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Subject: MECHANICAL VIBRATIONS (A.A. 2022/2023)


Course year 1
To be chosen by the student (lesson)
  • TAF: Optional subjects SSD: ING-IND/13 CFU: 6
Teachers: Matteo STROZZI
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Aula virtuale su Microsoft Teams

Exam type oral
Evaluation final vote
Teaching language Italiano
Contents download pdf download




The Course provides fundamental concepts and methods for dealing with problems of practical interest related to mechanics applied to machines. The first part of the Course deals with the basic notions of dynamics of mechanical systems. In the second part of the Course, fundamental topics of vibration mechanics are illustrated. The theoretical topics developed in the first and second part of the Course are accompanied by numerical exercises. At the end of the Course, the Student should be able to independently tackle and solve complex machine dynamics problems. For a more complete understanding of the training objectives, please refer to the reading of the learning outcomes expected following the carrying out of this Course.

Admission requirements

Preliminary knowledge of mathematical analysis and physics of bodies, with specific reference to derivatives, cardinal equations of dynamics and friction laws.

Course contents

Dynamics of mechanical systems: dynamic equilibrium, Newton-Euler equations, D'Alembert's principle, energy balance, mechanical energy conservation theorem, power balance equation, efficiency of machines arranged in series and in parallel, power flow in transmissions, retrograde power flow (2 CFU – 18 hours).
Exercises in dynamics of mechanical systems (1 CFU – 9 hours).
Mechanical vibrations: single degree of freedom systems, free vibrations, harmonic motion, natural pulsation, undamped harmonic oscillator, dissipation, damped harmonic oscillator, critical damping, damping ratio, forced vibrations, sinusoidal forcing (2 CFU – 18 hours).
Exercises in mechanical vibrations (1 CFU – 9 hours).

Teaching methods

The Course includes theoretical lessons integrated with numerical exercises. The Course takes place face to face and is delivered in Italian. Attendance to lectures and exercises is optional. The Professor receives the Students at the end of each lesson and by appointment for clarification and personalised tutoring.

Assessment methods

The Exam, set at the end of the Course, consists of an oral test lasting about 45 minutes which covers all the topics treated during the Course. During the Exam, it will be required to carry out a numerical exercise related to the part of dynamics of mechanical systems or to the part of mechanical vibrations. The use of any material is not allowed during the test. The outcome of the Exam is communicated to the Candidate immediately at the end of the test itself. The Exam evaluation indicators are: - Ability to use knowledge (20%); - Ability to connect knowledge (20%); - Autonomy of judgment and execution (30%); - Mastery of scientific language (10%); - Ability to interpret the results obtained (20%). It is emphasized that the rules described above are applied to Exams as carried out in person. Times and methods may vary as a result of contingent situations that force to provide online Exams.

Learning outcomes

Knowledge and understanding
At the end of the Course the Student will have acquired the ability to understand and analyze fundamental kinematic relationships and characteristic dynamic equations of a mechanical system.
Applied knowledge and understanding
At the end of the Course the Student will have acquired the ability to solve both exercises and problems of machine dynamics by applying the acquired knowledge.
Autonomy of judgment
At the end of the Course the Student will have developed the ability to independently choose the method of analysis and resolution of machine dynamics problems.
Communication skills
At the end of the Course the Student will have developed the ability to explain in a clear, rigorous and concise way all the concepts dealt with during this training course.
Ability to learn
At the end of the Course the Student will have developed the ability to investigate in an autonomous and critical way some relevant collateral aspects of the proposed topics.


Testo di riferimento:
Dispense utilizzate dal Docente nel corso delle lezioni frontali e delle esercitazioni numeriche (rese disponibili sulla pagina del portale Moodle-Teams relativa all’Insegnamento di Meccanica delle Vibrazioni).
Testi di consultazione (materiali didattici aggiuntivi facoltativi, utili per eventuali approfondimenti):
1) Massimo Callegari, Pietro Fanghella, Francesco Pellicano, “Meccanica applicata alle macchine” (II Edizione), Città Studi Edizioni, Torino, 2017.
2) Ettore Funaioli, Alberto Maggiore, Umberto Meneghetti, “Lezioni di Meccanica applicata alle macchine. Prima parte: Fondamenti di Meccanica delle macchine”, Pàtron Editore, Bologna, 2005.