525307 mechanical vibrationeng.sut.ac.th/me/2014/document/mechanicalvibration/vibration b1.pdf · 3...
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525307 Mechanical Vibration
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Week 1-6 Introduction to mechanical vibrations SCE Lab
Free vibration SDOF Monday, B3101
Undamped system 08.00-10.00
Damped system Wednesday, B2104
Logarithmic decrement 08.00-10.00
MATLAB&Simulink application
Force vibration SDOF
Undamped system
Force vibration SDOF
Undamped/Damped system
Base excitation
Rotating unbalance
General force response
Spectrum analysis
Force vibration SDOF
Frequency responses
Free vibration MDOF
Undamped system
Mode Shapes, Nodes
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Free vibration MDOF
Modal analysis
Damped system
Force vibration MDOF
Undamped /Damped system
Stability analysis
15 January 2019 Midterm Examination : Mechanical Vibration 9.00 - 11.00
Week 8 -11 Continuous systems using Solidworks Monday, B3101
Transverse vibration of a string 08.00-10.00
Longitudinal vibration of a rod Wednesday, B2104
Torional vibration of a rod 08.00-10.00
Lateral vibration of a beam
Vibration measurement
Vibration Control & Analysis
Static balance /Critical speed
Isolator design
Absorber design
Vibration analysis for CBM
1 March 2019 Final examination : Mechanical Vibration 09.00-12.00
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• A 80-100• B+ 75-79• B 70-74• C+ 60-69• C 50-59• D+ 45-49• D 40-44• F 0-39
Midterm Exam: 30
Final Exam: 30
Vibration modeling of MDOF using Simulink test:15
Continuous system using SolidWorks test: 15
Home work, Quiz , Classroom: 20
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Recommended reading : Mechanical Vibrations, Srisertpol, 2014 Daniel J.Inman:Engineering Vibration,Third Edition,Pearson Education,2008 Leonard Meirovitch : Fundamentals of Vibrations , Mc-Graw Hill 2001. Kelly S. Graham : Fundamentals of Mechanical Vibrations,
Mc-Graw Hill 2000.
Textbook: Singiresu S.Rao : Mechanical Vibration(Fourth Edition), Prentice Hall 2004. SI Edition
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The Spring-Mass-Damper model
Degree of Freedom (DOF)
Relationship between Displacement, Velocity and Acceleration
Representations of harmonic motion
Classification of mechanical vibration
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7School of Mechanical Engineering 7
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8School of Mechanical Engineering 8
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ล ำดบัขัน้ควำมเป็นอิสระ (Degree of Freedom, DOF) - จ ำนวนพิกดั(Coordinate) ท่ีน้อยท่ีสดุท่ีไม่ขึน้ต่อกนัซ่ึงจ ำเป็นต้องใช้อธิบำยต ำแหน่งต่ำงๆ ของทุกส่วนในระบบท่ีขณะเวลำหน่ึง
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Discrete System (Lumped System) Continuous System (Distributed System)
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การสัน่แบบอสิระ (Free Vibration) การสัน่แบบบงัคบั (Forced Vibration) การสัน่แบบไมม่คีวามหน่วง (Undamped Vibration) การสัน่แบบมคีวามหน่วง (Damped Vibration) การสัน่แบบเชงิเสน้ (Linear Vibration) การสัน่แบบไมเ่ชงิเสน้ (Nonlinear Vibration) การสัน่แบบก าหนดได้ (Deterministic Vibration) การสัน่แบบสุม่ (Random Vibration)
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kxF
stiffness springor contant springk
tion)nt(deformadisplacemex
2
2
1 :spring in theenergy Potential kxU
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where
equation mEquilibriu
21
21
kkk
kW
kkW
eq
steq
stst
neq
eq
kkkkk
k
321
parallelin constant spring Equivalent
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21 system theof Static 1. stst
22
11
equation mEquilibriu 2.
kW
kW
steqeq kWk deflection static same for the .3
neq
eq
kkkkk
k
11111
seriesin constant spring Equivalent
321
, or
2
2
1
1
2211
k
k
k
k
kkk
steqsteq
steq
21
111 is, that
kkkeq
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cm 2ddiameter wire
cm 20Ddiameter coilmean
mN 1080G modulusshear 29
The stiffness of helical spring is given by
mN 000,4052.08
108002.0
83
94
3
4
nD
Gdk
The equivalent spring constant of the suspension system is given by
mN 120,000 000,4033 kkeq
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ตวัหน่วงเน่ืองจากความหนืด ตวัหน่วงเนื่องจากแรงเสียดทานระหวา่งของแข็งกบัของแข็ง
ตวัหน่วงเน่ืองจากความไมย่ืดหยุน่ของวสัด ุ
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All real systems dissipate energy when they vibrate. To
account for this we must consider damping. The most simple
form of damping (from a mathematical point of view) is called
viscous damping. A viscous damper (or dashpot) produces a
force that is proportional to velocity.
Damper (c)
( ) ( )cf cv t cx t x
fc
Mostly a mathematically motivated form, allowing
a solution to the resulting equations of motion that predicts
reasonable (observed) amounts of energy dissipation.
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neq
eq
cccc
c
1111
seriesin constant damping Equivalent
21
321
parallelin constant damping Equivalent
cccc
c
eq
eq
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มวลเทียบเท่ำของล้อมวลเทียบเท่ำของสปริง
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กฎการเคลือ่นทีข่องนิวตนั กฎการอนุรกัษ์พลงังาน
สมการลากรานส ์
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การแกส้มการอนุพนัธ์ การเปลีย่นรปูของลาปลาซ วธิเีชงิตวัเลข
Dynamic System Modeling and Analysis, Hung V Vu and Ramin S. Esfandiari,
McGraw-Hill 1998
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◦
◦
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Simple model• Single-degree of freedom model as shown in b.
stiffness. equivalent,, srteq kkkk
constant. damping equivalent, rseq ccc
mass equivalent,, wvreq mmmm
wheels, body, vehicle, struts tires,,rider wvstr
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wheels, body, vehicle, struts tires,,rider wvstr
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wheels, body, vehicle, struts tires,,rider wvstr
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wheels, body, vehicle, struts tires,,rider wvstr
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การเคลือ่นทีแ่บบฮารโ์มนิกสอ์ยา่งงา่ย
รปูแบบของฟังกช์ัน่ฮารโ์มนิกส์
การสัน่ทีม่ขีนาดแบบเอก็โปแนนเชยีล
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2 2
Displacement: ( ) sin
Velocity: ( ) cos sin2
Acceleration: ( ) sin sin
y t A t
y t A t A t
y t A t A t
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0 1 2 3 4 5 6 7 8 9 10-20
-15
-10
-5
0
5
10
15
20
Time,(sec)
Displacement
Velocity
Acceleration
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t/T, sec
T=1 sec
T= 0.5 sec
T= 2 sec
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0 2 4 6 8 10 12 14
-0.4
-0.2
0
0.2
0.4
0.6
Time, (sec)
y(t
)
0 2 4 6 8 10 12 14-800
-600
-400
-200
0
200
400
600
Time, (sec)
y(t
)
Stable system
Unstable system
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Degree of freedom
Types of vibration motion
Elements of Mechanical system Mass, Inertia
Damper
Spring
Vibration analysis procedure
Mathematical model
Simple harmonic motion
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