# Elements Of Vibration In Mechanical Engineering

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A Study of Elements of Vibration in Mechanical Engineering Bilal Ahmad Malik Department of Mechanical Engineering, Techno Global University, Meghalaya. Email: bilalmalik15@gmail.com Introduction With the discovery of musical instruments like drums, the vibration becomes a point of interest for scientists and since then there has been much investigation in the field of vibration. All bodies having mass and elasticity are capable of vibration. The mass is inherent of the body and elasticity causes relative motion among its parts. When body particles are displaced by the application of external force, the internal forces in the form of elastic energy are present in the body.…show more content…
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. The vibration causes rapid wear of machine parts such as bearings and gears. Unwanted vibrations may cause loosening of parts from the machine. Because of improper design or material distribution, the wheels of locomotive can leave the track due to excessive vibration which results in accident or heavy loss. Many buildings, structures and bridges fall because of vibration. If the frequency of excitation coincides with one of the natural frequencies of the system, a condition of resonance is reached, and dangerously large oscillation may occur which may result in the mechanical failure of the system. Sometimes because of heavy vibrations proper readings instruments cannot be taken. Excessive vibration is dangerous for human beings. Thus keeping in view all these devastating effects, the study of vibration is essential for a mechanical engineer to minimize the vibrational effects over mechanical components by designing them…show more content…
The motion is periodic and its acceleration is always directed towards the main position and is proportional to its distance from mean position. The motion of a simple pendulum as shown in figure below is simple harmonic in nature. Ɵ Ball Mean position Let a body having simple harmonic motion is represented by the equation: x=A sinωt x ̇=Aω cosωt x ̈= -Aω^2 sinωt x ̈=-ω^2 x Where x,x ̇ and x ̈ represents the displacement, velocity and acceleration of the body respectively. Damping: It is the resistance to the motion of a vibrating body. The vibrations associated with this resistance are known as damped vibrations. Phase difference: Suppose there are two vectors x_1 and x_(2 )having frequencies ω rad/sec each. The vibrating motion can be expressed as x_1 = A_1 sinωt x_(2 )= A_2 sin⁡(ωt + ϕ) In the above equation the term ϕ is known as the phase