Advanced Mechanical Vibrations
Advanced mechanical vibrations support covering discrete and continuous systems, modal analysis, damping, and approximate methods.

Course Content
Weekly contentThis module covers Introduction to advanced mechanical vibrations: influence coefficients, stiffness, and mass matrices through conceptual framing and problem solving.
This module covers Introduction to advanced mechanical vibrations: coordinate transformations and constraints through conceptual framing and problem solving.
This module covers Natural modes and free vibration in discrete systems: eigenvalue problem and modes through conceptual framing and problem solving.
This module covers Natural modes and free vibration in discrete systems: semidefinite systems through conceptual framing and problem solving.
This module covers Natural modes and free vibration in discrete systems: semidefinite system applications through conceptual framing and problem solving.
This module covers Natural modes and free vibration in discrete systems: Rayleigh quotient and Dunkerley formula through conceptual framing and problem solving.
This module covers Free vibration of continuous systems: boundary-value and eigenvalue problems through conceptual framing and problem solving.
This module covers Continuous-system vibrations: strings, longitudinal bar vibration, and torsional shaft vibration with Newton method through conceptual framing and problem solving.
This module covers Continuous-system vibrations: equations of motion with Hamilton principle through conceptual framing and problem solving.
This module covers Bending vibrations of beams with Hamilton principle through conceptual framing and problem solving.
This module covers Bending vibrations of beams: advanced applications through conceptual framing and problem solving.
This module covers Approximate methods for natural modes and frequencies through conceptual framing and problem solving.
This module covers Damped vibration of discrete systems through conceptual framing and problem solving.
This module covers Damped vibration of continuous systems through conceptual framing and problem solving.
Targeted Learning Outcomes
- Model discrete and continuous vibration systems with appropriate coordinates
- Apply eigenvalue, modal analysis, and Rayleigh-Ritz methods
- Use Hamilton principle with clearer physical interpretation
Recommended Prerequisites
- Linear algebra, especially eigenvalues and eigenvectors
- Differential equations and basic vibrations
- Dynamics or basic mechanics