Fundamentals of vibration
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The document discusses the fundamentals of vibration, defining it as a mechanical phenomenon involving oscillation around an equilibrium point due to mass and elasticity. It categorizes vibrations into free (longitudinal, transverse, and torsional), forced, damped, and undamped vibrations, as well as linear and non-linear vibrations. Key concepts such as resonance and the distinction between continuous and discrete systems are also covered, along with an introduction to Fourier series for analyzing vibration results.
Fundamentals of vibration
- 1. FUNDAMENTALS OF VIBRATION BY:- SHUBHAM CHAURASIYA (DEPARTMENT OF MECHANICAL ENGINEERING PUNJAB UNIVERSITY)
- 2. BASIC CONCEPTS OF VIBRATION? Vibration is a mechanical phenomena whereby oscillation occur about an equilibrium point All bodies having mass and elasticity are capable of producing 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 In this way, vibratory motion is repeated indefinitely and exchange of energy takes place
- 4. FREE AND ITS SUB TYPES FREE VIBRATION:- In Free vibration, the object is not under the influence of any kind of outside force. a)Longitudinal vibration: when the particles of the body move parallel to the axis of the body, the vibration is known as longitudinal vibration. b)Transverse vibration: hen the particles of the body move nearly perpendicular to the axis of the body, the vibration is known as transverse vibration. c)Torsional vibration: When the particles of the body move in a circle about the axis of the body, the vibration is known as torsional vibration.
- 6. FORCED VIBRATION When a periodic disturbing force keeps the body in vibration through out its entire period of motion, such vibration is said to be a forced vibration. The frequency of vibration of the body is same as the frequency of the applied force.
- 7. DAMPED VIBRATION If the vibratory system has a damper the motion of the system will be dissipated in friction.this type of vibration is called damped vibration
- 8. UNDAMPED VIBRATION On the contrary,the system no damper is known as undamped vibration
- 9. LINEAR AND NON-LINEAR VIBRATION If in a vibratory system mass,spring and damper behave in a linear manner,the vibrations caused are known as linear in nature.Linear vibrations are governed by linear differential equations.They follow the law of superposition.Mathematically if a1 and a2 are solution of 1 &2 then a1+a2 is solution of 3 1 2 3 On the other hand if the amplitude of vibration is very high it Becomes non linear in nature
- 10. RESONANCE When the frequency of external excitation is equal to the natural frequency of a vibrating body,the amplitude of a vibration becomes excessively large.This concept is known as resonance
- 11. CONTINUOUS SYSTEM Most of the mechanical system include elastic members which have infinite no. Of degree of freedom are called continuous system cantilever beam a typical example of continuous system
- 12. DISCRETE SYS System with finite number of degree of freedom are called discrete or lumped system System with 1 degree of freedom System with 2 degree of freedom
- 14. SHM
- 17. ADDITION OF SHM
- 18. FOURIER SERIES J.Fourier, a French mathematician, developed this It is a periodic function in terms of series of sines and cosines With the help of this series vibration results obtained experimentally can be analysed analytically
- 19. MATHEMATICAL FORM OF FOURIER SERIES