
Course unit
MECHANICAL VIBRATIONS
IN05105686, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
INGIND/13 
Applied Mechanics for Machinery 
9.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
72 
153.0 
No turn 
Prerequisites:

Calculus I
Physics
Fundamentals of Linear Algebra and Geometry
Numerical analysis
Calculus II
Mechanics of machines*
Mechanics of Solids
* Only for students of Mechanical and Aerospace Engineering 
Target skills and knowledge:

Provide students with the theoretical and computational tools needed to solve vibration problems in mechanical systems.
Provide students with the basics of the techniques of identification and monitoring of mechanical systems. 
Examination methods:

The exam focuses on the entire program and consists mainly of a written test, which includes both numerical exercises and theory questions.
Approximately there are 23 exercise questions and 23 theory questions. Each question is associated with a score that appears in the exam track, so that the student can have an indication of the score he can reach.
The total duration of the written test is at least 2 hours.
The oral exam is only foreseen in three cases
a) If the result in the written test is 16 or 17/30. In this case, the student is given the opportunity to achieve sufficiency by an oral exam on the date indicated by the teacher.
b) If the student wishes to improve any sufficient mark obtained in the written test, even in this case the oral test must be sustained in the same appeal on the date indicated by the teacher.
c) If the student obtained a very negative mark (<10/30) in a previous written test, even in this case the oral test must be sustained in the same appeal on the date indicated by the teacher 
Assessment criteria:

To pass the exam the student must demonstrate the ability of modeling vibrating systems with concentrated and distributed parameters and the ability of understanding the physical phenomena that govern the vibrations of mechanical systems.
In detail, numerical exercises are evaluated positively if the calculation method adopted is correct and the final result is correct.
The answers to the theory questions are evaluated positively, if the physical / mathematical treatment is correct, the exposure is clear and the treatment is complete. 
Course unit contents:

Frequency analysis of vibrations.
Linear systems with one degree of freedom: Free and forced vibrations in the presence of harmonic, transient, periodic and random forces.
Linear systems with concentrated parameters and n degrees of freedom: equations of motion in matrix form, free vibrations (natural frequencies and mode shapes) and forced vibration.
Modal approach and experimental modal analysis.
Continuous systems: vibrations of beams and ropes, analytical solutions and approximate methods.
Introduction to numerical methods for the study of the vibrations.*
Selfexcited vibrations and dynamic stability.*
Applications:
Vibration isolation.
Dynamic absorbers.*
Rotor dynamics.*
Elements of Sound and Vibration.*
Notes on active vibration control.*
Outline of energy harvesting techniques.
*Only for students of Mechanical and Aerospace Engineering 
Planned learning activities and teaching methods:

Lectures of theory and exercises.
Laboratory on experimental modal analysis. 
Additional notes about suggested reading:

Lecture notes in Moodle DII 
Textbooks (and optional supplementary readings) 

S. Bergamaschi V. Cossalter, Esercizi di Meccanica delle Vibrazioni. Padova: Cortina, 1983.

D. J. Inman, Engineering Vibration  second edition. Upper Saddle River NJ: Prentice Hall, 2000.

D Thorby, Structural Dynamics and Vibration in Pratice. Amsterdam: Elsevier, 2008.

R. Basso, Elementi di Meccanica delle Vibrazioni II Edizione. Padova: Ed. Librerie Progetto, 2014.

Innovative teaching methods: Teaching and learning strategies
 Laboratory
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 ModalView
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