Vibrations of strings and bars: equations of motion, modal analysis, approximate methods, initial value problem, forced vibrations, damped vibrations.
Wave propagation and scattering: d'Alembert solution, harmonic waves, scattering, applications of wave solution.
Vibrations of beams: equation of motion, modal analysis, approximate methods, initial value problem, forced vibrations, special problems, wave propagation.
Vibrations of membranes: equations of motion, modal analysis, approximate methods.
Vibrations of plates: equations of motion, modal analysis, approximate methods.
Course modules:
- Vibrations of Strings and Bars
- Wave Propagation and Scattering
- Vibrations of Beams
- Vibrations of Membranes
- Vibrations of Plates
Course topics:
- Transverse Vibrations of Strings
- Axial and Torsional Vibrations of Bars
- Variational Formulation
- Modal Analysis
- Properties of Eigenvalue Problem
- Modal Analysis: Approximate Methods
- Initial Value Problem
- Forced Vibration Analysis
- Damping in Structures
- Axially Translating Strings
- d’ Alembert’s Solution
- Harmonic Waves and Energetics of Wave Motion
- Scattering of Waves
- Applications of Wave Solution
- Beam Models
- Modal Analysis of Beams
- Application of Modal Solution
- Approximate Methods
- Topics in Beam Vibrations
- Wave Propagation in Beams
- Dynamics of Curved Beams
- Vibrations of Rings and Arches
- Dynamics of Membranes
- Vibrations of Rectangular Membrane
- Vibrations of Circular Membrane
- Special Problems in Membrane Vibrations
- Dynamics of Plates
- Vibrations of Rectangular Plates
- Vibrations of Circular Plates
- Special Problems in Plate Vibrations
