frequency and has units of cycles per
second expressed in terms of hertz (Hz)

NATURAL FREQUENCY



Without affect of any external excitation, the frequency at which a body tends to oscillates is known as natural frequency. In this case the body will remain to oscillate for infinite period of time since there is no damping


DAMPED FREQUENCY 

In damped frequency the body will reach to rest point and finally comes to zero oscillation.
Initially the body is set to oscillates from initial condition without affect of external source and slowly it retards to zero.

RESONANCE





When the body is subjected with external excitation at natural frequency of system it is said to have resonance. It is unwanted as it produces high system response.


DEGREE OF FREEDOM



Degrees of freedom determines the position and orientation of the body in the space. This is useful in several fields of study such as robotics and vibrations.


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