mak4041-mechanical vibrations important notes: the course notes were compiled mostly from 1) the...
TRANSCRIPT
![Page 1: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/1.jpg)
MAK4041-Mechanical MAK4041-Mechanical VibrationsVibrations Important Notes:Important Notes:
The course notes were compiled mostly from
1) The book by Graham Kelly, “Mechanical Vibrations, Theory and Applications”, 2012.
2) Bruel Kjaer Technical notes,
3) Dan Russel’s webpage: http://www.acs.psu.edu/drussell
Therefore, they are gratefully acknowledged.
Assoc. Prof. Dr. Abdullah Assoc. Prof. Dr. Abdullah SeçginSeçgin
![Page 2: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/2.jpg)
WEEK-1: WEEK-1: Introduction to Mechanical Introduction to Mechanical
VibrationsVibrationsAssoc. Prof. Dr. Abdullah Assoc. Prof. Dr. Abdullah SeçginSeçgin
![Page 3: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/3.jpg)
What is vibration? Vibrations are oscillations of a system about
an equilbrium position.
![Page 4: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/4.jpg)
Vibration…
It is also an everyday phenomenon we meet on everyday life
![Page 5: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/5.jpg)
Vibration …Useful Vibration Harmful vibration
Noise
Destruction
Compressor
Ultrasonic cleaning
Testing
Wear
Fatigue
![Page 6: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/6.jpg)
Vibration parameters
All mechanical systems can be modeled by containing three basic components:
spring, damper, mass
When these components are subjected to constant force, they react with a constant
displacement, velocity and acceleration
![Page 7: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/7.jpg)
Free vibration
Equilibrium pos.
When a system is initially disturbed by a displacement, velocity or acceleration, the system begins to vibrate with a constant amplitude and frequency depend on its stiffness and mass.
This frequency is called as natural frequency, and the form of the vibration is called as mode shapes
![Page 8: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/8.jpg)
Forced Vibration
If an external force applied to a system, the system will follow the force with the same frequency.
However, when the force frequency is increased to the system’s natural frequency, amplitudes will dangerously increase in this region. This phenomenon called as “Resonance”
’
![Page 9: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/9.jpg)
Bridge collapse:
http://www.youtube.com/watch?v=j-zczJXSxnw
Hellicopter resonance: http://www.youtube.com/watch?v=0FeXjhUEXlc
Resonance vibration test:
http://www.youtube.com/watch?v=LV_UuzEznHs
Flutter (Aeordynamically induced vibration) :
http://www.youtube.com/watch?v=OhwLojNerMU
Watch these …
![Page 10: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/10.jpg)
Lumped (Rigid) Modelling
Numerical Modelling
Element-based methods(FEM, BEM)
Statistical and Energy-based methods
(SEA, EFA, etc.)
Modelling of vibrating systems
![Page 11: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/11.jpg)
• Mathematical modeling of a physical system requires the selection of a set of variables that describes the behavior of the system.
• The number of degrees of freedom for a system is the number of kinematically independent variables necessary to completely describe the motion of every particle in thesystem
DOF=1
Single degree of freedom (SDOF)
DOF=2
Multi degree of freedom (MDOF)
Degree of Freedom (DOF)
![Page 12: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/12.jpg)
Equivalent model of systemsExample 1: Example 2:
SDOF
DOF=1
MDOF
DOF=2
![Page 13: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/13.jpg)
Equivalent model of systemsExample 3:
SDOF
MDOF
DOF=2
DOF= 3 if body 1 has no rotation
DOF= 4 if body 1 has rotation
body 1
![Page 14: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/14.jpg)
What are their DOFs?
![Page 15: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/15.jpg)
SDOF systems Helical springs
F: Force, D: Diameter, G: Shear modulus of the rod, N: Number of turns, r : Radius
Shear stress:
Stiffness coefficient:
Springs in combinations:
Parallel combination Series combination
![Page 16: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/16.jpg)
Elastic elements as springs
![Page 17: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/17.jpg)
Moment of Inertia
![Page 18: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/18.jpg)
What are the equivalent stiffnesses?
![Page 19: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/19.jpg)
Example A 200-kg machine is attached to the end of a cantilever beam of length L=
2.5 m, elastic modulus E= 200x109 N/m2, and cross-sectional moment of inertia I = 1.8x10–6 m4. Assuming the mass of the beam is small compared to the mass of the machine, what is the stiffness of the beam?
![Page 20: MAK4041-Mechanical Vibrations Important Notes: The course notes were compiled mostly from 1) The book by Graham Kelly, “Mechanical Vibrations, Theory and](https://reader033.vdocuments.us/reader033/viewer/2022061504/56649d355503460f94a0be3b/html5/thumbnails/20.jpg)
Damping Viscous Damping