## MECHANICAL VIBRATIONS

Teachers:
Credits:
6
Site:
PARMA
Year of erogation:
2021/2022
Unit Coordinator:
Disciplinary Sector:
Applied Mechanics for Machinery
Semester:
Second semester
Year of study:
1
Language of instruction:

Italian

### 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.

### Prerequisites

Mechanics of machines

### Course contents summary

Free and forced vibrations of systems with a degree of freedom. Excitation of the base. Rotating machines. Jeffcott rotor.
Dynamic vibration absorber.
Vibrations of system parameters concentrated at many degrees of freedom. Writing the 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 frequencies and natural modes. Normalization, orthogonality, expansion theorem. Modal analysis; solution of the free and forced problem. Proportional damping and modal damping. Non-proportional damping: state vector. Complex ways. Technical applications and exercises.

### Course contents

Vibrations of single degree of freedom systems.
Vibration isolation.
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.

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.

### Teaching methods

Lectures and practical exercising

Written exam

None