Learning outcomes of the course unit
Knowledge and understanding: At the end of the course the student will have the knowledge of the main problems related to mechanical vibrations and their isolation, as well as the understanding of the mechanisms that generate these vibrations and the methods of engineering analysis.
Skills: The student will have the necessary expertise to deal with a problem of vibrations isolation and experimental analysis.
Making judgments: the student will possess the ability to undertake, where necessary, an experimental campaign of measurement and analysis.
Communication skills: students will be able to interact with engineers and scientists in the field of mechanical vibration, and will have the know how to interpret graphs of even complex vibration monitoring.
Learning skills: capacity will be those related to the analysis of a practical problem.
Course contents summary
The course provides students with the necessary knowledge related to the diagnostics of machines, the analysis of signal, the experimental measurement of the vibration and the study of vibrations of lumped parameter systems with many degrees of freedom.
Vibrations of single degree of freedom systems.
Vibrations of systems with concentrated parameters with many degrees of freedom.
Writing of the equations of motion in matrix form.
Free vibration of conservative systems, reduction of the eigenvalue problem in standard form. Definite matrices and semidefinite.
Properties of frequencies and natural modal forms.
Normalization, orthogonality, expansion theorem.
Linear transformations of coordinates and modal coordinates; forced solution of the problem. Proportional damping and modal damping.
Non-proportional damping: method of the transition matrix. Complex modes.
Practical examples of experimental modal analysis in laboratory.
Technical applications and exercises.
Vibration of continuous systems: local and global discretization methods (Rayleigh-Ritz, Galerkin FEM), vibration of beams and thin-walled structures. Effects of added mass.
Applications to real problems.
Experimental exercises in laboratory.
S.S. RAO, 2004, Mechanical Vibrations, 4a edizione, Pearson.
L. MEIROVITCH, 1986, Elements of Vibration Analysis, 2nd edition, McGraw Hill.
D. J. INMAN, 1989, Vibration with control measurement and stability. Prentice-Hall.
Lectures and practical exercising
Assessment methods and criteria