as jatav...ppt on vibration
DESCRIPTION
seminarTRANSCRIPT
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A body is said to be vibrate if it has a to-and-fro motion.
Most vibrations in machines and structures are undesirable due to increased stresses and energy losses.
If body has harmonic motion it will also be vibrate.
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Longitudinal vibration- The different particles of the body move parallel to the axis of the body.
Transverse vibration- When the shaft is bent alternately and tensile and compressive stresses due to bending result, the vibrations are said to be transverse.
Torsional vibration- Because of twisting of shaft alternately torsional vibrations are created. The particles of the body move in a circle about the axis of the shaft.
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Free (Natural) Vibration- No friction and no external forces after the initial release of the body.
Damped Vibration- In this vibrating system energy is dissipated by friction and other resistances.
Forced Vibration- Repeated force continuously acts on a system, vibration are said to be forced.
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It states that the inertia forces and
couples, and the external forces
and torques on a body together
give statically equilibrium.
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i. Kinetic storing device (mass - m)
ii. Potential storing device (Stiffness – s)
iii. Kinetic Friction (never equals to zero).
iv. Vibrating causing harmonic force.
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If a particle is displaced through a distance xm from its equilibrium position and released with no velocity, the particle will undergo simple harmonic motion, 0=+ kxxm
( )φω += txx nm sin
xv =xa =
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• Spring-MassSystem in VerticalPosition
0=+ kxxm
=
m
knω
( )φω += txx nm sin
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Vibrating systems can encounter damping in various ways like
Intermolecular frictionSliding frictionFluid resistance2. Damping estimation of any system is the most
difficult process in any vibration analysis.
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Technical name of friction in vibration is known as damping.
High damping/ coulomb damping – Due to friction between dry surfaces.
Low damping/viscous damping – Friction because of fluid layer due to lubrication.
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Damped SDF and free body diagramThe eqn of motion is given by
A particular solution is given byHence
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The two roots of the above equation are given by
A general solution is given byTo make the solution more general the critical damping coefficient is defined as
which gives the criteria for various damping properties where ξ= C/c
So the solution now becomes in terms of as ξ
This gives rise to four cases as discussed next
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Type of System depends on Damping Factor
Under damped ξ<1
Undamped ξ =0
Over damped ξ >1
Critically damped ξ=1
.
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The general solution becomes
The solution will be non oscillatory and gradually comes to rest
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The solution will be
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Critical Damping response Is more fast than over damping.
Damping factor= actual damping coefficient/critical damping
coefficient
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The ratio of the force transmitted to the foundation to the force applied.It is the measure of the effectiveness of the vibration isolating material.
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