The aim of the subject is to provide the students with the basic knowledge needed for the structural dynamic analysis and the dynamic design of machines. Computational methods, and more in detail the numerical methods more common in the design practice will be intorduced. Theoretical aspects needed to obtain the deeper knowledge of the subject required to operate in the present innovative industrial environment are not neglected. The last part of the course is dedicated to the study of the dynamic analysis of rotating machinery, reciprocating engines, dynamic behaviour of electromagnetic controlled systems.

Students are required to learn the basics of the dynamics of vibration and of the analytical and numerical methods commonly used for machine design. Students must learn how to apply this knowledge to the actual dynamic study of machines and their elements, using them in a machine design context. The ability of interpreting in a critical way the results obtained, in particular through numerical methods, is also required. Student must also learn to produce technical documentation of the work done.

A good knowledge of the basic concepts of applied mechanics and of the methods of static stress analysis is required. A basic ability in using the relevant computer codes is also required, although no previous experience with specific numerical tools is needed.

Here below is reported the Course Syllabus. Introduction to the course (2 hours). Mechanical design, static and dynamic stress analysis. Classical and numerical approach. Automatic computation in design. Numerical simulation. Computer aided engineering (CAE). Part 1 (9 hours of theory lectures, 6 hours of classroom exercise lectures). Overview on the dynamic analysis of linear systems. Discrete linear systems: equations of motion in the configuration space; equations in Lagrange form. State space. Block diagrams. Free behaviour of single and multi-d.o.f. systems. Modal uncoupling; modal participation factors. Forced response to harmonic excitation. Viscous, Viscoelastic, Electromagnetic, Structural damping. Systems with frequency dependent parameters. Forced response to non harmonic excitation; short account of random vibrations. Exercises addressing specific issues on the subject. Assignment of a project work dedicated to the fatigue design of mechanical parts in a mechanical subsystem affected by the vibration motion of the same subsystem. Part 2 (18 hours of theory lectures, 9 hours of classroom exercise lectures, 3 hours of laboratory experience). Numerical methods and discretization techniques. Lumped parameter methods, Finite element method in dynamics. Reduction techniques. Time domain and frequency domain solutions, numerical simulation. Specific exercises addressing the issues on the subject. Assignment of a project work dedicated to the design of a dynamic damper of a vibrating structure. Laboratory experience on the identification of the parameters of a vibrating structure. Part 3 (15 hours of lectures, 9 hours of exercises, 3 hours of laboratory exercises). Dynamics of rotating machines. Vibrations of rotors: Campbell diagram, critical speeds and fields of instability. Undamped and damped Jeffcott rotor. Rotor with 4 degrees of freedom, gyroscopic effect. Rotors with many degrees of freedom. Nonisotropic machines. Rotors on rolling, hydrodynamic and magnetic bearings. Balancing of rotors. Specific exercises addressing the issues on the subject. Assignment of a project work dedicated to the design of support stiffness and damping of a rotating machinery modelled using a FE approach. Laboratory experience on the test of a rotor affected by rotating and non - rotating damping. Part 4 (9 hours of lectures, 3 hours of exercises). Dynamics of reciprocating machines: Vibration of reciprocating engines and compressors, classical frequency domain and numerical time domain methods, equivalent system for torsional vibration, damping system for torsional vibrations of crankshafts (dynamic dampers). Specific exercises addressing the issues on the subject. Part 5: An overview on nonlinear vibration (3 hours): approximated methods, Duffing equation, jump phenomenon. Numerical simulation, basic concepts on chaotic vibration. Specific exercises addressing the issues on the subject. Part 6: Short Outline in Controlled Electromagnetic and Electromechanical Systems (7,5 hours of lectures, 3 hours of laboratory exercises): general considerations, open-loop control, closed-loop control, basic control laws, design of controlled systems. Specific exercises addressing the issues on the subject. Laboratory experience on the tuning of the control parameters of active magnetic bearings.

The course is based on a total of 64 hours of lectures plus 36 hours of classroom and laboratory exercises. Lectures will be held with the support of the blackboard, slides and notes. The exercise classes will deal with a number of exercises aimed to a better understanding of the subjects dealt with during theoretical classes and in a number of projects, the students will prepare in team. The technical reports on the projects will deal specific problems of dynamic structural analysis related to specific machine elements. Some of these exercises will be performed in a computer lab, using specific numerical tools, while others will be performed in the experimental lab. The documentation used during the theoretical classes and the exercises will be made available to the students through the website.

