Aims

Introduceh students to the specific techniques of mechanical vibrations, via simplified models.
Apply these techniques to important basic applications : suspensions, vibration isolation, measurement devices, vehicles, structures, …

Main themes

- Mathematical modelling of discrete and continuous systems, degrees of freedom, (non)linearity, stiffness, damping.
- Eigenvalue problems for discrete and continuous linear systems
- Forced response : frequency response functions, resonance, antiresonance.
- Specific investigation of vibration isolation and measurement devices.

Content and teaching methods

The mathematical models studied follow a gradually increasing complexification, both as regards number of degrees of freedom and physical terms involved. The course is subdivided into three main parts :

- Linear 1-degree-of-freedom systems : undamped free vibrations, harmonic oscillator, damped vibrations, forced vibrations, applications, vibration transmission to foundations, vibration isolation, measurement devices.
- Linear N-degree-of-freedom systems : undamped free vibrations, eigenvalue problem, normal modes of vibration, modal analysis, orthogonality, damped free vibrations, forced vibrations, anti-resonance, vibration absorbers, modal truncation, approximative methods in modal analysis (Rayleigh, Rayleigh-Ritz, …)
- Continuous systems : eigenvalue problem, boundary conditions, free vibrations of strings, shafts, beams, membranes, plates. Variational approach : approximative methods in modal analysis (Rayleigh, Rayleigh-Ritz, …).

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prequisites :
Analytical mechanics, applied mathematics.

References :
Meirovitch Analytical Methods in Vibrations
Craig, R.R. Structural Dynamics
Dimaragonas Vibration for Engineers
Geradin, Rixen Vibration Theory