Learning outcomes of the course unit
Knowledge and ability to understand: 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 of the engineering analysis methods.
Skills: the student will have the necessary competence to deal with a problem of vibration damping and the experimental analysis of the same.
Making judgments: the student will have the ability to undertake an experimental measurement and analysis campaign where necessary.
Communication skills: knowing how to interact with technicians and engineers in the field of mechanical vibrations, knowing how to interpret complex monitoring graphs.
Learning skills: the greatest skills will be those related to the analysis of a practical problem.
Mechanics of machines
Course contents summary
Free and forced vibrations of systems with a single degree of freedom. Excitation of the base. Rotating machines. Jeffcott rotor.
Dynamic vibration absorber.
Vibrations of system with multi degrees of freedom. Equations of motion in matrix form. Free vibrations of conservative systems; reduction of the problem to the eigenvalues in standard form. Definite and semidefinite matrices. Properties of natural frequencies and natural modes. Normalization, orthogonality, expansion theorem. Modal analysis; solution of the free and forced vibration problem. Proportional damping and modal damping. Non-proportional damping: state vector. Complex modes. Technical applications and exercises.
Vibrations of single degree of freedom systems.
Vibrations of systems with concentrated parameters with multi 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.
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