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 particularly the numerical methods more common in the design practice. 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 subject is dedicated to the study of the dynamic analysis of rotating machinery, reciprocating engines, dynamic behaviour of 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 the Subject Syllabus is reported. Introduction to the subject (1 hours): Mechanical design, static and dynamic stress analysis. Classical and numerical approach. Automatic computation in design. Numerical simulation. Computer aided engineering (CAE). Part 1: an overview on the dynamic analysis of linear systems (14 hours): Discrete linear systems: equations of motion in the configuration space; equations in Lagrange form. State space. Block diagrams. Free behavior 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. General considerations on continuous systems, Beams and bars. Euler-Bernoulli beams. Modes of continuous systems. Timoshenko beams. Effect of axial forces on flexural behaviour of beams; vibrating strings. Part 2: numerical methods and discretization techniques (16 hours): Discretization methods. Assumed modes and lumped parameter methods. Finite element method in dynamics. Static, dynamic and Guyan reduction. Time domain and frequency domain solutions, numerical simulation. Part 3: Dynamics of rotating machines (14 hours): 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. Part 4: Dynamics of reciprocating machines (10 hours): Vibration of reciprocating engines and compressors, classical frequency domain and numerical time domain methods, equivalent system for torsional vibration, damping of torsional and axial vibrations of crankshafts. Part 5: An overview on nonlinear vibration (2 hours): approximated methods, Duffing equation, jump phenomenon. Numerical simulation, basic concepts on chaotic vibration. Part 6: Short Outline in Controlled and Active Systems (3 hours): general considerations, open-loop control, closed-loop control, basic control laws, design of controlled systems.

The subject is based on a total of 60 hours of lectures plus 40 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 suggested for this subject 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 subject 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 subject 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 - aimed at evaluating the comprehension of the subject, both its theory and practical contents - 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 subject 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.