ME 845, Vibration of Continuous Media:


Vibrations of lumped-parameters systems; free and forced vibrations of SDOF and MDOF systems, general eigenvalue problem and modal analysis. Variational approach and energy methods. Vibrations of distributed-parameters systems; strings, bars, shafts, beams, membranes and plates. Approximate methods; Rayleighâs Quotient, Rayleigh-Ritz methods, method of functions expansion, Galerkinâs and assumed mode methods.

Topical Course Outline:

  1. Introduction and Background Review: Introduction and Familiarization with Course Objectives and Topics, Reviewing Topics from Linear and Nonlinear Vibrations, and Examples.
  2. Vibration of Lumped-Parameters Systems: Free and Forced Vibrations, Damped Vibrations, General Eigenvalue Problem, Modal Analysis Software, and Illustrative examples.
  3. Variational Approach and Energy Methods: Calculus of Variations, Function and Functional, Boundary Conditions, Hamiltonâs and Extended Hamiltonâs Principles, Illustrative examples.
  4. Mechanics of Deformable Body in 3D: Introduction to Stress-Strain Relationship, Strain Comparability, Work of Deformable Body, Illustrative Problems and Example Case Studies.
  5. Transverse Vibration of Strings: Equations of Motion, Free and Forced Vibration of Strings, Boundary Conditions, Illustrative Problems and Examples.
  6. Longitudinal Vibration of Bars: Equations of Motion, Free and Forced Vibration of Bars, Orthogonality of Eigenfunctions, Boundary Conditions, and Example Case Studies.
  7. Torsional Vibration of Shafts: Equations of Motion, Free and Forced Vibration of Shafts, Uniform and Non-uniform Shafts, Example Case Studies and Problems.
  8. Transverse Vibration of Beams: Euler-Bernoulli Theory (Thin Beams), Mode Shapes, Boundary Conditions, Free and Forced Vibrations, Timoshenko (Thick) Beams.
  9. Approximate Analytical Methods: Rayleighâs Quotient, Rayleighâs and Rayleigh-Ritz Methods, Assumed Mode Methods and Example Case Studies and Problems.
  10. Vibration of Membranes: Free and Forced Vibrations of Rectangular Membranes, Circular Membranes, Example Case Studies and Problems.
  11. Transverse Vibration of Plates: Classical Plate Theory, Free and Forced Vibrations of Rectangular Plates, Circular Plates, Thin and Thick Plates, Example Case Studies.

[Sample Project]

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