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Mechanical Vibration


The main objective of the course is to obtain the dynamic response of single and multiple degree-of-freedom (DOF) systems.

  1. Math preliminaries
  2. Developing equations of motion
  3. Single DOF Vibrations
  4. Multiple DOF Vibrations
  5. Vibration absorbers
  6. Natural frequencies and Mode shapes n
  7. Mode shapes normalization and modal analysis
  8. Solving for discrete system vibration




  • Mathematical preliminaries
  • Oscillatory motion
  • Industrial applications

Single degree of freedom (SDoF) systems

  • Derive the equations of motion for SDof system
  • Newton’s equation of motion
  • Work and energy equation
  • Free vibration of undamped SDoF systems
  • Forced Vibration of undamped SDoF systems

Types of damping in structures

  • Viscous damping
  • Coulomb damping
  • Structural damping

Single degree of freedom (SDoF) systems

  • Free vibration of damped SDoF systems
  • Forced vibration of damped SDoF systems
  • Vibration isolation
  • Transmissibility
  • Transient analysis of SDoF systems
  • Equation of motion

Multi degrees of freedom (MDoF) systems

  • Free vibration of undamped MDoF systems
  • Natural frequencies
  • Mode shapes
  • Time response of MDoF systems
  • Forced response of MDoF systems
  • Base motion
  • Vibration absorbers
  • Lagrange’s method
  • Modal superposition

Approximation techniques in estimation of natural frequencies and mode shapes

  • Dunkerely’s method
  • Rayliegh’s method
  • Direct iteration method


Engineering Mathematics

Differential Equations

Grading Policy: 

40% Midterm Exam

50% Final Exam

10% Homeworks + Quiz

Teacher Assistants: 

Miss S Rashidi, PhD student


Saturday 9:30 -11:00

Monday 9:30 -11:00


Class 3, Mechanical Engineering Department

Spring 2020

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