• 052840 - FUNDAMENTALS OF VIBRATION ANALYSIS

This module deals with mechanical vibrations of lumped parameter systems, considering both theory and applications. First, it covers free and forced vibration of linear single-degree-of-freedom systems. It then extends this analysis to two- and multi-degree-of-freedom linear systems. Particular attention is given to frequency domain models and to the principal coordinate formulation based on modal superposition approach.

The course will provide students with:

• a knowledge of different modelling approaches for the analysis of the vibrations of lumped-parameter system (DD1),
• the ability to numerically analyse (with the use of computer programs) the behaviour of simple multi-degree-of-freedom linear systems (DD2/DD3).
• an opportunity to develop skills in summarizing and presenting results of computer laboratory activities (DD4)

Vibration of single d.o.f. linear systems:

• Derivation of the equation of motion of single degree of freedom linear systems through dynamic equilibrium equations and Lagrange equations
• Free vibration: response of the system to initial conditions, definition of natural frequency and damping ratio
• Forced vibration: response to constant, harmonic and periodic forces, frequency response function

Vibration of single d.o.f. non-linear systems:

• Analysis of static equilibrium positions
• Linearization of the equation of motion about a static equilibrium position: effect of constant forces

Vibration of two- and multi-d.o.f. linear systems:

• Definition of the equations of motion of the system through Lagrange equations (scalar and matrix formulations)
• Vibration modes: definition of natural frequencies, damping ratios and mode shapes.
• Analysis of free and forced vibrations
• State space and frequency response models

Modal superposition approach for multi d.o.f. systems

• Formulation of the equations of motion in terms of principal coordinates
• Modal parameters of the system
• Analysis of free and forced vibration in principal coordinates
• Representation of the frequency response functions in terms of modal coordinates

Basic knoledge of the Kinematics and Dynamics of ridid-body systems in plane motion.

During exercise classes, students are assigned case studies on the modelling and numerical analisys of vibrating systems. Students are requested to prepare short reports on the assignments to be delivered at the final exam. The final exam consists in an oral discussion of the different theoretical topics of the course starting from a critical review of the results presented in the reports.