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# Vibration and damping

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### Vibration and damping

1. 1. A Seminar On Vibration Analysis And Damping In Structures Submitted to: Submitted By: Mr Rahul Bhaiji Divya Lattoo Utkarsh Tiwari
2. 2. Introduction Structure – A structure is a combination of parts fastened together to create a supporting framework, which may be part of a building, ship, machine, space vehicle, engine or some other system. Vibrations –
3. 3. THE CAUSES AND EFFECTS OF STRUCTURAL VIBRATION Cause Effect
4. 4. THE REDUCTION OF STRUCTURAL VIBRATION
5. 5. THE ANALYSIS OF STRUCTURAL VIBRATION Stage I. Devise a mathematical or physical model of the structure to be analysed. Stage II. From the model, write the equations of motion. Stage III. Evaluate the structure response to a relevant specific excitation.
6. 6. The Vibration Of Structures With One Degree Of Freedom FREE UNDAMPED VIBRATION Translation vibration
7. 7. Torsional vibration
8. 8. Energy methods for analysis • For undamped free vibration the total energy in the vibrating system is constantthroughout the cycle. Therefore the maximum potential energy V(max), is equal to the maximum kinetic energy T(max) , although these maxima occur at different times during the cycle of vibration. Furthermore, since the total energy is constant, • T + V = constant, • d(T + V)/dt = 0 • ω = (k/m)1/2 • Condition of stability – .
9. 9. FREE DAMPED VIBRATION The most common types of damping are Viscous dry friction hysteretic
10. 10. Vibration with viscous Damping • Case 1 ζ less than 1, that is, damping less than critical • The motion of the body is therefore an exponentially decaying harmonic oscillation • Case 2 ζ = 1; that is, critical damping • Critical damping represents the limit of periodic motion; hence the displaced body isrestored to equilibrium in the shortest possible time, and without oscillation or overshoot. • Case 3 ζ greater than critical, • Since both values of s are negative the motion is the sum of two exponential decays
11. 11. Vibration with Coulomb (dry friction) damping Equation Of Motion - m = Fẍ d – kx 
12. 12. Vibration with hysteretic damping Experiments on the damping that occurs in solid materials and structures that have been subjected to cyclic stressing have shown the damping force to be independent of frequency internal, or material, damping is referred to as hysteretic damping. the induced stress is σ = σ0sin (Vt+ α)
13. 13. FORCED VIBRATION The equation of motion is X/Xs is known as the dynamic magnification factor
14. 14. Resonance The phenomenon known as resonance occurs when the forcing frequency is equal to the natural frequency, that is when v/ω = 1. The maximum value of X/Xs actually occurs at values of v/ω less than unity:
15. 15. Response of a viscous damped Structure supported on a foundation subjected to harmonic vibration Equation Off Motion
16. 16. Vibration Isolation The force transmitted to the foundation is the sum of the spring force and the damper force. Thus the transmitted force = kx + cẋ and Fx the amplitude of the transmitted force is given by –
17. 17. Response of a Coulomb damped structure to a simple harmonic exciting force with constant amplitude The equation of motion is non-linear because the constant friction force F, always opposes the motion:
18. 18. Response of a structure to a suddenly applied Force The equation of motion can be written If the structure possesses viscous damping of coefficient c, the solution to the equation of motion is
19. 19. Shock excitation Some structures are subjected to shock or impulse loads arising from suddenly applied, non-periodic, short-duration exciting forces. X(t) =
20. 20. Wind- or current-excited oscillation A structure exposed to a fluid stream is subjected to a harmonically varying force in a direction perpendicular to the stream. This is because of eddy, or vortex, shedding on alternate sides of the structure on the leeward side.
21. 21. Damping In Structures • Sources of damping – Inherent damping – Hysteretic or material damping – Damping in structural joints – Acoustic radiation damping – Air pumping – Aerodynamic damping • Added damping – High damping alloys – Composite materials – Viscoelastic materials – Constrained layer damping – Vibration dampers and absorbers
22. 22. Vibration Isolation The force transmitted to the foundation is the sum of the spring force and the damper force.  Motion Transmission TR = X/A =
23. 23. BIBLIOGRAPHY • Structural Vibration and Damping By C. E Beards www.howstuffwork.com Theory Of Machine By R.S.Khurmi
24. 24. Questions And Query Are Welcome