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Academic year
Didactic period
Secondo Semestre

Training objectives

The course provides the basic knowledge and methods in order to solve technical problems concerning the dynamic and vibration behaviour of machinery and mechanical systems. In particular, the course deals with the criteria and methods for the vibration modelling of the mechanical systems, as well as the analytical, numerical (Finite Element Method) and experimental methods for vibration analysis.
The course takes into account both the theoretical and the applicative point of view and includes numerical exercises.


Courses of Mathematics, Physics, Theoretical Mechanics and Mechanics of Machines.

Course programme

Single degree-of-freedom systems. Damping. Free and forced vibrations. Rayleigh''s method. Vibration isolation.
Two and multi degree-of-freedom systems. Eigenvalues and eigenvectors. Modal approach. Free and forced vibrations. Modelling mechanical systems by lumped parameter models.
Mono-dimensional continuous systems.
Finite element method.
Balancing of rotating machines.
Experimental methods. Instrumentation for vibration measurement. Experimental modal analysi

Didactic methods

Theoretical and applicative lectures, numerical exercises.

Learning assessment procedures

Oral examination. The examination consists in 3 questions. The final remarks is the mean of the 3 marks relative to the 3 questions. The oral examination accounts also the exercises to be carried out and to be presented during the examination.

Reference texts

• Meneghetti, Maggiore, Funaioli, Lezioni di meccanica applicata alle macchine. Vol. 3: Dinamica e vibrazioni delle macchine, Pàtron, 2010.

• Funaioli, Maggiore, Meneghetti, Meccanica applicata alle macchine, Vol. II (vecchia edizione), Ed. Patron, Bologna.

• E. Funaioli, A. Maggiore, U. Meneghetti, Lezioni di meccanica applicata alle macchine. Vol. 1: Fondamenti di Meccanica delle Macchine, Pàtron, 2005.
• Rao, Mechanical Vibrations, 3rd ed., New York, Addison-Wesley, 1995.
• Thomson W., Theory of Vibration with Applications, 4th edition, New York, Chapman & Hall, 1993.