The course provide the students with the basic concepts and the methods to analysze vibrating systems, both from the numerical and the experimenal point ov view.

The course promotes the develpmpment of the knowledge and the understaning of the technical problems relatet to the mechanical vibration; develop the autonomy in judgment and learning and increase the communication skills.

suggested: Physiscs 1, Mathemetical Analysis 1, Analystical mechanics, Applied Mechanics.

Single degrees of freedom systems

Mathematical models
Lumped parameters systems - Newton laws
Lumped parameters systems - Virtual Work Principle
Distributed parameters systems - Virtual Work Principle
Modal Approach

Free vibrations
Undamped system
Damped system with Viscous Colombian Hysteric Damping

Forced Vibration
Harmonic Excitation
Undamped system
Damped system
Base excitation
Unbalance Excitation
Vibration sensors
Non-Harmonic excitation
Step, impulse, generic excitation
Duhamel integral
Frequency analysis

Signal Processing
Signal Classification
Signal Transform
Laplace and Fourier Transform
Shannon, Nyqvist Perceval Theorem
Aliasing, Leakage
A/D D/A conversion
Signal analysis functions
In time and frequency domain
Auto power cross power Cohernce, frequency and impulse response functions
H estimators
System excitation


Multiple degrees of freedom systems

Mathematical models
Lumped parameters systems - Newton laws
Lumped parameters systems - Lagrange approach
Modal Approach
Coordinates coupling

Free vibrations
Undamped system
Damped system with Viscous Colombian Hysteric Damping

Forced Vibration
Harmonic Excitation
Undamped system
Damped system
Resonance, antiresonance, pseudo resonance

Special systems
Dynamic absorbers
Torsional damper

Modal analysis
response models
Impulse and frequency response function
Eigenvalues problems
Modal shapes
Scaling of modal shapes
Residuals and modal partecipazione factors
Model Identification
Use of modal parameters

Continuos systems
hints

Non linear systems
hints

Active vibration and noise control
hints

Vibration effects on humans
hints

Noise and Vibration Analysis - Anders Brandt - Wiley
Structural
Dynamics - Roy Craig - Wiley
Modal Analysi Theory and testing - Ward Heylen et al - KUL
Analog and digital signal processing - Ashok Ambradar -
Vibration based condition monitoring - Robert Randall - Wiley

Single degrees of freedom systems

Mathematical models
Lumped parameters systems - Newton laws
Lumped parameters systems - Virtual Work Principle
Distributed parameters systems - Virtual Work Principle
Modal Approach

Free vibrations
Undamped system
Damped system with Viscous Colombian Hysteric Damping

Forced Vibration
Harmonic Excitation
Undamped system
Damped system
Base excitation
Unbalance Excitation
Vibration sensors
Non-Harmonic excitation
Step, impulse, generic excitation
Duhamel integral
Frequency analysis

Signal Processing
Signal Classification
Signal Transform
Laplace and Fourier Transform
Shannon, Nyqvist Perceval Theorem
Aliasing, Leakage
A/D D/A conversion
Signal analysis functions
In time and frequency domain
Auto power cross power Cohernce, frequency and impulse response functions
H estimators
System excitation


Multiple degrees of freedom systems

Mathematical models
Lumped parameters systems - Newton laws
Lumped parameters systems - Lagrange approach
Modal Approach
Coordinates coupling

Free vibrations
Undamped system
Damped system with Viscous Colombian Hysteric Damping

Forced Vibration
Harmonic Excitation
Undamped system
Damped system
Resonance, antiresonance, pseudo resonance

Special systems
Dynamic absorbers
Torsional damper

Modal analysis
response models
Impulse and frequency response function
Eigenvalues problems
Modal shapes
Scaling of modal shapes
Residuals and modal partecipazione factors
Model Identification
Use of modal parameters

Continuos systems
hints

Non linear systems
hints

Active vibration and noise control
hints

Vibration effects on humans
hints

Class lesson, laboratory activities, homework activities

The extensive use of Matlab, Ansys Workbench and Dewesoft are strongly suggested to consolidate the theoretical aspects presented during the course.

In case new safety protocols linked to the COVID19 emergency will arise, communication will be shared trough the Department
and courses websites

Oral examination, subject to written dissertation.
The exam will evaluate the capability of the student to apply what has been presented during the course, to real case scenarios' problems.

To take the exam it is necessary to submit a written paper previously agreed with the professor at the signup time.
(topics chosen by the student on numerical simulations, experimental tests, correlations between numerical models and measures ..)

The exam consists of an exercise, discussion of the paper and questions on the course's theory.

The exercise can have three outcomes:
Correct execution, correct numerical processing> the candidate proceeds in the exam being able to reach the mark of 30/30 and L
Correct execution, wrong numerical processing> the candidate proceeds in the exam being able to reach a maximum grade of 27/30
Wrong numerical processing> the candidate does not proceed with the exam and can resume at the next session

The paper is worth a maximum of 5 points,
2.5 points for the method,
1.5 points for the results obtained,
1 point for the quality of the bibliographic research.

The theory questions are worth a maximum of 7 points
2 points for understanding the questions,
4 points for knowledge of the subject and the ability to apply what has been learned,
1 point for communication skills.

Honors are awarded when the candidate demonstrates that he has mastered the subject and he is able to explain it.

Students can withdraw from the exam, not reject the evaluation.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)