Theory of Vibration

(Department)  Biomedical Engineering         (Division)     
 
 (Level and Major) 
 

Course Title                Theory of Vibration
 
Number of Credits       3             Prerequisite


Course Topics:
  •          The Study of Vibrations
  •          Mathematical Modeling
  • Generalized Coordinates
  • Classification of Vibration
  • Simple Harmonic Motion & Review of Dynamics
  • Springs & Springs in Combination
  • Sources of Potential Energy
  • Viscous Damping & Energy Dissipated by Viscous Damping
  • Inertia Elements
  • External Sources
  • Free-Body Diagram Method
  • Static Deflections and Gravity
  • Small Angle or Displacement Assumption
  • Equivalent Systems Method
  • Standard Form of Differential Equation
  • Free Vibrations of an Undamped System, Underdamped, Critically Damped & Overdamped Systems
  • Coulomb Damping
  • Forced Response of a Viscously Damped System
  • Frequency-Squared Excitations
  • Response Due to Harmonic Excitation of Support
  • Vibration Isolation from Frequency-Squared Excitations
  • Practical Aspects of Vibration Isolation
  • Multifrequency Excitations
  • Impulse & Derivation of Convolution Integral
  • Response Due to a General Excitation
  • Excitations Whose Forms Change at Discrete Times
  • Transient Motion Due to Base Excitation
  • Shock Spectrum
  • Derivation of the Equations of Motion
  • Natural Frequencies and Mode Shapes
  • Free Response of Undamped Systems
  • Free Vibrations of a System with Viscous Damping
  • Principal Coordinates
  • Harmonic Response of Two Degree-Of-Freedom Systems
  • Dynamic Vibration Absorbers
  • Derivation of Differential Equations Using the Free-Body Diagram Method
  • Matrix Formulation of Differential Equations for Linear Systems
  • Stiffness Influence Coefficients
  • Normal-Mode Solution
  • Determination of Natural Frequencies and Mode Shapes
  • Normalized Mode Shapes
  • Principal Coordinates
 
Reading Resources:
 
Evaluation:

30% Final Exam
60%  Midterm Exam
10% Homework
 
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