After this course, students will understand how to evaluate the dynamic behavior of mechanical systems. Students will acquire the ability to integrate structure dynamics in a wider spectrum of machine design problems. The ability to critically interpret the results will also be acquired. In addition, students will learn how to produce a technical report to disseminate the work done during the Project activities. More specifically, those who assimilate the course topics will -) know how to calculate natural frequencies, modal shapes and frequency response of multi degrees mechanical systems, -) be familiar with modal parameters and the modeling of mechanical system with modal coordinates, -) understand how to deal with nonlinear systems. -) be able to build a simplified Finite Element model and use it to analyze the dynamic behavior of simple structures, -) be capable to obtain a Reduced Order Model of a Finite Element model.

To fully understand the topics of this course, students need a good knowledge of the basic concepts of kinematics, force-momentum formulation for systems of particles and rigid bodies and static stress analysis. Students should also be familiar with work-energy concepts such as virtual work and Lagrange's equations. Basic skills in the use of relevant computer codes are also required, although no previous experience with specific numerical tools is necessary.

Here below is reported the Course Syllabus. Introduction to the course (1.5 hours). Static and dynamic stress analysis. Classical and numerical approach. Automatic computation in design. Numerical simulation. Part 1 (Lectures, 12 hours; classroom exercises, 6 hours). 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 behavior of single and multi-dof systems. Modal uncoupling; modal participation factors. Forced response to harmonic excitation. Viscous, Electromagnetic, Structural damping. Forced response to non-harmonic excitation, short account of random vibrations. Solution of nonlinear system with Harmonic Balance Method. Numerical 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 (Lectures, 12 hours; classroom exercises, 3 hours; laboratory experience, 3 hours). 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 4 (Lectures, 7.5 hours; classroom exercises, 3 hours; laboratory experience, 3 hours). Short Outline in Controlled Electromagnetic and Electromechanical Systems: 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. Part 3 (Lectures, 6 hours; classroom exercises, 3 hours). Dynamics of rotating machines. Vibrations of rotors: Campbell diagram, critical speeds and fields of instability. Undamped and damped Jeffcott rotor. Specific exercises addressing the issues on the subject.

The overall course includes 39 hours of lessons and 21 hours shared between classroom exercises (Tutorial) and laboratory exercises. Lectures take place with the support of the blackboard, slides and notes. Tutorials aim to a better understanding of the subjects covered during the lessons. The activities indicated as “Project” deal with specific dynamic problems related to the elements of the machine. The technical Reports on the Projects will be discussed during the oral exam. We recommend that students join a team of 2/3 people team to prepare the Technical Reports. The documentation used during the theoretical lessons and the tutorial will be made available to the students through the website.

The textbook for the subject is: Genta G., Vibration Dynamics and Control, Springer, New York, 2009, ISBN 978 0 387 79579 9 or, 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 subject website.

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

At the end of the course the assessment of learning is performed with an exam consisting of a written and an oral test. The written test has a total duration of 2 hours. The oral test lasts approximately 30 minutes. If students wish to withdraw from the examination they have to inform one of the examiner before the end of the written test. The evaluation of the exam is assessed according to the following criteria: -) Exhaustive and complete knowledge of the subject combined with an excellent ability to understand and solve a problem applying concepts and tools developed during the course, outstanding capability to establish disciplinary and multidisciplinary links and to critically review the work done and the results obtained: 30/30 with honors (cum laude). -) Very good knowledge of the subject and good skills; good ability to understand and solve problems related to the structure dynamics, good capacity to make disciplinary and multidisciplinary connections: 26/30. -) Correct knowledge and sufficient skills; good understanding and application of knowledge: 22/30. -) Sufficient knowledge of the main aspects of the topics and essential skills while making minor mistakes: 18/30. -) Incomplete knowledge and insufficient skills; knowledge applied incompletely and inaccurately; errors and deficiency in critical thinking: 14/30. -) Serious gaps in knowledge and skills; major errors in understanding and finding solutions; serious shortcomings during the logical revision phase: 8/30. -) Completely missing or fragmented knowledge and skills; insufficient understanding of the problem and inability to find an adequate solution; lack of logical thinking and incapacity to review the work done: 2/30 The exam score is shared between the written test (max 24 points), the oral exam (max 4 points) and the discussion of the Projects (max 4 points). The final score is given by the sum of the three parts. Scores of 32 points will be reported as 30/30 with honors (cum laude). The written test consists of three questions related to the theoretical part and the application of the theory (i.e. 2 open questions on theory + 1 exercise or 1 open question about theory + 2 exercises). To take the oral exam the student must have passed the written test with at least 18/30 (14/24 according to the maximum score of the written test). During the exam books, notes or other auxiliary material on any media are not allowed. Students must not have mobile phones, smart watches or other communication devices. Students will discuss their Projects during the oral exam, then students will attend the Projects discussion with a copy (printed or electronic-copy) of their own Projects. The examiner will evaluate the completeness and correctness of the Projects technical reports and the students’ ability to explain their Projects in detail.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.