Mechanical Vibration-P2
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Degree of Freedom of Vibration system 26 Three degree of freedom Degree of Freedom Mechanical Vibrations – 3rd year
Transcript of Mechanical Vibration-P2
Degree of Freedom of Vibration system
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Three degree of freedom
Degree of Freedom
Mechanical Vibrations – 3rd year
Degree of Freedom of Vibration system
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Degree of Freedom
Mechanical Vibrations – 3rd year
Steps for Solving and Analysis a Vibration Problems
Steps for Solving and Analysis a Vibration Problems
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Physical model Mechanical
model
Mathematical
model
System model
Analysis of the
system model
Dynamic
response Qualitative
analysis
Mechanical Vibrations – 3rd year
Mechanical Model
Steps for Solving and Analysis a Vibration Problems
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Physical model Mechanical model
Mechanical Vibrations – 3rd year
Mechanical Model
Steps for Solving and Analysis a Vibration Problems
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Physical model Mechanical model
2
k2
k
2
c2
c
m
Mechanical Vibrations – 3rd year
Mechanical Model
Steps for Solving and Analysis a Vibration Problems
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Physical model
Mechanical model of machine tool
Mechanical Vibrations – 3rd year
Mechanical Model
Steps for Solving and Analysis a Vibration Problems
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Mechanical model of radio telescope
Mechanical Vibrations – 3rd year
Mechanical Model
Steps for Solving and Analysis a Vibration Problems
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Mechanical model of cam and follower
Mechanical Vibrations – 3rd year
Mechanical Model
Steps for Solving and Analysis a Vibration Problems
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Mechanical Vibrations – 3rd year
Mechanical Model Main Elements
Steps for Solving and Analysis a Vibration Problems
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Mechanical Vibrations – 3rd year
Spring Stiffness Equivalent
Steps for Solving and Analysis a Vibration Problems
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Mechanical Vibrations – 3rd year
Spring Stiffness Equivalent
Steps for Solving and Analysis a Vibration Problems
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Mechanical Vibrations – 3rd year
Spring Stiffness Equivalent
Steps for Solving and Analysis a Vibration Problems
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Mechanical Vibrations – 3rd year
Damping Elements
Steps for Solving and Analysis a Vibration Problems
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1. Viscous Damping (a) Fluid films between sliding surfaces
(b) Fluid flow around a piston in a cylinder
(c) Fluid flow through an orifice and
(d) The fluid flow around a journal in a bearing.
1. Coulomb or dry-friction damping
2. Material or Solid or Hysteretic Damping
Mechanical Vibrations – 3rd year
Harmonic Motion
Harmonic Motion
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Scotch yoke mechanism
tAAx sinsin
tAdt
dx cos
xtAdt
xd 22
2
2
sin
Mechanical Vibrations – 3rd year
Harmonic Motion
Harmonic Motion
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1. Cycle: motion of body from equilibrium position >
extreme position > equilibrium position > extreme
position in other direction > equilibrium position .
2. Amplitude: Maximum value of motion from
equilibrium. ( Peak min + Peak max = 2 × amplitude)
3. Period: Time taken to complete one cycle,
Mechanical Vibrations – 3rd year
Harmonic Motion
Harmonic Motion
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4. Frequency: number of cycles per unit time,
5. Phase angle: the difference in angle (lead or lag) by which two harmonic motions of the same frequency reach their corresponding value (maxima, minima, zero up-cross, zero down-cross)
Vectorial Representation of Harmonic Motion 43
Harmonic Motion
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Application
Mechanical Vibrations – 3rd year
Harmonic Motion
Example 1: Mathematical Model of a Motorcycle
Solved Examples
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Mechanical Vibrations – 3rd year
Example 2: Torsional Spring Constant of a Propeller Shaft
Solved Examples
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N/m105255.25232
2.03.01080
32
6449
12
4
12
4
12
12
1212
l
dDG
l
GJkt
N/m109012.8232
15.025.01080
32
6449
23
4
23
4
23
23
2312
l
dDG
l
GJkt
N/m105997.6105255.25109012.8
105255.25109012.8 6
66
66
2312
2312
tt
ttteq
kk
kkk
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Quiz
Homework
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Mechanical Vibrations – 3rd year
Devise a mechanical models for the crane of the following Figure
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