The textbook for the course is: Genta G., Vibration Dynamics and Control, Springer, New York, 2009, ISBN 978 0 387 79579 9 or, alternatively, , Genta G., Vibrazioni delle strutture e delle macchine, Levrotto e Bella, Torino, 1996. Other textbooks that can be used for specific parts of the course are Genta G, Vibration of structures and machines, III ed., Springer, New York, 1998, ISBN: 0 387 98506 9 and Genta G., Dynamics of Rotating Systems, Springer, New York, 2005 ISBN: 0-387-20936-0. Additional material for exercises will be supplied through the course website

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa; Elaborato scritto prodotto in gruppo;

Exam: Written test; Optional oral exam; Group essay;

... The assessment will include a written test followed by an oral examination. To be allowed to the oral exam the student must have passed the written test with at least 18/30 rating. Written test The written test will consist of 30 multiple choice tests (correct answer: 1 point; no answer 0 points; wrong answer: -0.5 points) plus 8 exercises (correct answer: 2 points; no or wrong answer: 0 points) to be answered in 2 hours. At least 15 tests and 4 exercises must be answered. No books, notes or other material are allowed at the written test. Use of a cell phone or other communication device will cause immediate expulsion. Oral exam If the rating of the written test is between 18/30 and 23/30 (included) the oral exam may be substituted by a discussion on the project report. This can produce an increase or a decrease of the rating up to 2 points, depending on how the project are made. A complete failure of answering questions about the project report causes a failure of the exam. If the student aims to obtain more than 23/30 or he has answered less than 15 tests and 4 exercises the oral exam is compulsory. If the rating of the written test is in between 24/30 and 30/30 the oral exam is compulsory. The oral exam includes at any rate a discussion on the project reports. A failure of answering the questions on the project reports or the presentation of incomplete projects causes a complete failure of the exam. It is recommended to book the exam only when there is a reasonable expectation to actually giving the exam. The exam rules stated for the past years will apply to students who have followed the course in the past.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

Modalità di esame: Prova orale facoltativa; Elaborato scritto prodotto in gruppo; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;

The assessment will include a written test followed by an oral examination. To be allowed to the oral exam the student must have passed the written test with at least 18/30 rating. Written test The written test will consist of 30 multiple choice tests (correct answer: 1 point; no answer 0 points; wrong answer: -0.5 points) plus 8 exercises (correct answer: 2 points; no or wrong answer: 0 points) to be answered in 2 hours. At least 15 tests and 4 exercises must be answered correctly to pass to the oral exam. The written exam is valid only within the current exam session. No books, notes or other material are allowed at the written test. Use of a cell phone or other communication device will cause immediate expulsion. Oral exam If the rating of the written test is between 18/30 and 23/30 (included) the oral exam may be substituted by a discussion on the project report. This can produce an increase or a decrease of the rating up to 2 points, depending on how the project are made. A complete failure of answering questions about the project report causes a failure of the exam. If the student aims to obtain more than 23/30 or he has answered less than 15 tests and 4 exercises the oral exam is compulsory. If the rating of the written test is in between 24/30 and 30/30 the oral exam is compulsory. The oral exam includes at any rate a discussion on the project reports. A failure of answering the questions on the project reports or the presentation of incomplete projects causes a complete failure of the exam. It is recommended to book the exam only when there is a reasonable expectation to actually giving the exam. The exam rules stated for the past years will apply to students who have followed the course in the past.

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo; Elaborato progettuale in gruppo;

The assessment will include a written test followed by an oral examination. To be allowed to the oral exam the student must have passed the written test with at least 18/30 rating. Written test The written test will consist of 30 multiple choice tests (correct answer: 1 point; no answer 0 points; wrong answer: -0.5 points) plus 8 exercises (correct answer: 2 points; no or wrong answer: 0 points) to be answered in 2 hours. At least 15 tests and 4 exercises must be answered correctly to pass to the oral exam. The written exam is valid only within the current exam session. No books, notes or other material are allowed at the written test. Use of a cell phone or other communication device will cause immediate expulsion. Oral exam If the rating of the written test is between 18/30 and 23/30 (included) the oral exam may be substituted by a discussion on the project report. This can produce an increase or a decrease of the rating up to 2 points, depending on how the project are made. A complete failure of answering questions about the project report causes a failure of the exam. If the student aims to obtain more than 23/30 or he has answered less than 15 tests and 4 exercises the oral exam is compulsory. If the rating of the written test is in between 24/30 and 30/30 the oral exam is compulsory. The oral exam includes at any rate a discussion on the project reports. A failure of answering the questions on the project reports or the presentation of incomplete projects causes a complete failure of the exam. It is recommended to book the exam only when there is a reasonable expectation to actually giving the exam. The exam rules stated for the past years will apply to students who have followed the course in the past.