1. In the Name of Allah, the Gracious, the Merciful

2. By Muhammad Ishfaq Khan
Engineering Dynamics By
Muhammad Ishfaq Khan

3. Thesis Defense Worskhop
Lecture 1
UTSI-NSBE
Thesis Defense Worskhop

4. Course Content B-Tech Vibration: Revision of matrix algebra:
Introduction,
types of vibration, basic concepts and terminologies
Revision of matrix algebra:
Characteristic equations, solution methods, free vibration, equation of motion, energy methods, series and parallel combination, viscously damped free vibration, logarithmic decrement, coulomb damping.
Harmonically excited vibration:
Forced harmonic vibration, rotating unbalanced, and vibration measuring instruments.

5. Physical stiffness of elements: Eigen value analysis of:
Mechanical system:
Gravity pendulum, spring-mass vibrating system, compound gravity pendulum, stiffness, potential energy, stability, torsional pendulum, free vibration and resonance.
Physical stiffness of elements:
Rods, beams, stiffness coefficients as matrix elements.
Eigen value analysis of:
Two degree of freedom problems, three degree of freedom problems,
determination of modes of vibration.
Rayleigh’s method and its applications
Books Recommended:
1. Vibration theory and applications – William, T. and Thompson.
2. Fundamentals of mechanical vibrations by Kelly.
3. Mechanical Vibration by S. S. Rao

6. Thesis Defense Worskhop
Lab Outline
1. Demonstration on simple spring mass system and related calculation.
2. Demonstration simulation of beams and rod vibration.
3. Demonstration on damped vibration and analysis.
4. Computer simulation of whole range of vibrating components.
5. Application of computer for solving set of equations.
UTSI-NSBE
Thesis Defense Worskhop

7. Thesis Defense Worskhop
History
first musical instruments
4000 B.C. with 1st Musical Instument
Pythagoras’s Monotone ( B.C.)
1st Scientific Investigation!
UTSI-NSBE
Thesis Defense Worskhop

8. Zhang Heng measured earthquakes Time of Occurrence & Direction
Galileo Galilei ( ) From a Lamp in a Church in Pisa:
Time Period was Independent of Amplitude
Frequency of vibration on the length of a simple pendulum
Phenomenon of sympathetic vibrations i.e. resonance
Newton’s 2nd Law
J.B. Fourier Transformation
Charles Coulomb Discovered the period of oscillation is independent of the angle of twist
E. F. F. Chladni ( ) mode shapes of a Plate

9. Importance of Vibrations
Tacoma Narrows bridge during wind-induced vibration
Aero planes Vanished due to fatigue caused by wind on the wing and chassis vibrations
UTSI-NSBE
Thesis Defense Worskhop

10. Thesis Defense Worskhop
Introduction
What is Vibration?
Any motion that repeats itself after an interval of time is called vibration or oscillation.
Any movement w.r.t. reference position
Vibration of road surface!
Earth Quakes
Excited Tuning Fork
Speaking
Singing
UTSI-NSBE
Thesis Defense Worskhop

11. Basic Concepts & Terminologies
Means for Storing Potential Energy
Spring or Elasticity
a means for storing kinetic energy
mass or inertia
a means by which energy is gradually lost
damper
the transfer of its potential energy to kinetic energy and of kinetic energy to potential energy, alternately!
some energy is dissipated in each cycle of vibration due to damping
An external source if a state of steady vibration is to be maintained for damped system

12. Thesis Defense Worskhop
Bob of mass m be released at angle θ
At 1, K.E. 0, P.E. = mgl(cosθ-1)
a torque mglsinθ about the point O,
the bob starts swinging to the left
from position 1
At position 2, all of its potential energy will be converted into kinetic energy
Due to Inertia it wont stop!
mglsinθ now acts till pendulum stops at 3
So on and so forth
UTSI-NSBE
Thesis Defense Worskhop

13. Thesis Defense Worskhop
DOFs
The minimum number of independent coordinates required to determine completely the positions of all parts of a system at any instant of time defines the number of degrees of freedom of the system
Pendulum is 1 DOF System!
Why?
UTSI-NSBE
Thesis Defense Worskhop

14. Thesis Defense Worskhop
External Force
Types of Mechanical Vibrations
Free vibration
If a system, after an initial disturbance, is left to vibrate on its own
Any Example?
Forced vibration
If a system is subjected to an external force (often, a repeating type of force)
resonance
UTSI-NSBE
Thesis Defense Worskhop

15. Thesis Defense Worskhop
Resistance
Un-Damped
no energy is lost or dissipated in friction or other resistance during oscillation
Any Example?
Damped
UTSI-NSBE
Thesis Defense Worskhop

16. Thesis Defense Worskhop
Component Behavior
Linear
the basic components of a vibratory system behave linearly
Non-Linear
the basic components of a vibratory system behave non-linearly
UTSI-NSBE
Thesis Defense Worskhop

17. Thesis Defense Worskhop
Predictability
Deterministic
the value or magnitude of the excitation (force or motion) is known
Random
the value or magnitude of the excitation (force or motion) is not known
UTSI-NSBE
Thesis Defense Worskhop