In the name of God
Vibration-45144
Instructor: Hassan Haddadpour
Haddadpour@sharif.edu
Description: This course will address issues related to the mutual interaction of
elastic and inertial forces.
Course Objectives: This course is a collection of special topics in the application of
dynamics of elastic systems, which is called vibration or structural dynamics. It
quantifies the effects of the inertial and structural parameters that affect natural
frequency, damping, and structural response and the application of them for the
design of mechanical systems.
Prerequisites by Topic:
1. An understanding of differential equations.
2. Dynamics
3. Mechanics of Materials
Syllabus:
1. Introduction to Vibrations
 What is Vibration
 Application of Vibration
 A review on Dynamics
2. Oscillatory Motion
 Harmonic Motion
 Periodic Motion
 Vibration Terminology
3. Free Vibration
 Vibration Model
 Equation of Motion: Natural Frequency
 Energy Method
 Rayleigh Method: Effective Mass
 Principle of Virtual Work
 Viscously Damped Free Vibration
 Logarithmic Decrement
 Coulomb Damping
4. Harmonically Excited Vibration
 Forced Harmonic Vibration
 Rotating Unbalance
 Rotor Unbalance
 Whirling of Rotating Shafts
 Support Motion
 Vibration Isolation
 Energy Dissipated by Damping
 Equivalent Viscous Damping
 Structural Damping
 Sharpness of Resonance
 Vibration-Measuring Instruments
5. Transient Vibration
 Impulse Excitation
 Arbitrary Excitation
 Laplace Transform Formulation
 Pulse Excitation and Rise Time Shock Response Spectrum
 Shock Isolation
 Runge-Kutta Method
6. Systems with Two or More Degrees of Freedom
 The Normal Mode Analysis
 Initial Conditions
 Coordinate Coupling
 Forced Harmonic Vibration
 Vibration Absorber
 Vibration Damper
 Modal Analysis
7. Lagrange's Equation
 Generalized Coordinates
 Virtual Work
 Lagrange's Equation
 Kinetic Energy, Potential Energy, and Generalized Force in Terms of
Generalized Coordinates
 Assumed Mode Summation
Course Outcomes:
Students who successfully complete the course will demonstrate the following
outcomes.
1.
2.
3.
4.
Understand fundamentals of vibration (modeling and characterization).
Understand transmission and reduction of vibration.
Apply design principles to achieve vibration control.
Apply analytical and numerical methods to determine modal characteristics
and system response.
5. An understanding of interpreting the vibrational nature of systems from the
solutions to the mathematical models.
Grading:
Homework Sets:
Quiz Sets:
Mid Term Exam:
Final Exam:
10 %
20 %
30 %
40 %
Text:

W. T. Thomson et al., Theory of vibrations with applications, Prentice-Hall, 2000.
Other References:


Kelly, S. G., Fundamentals of Mechanical Vibrations, 3rd Ed., McGraw Hill,
2000.
Rao, S. S., Mechanical Vibrations, Addison-Wesley, 1995.