Dynamics of elastic systems. [ LMECA2410 ]

> https://icampus.uclouvain.be/claroline/course/index.php?cid=LMECA2410

• Analytical mechanics
• Applied mathematics.

• 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.

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.

Variational approach : approximative methods in modal analysis (Rayleigh, Rayleigh-Ritz).

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.

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