The students should acquire knowledge and comprehension of the fundamentals of theoretical, numerical and experimental analysis of vibrating structures. The students are asked to gain: the capability of modelling and analysing the dynamic behaviour of structures, with both analytic and numerical methods; the capability of dealing with the fundamentals of signal processing, both in time and frequency domains; the capability of designing and performing an experimental test campaign; the capability of describing and applying the simplest methods of modal parameters identification.

Prerequisites for attending the subject are the basic knowledge of theoretical mechanics, dynamics of single degree of freedom systems and elements of matrix calculus. A good attitude at basic algebra and numerical computing is helpful.

Summary of single degree of freedom systems: free and forced response, with viscous and hysteretic damping. (10 hours: lectures, tutorials, labs) Multi degrees of freedom systems with lumped parameters: modal coordinates, eigenvalues, eigenvectors and operational deflection shapes; free and forced (FRF) response; models and effects of damping. (20 hours: lectures, tutorials, labs) Signal processing: Fourier series and transform; analogue to digital conversion; correlation and spectra; numerical and practical aspects in the computation of FRFs (20 hours: lectures, tutorials, labs). Procedures and instrumentation of experimental modal analysis. (10 hours: lectures, tutorials, labs) Identification of vibrating systems and modal parameters extraction. (15 hours: lectures, tutorials, labs) Comparison of numerical and experimental results. (5 hours: lectures, tutorials, labs)

Theoretical lectures are often supported by examples and practical case studies. The ability of correctly handling the theoretical models is compulsory and practical examples, carried out in classroom, on computers or in laboratory, will give the student the ability to verify the comprehension of the fundamental theories, to implement the proposed numerical techniques and to acquaint with the experimental procedures of modal analysis. Numerical examples are weekly solved in class by the students by using Matlab® scripts, specifically prepared to exploit the material presented during the lectures. For this task students are continuously supported by staff members. The ability of using Matlab® will not be checked during the exam but the knowledge of the explained numerical techniques is compulsory. On the other hand, short reports based on the outcomes of these numerical models will possibly increment the final score. Students split in small groups will take part to lab demonstrations and hands-on lab examples to familiarise with the instrumentation and the basic procedures of sound and vibration tests. The correct execution of at least one experimental test should be presented in a short report which, again, will possibly increment the final mark. The active participation in these classes is anyway a viable method to link practice and theory. Lecturers and tutors are available through the year (contact them by e-mail) in order to meet students for consultation.

Maia, N. M. M., Silva, J. M. M. et al, Theoretical and experimental modal analysis, Research Studies Press Ltd., England Shin, K., Hammond, J.K., Fundamentals of Signal Processing for Sound and Vibration Engineers, John Wiley & Sons , England Leonard Meirovitch, Elements of Vibration Analysis, McGraw-Hill (or: Fundamentals of Vibrations, Waveland Pr Inc) Ewins D.J., Modal testing: theory and practice, Research Studies Press Ltd., England Fasana A., S. Marchesiello, Meccanica delle vibrazioni, CLUT, Torino Papers, notes, Matlab® scripts and links to specific websites will be given during the term.

Lecture slides; Lecture notes; Simulation tools;

Exam: Written test; Individual essay;

Achieved learning outcomes are assessed by means of a final closed-book, written only test, with a duration of 90 minutes. No books, no notes, no electronic supports are allowed, except a pocket calculator. Questions on different topics are proposed to assess the comprehension of both theoretical and practical aspects of the subject. A part of the test aims at assessing the theoretical knowledge of the subject, so that the capability of correctly handling analytical models and explaining the techniques presented throughout the subject will be required. Simple numerical examples, similar to those described during the practical lectures, will also be proposed to check the ability to properly use tools and methods for solving problems. An example of exam is thoroughly discussed during the lectures, with examples and comments on typical errors and hints on evaluation criteria. The final mark depends on this text and the grade is proportional to the correctness and completeness of the answers: The maximum obtainable score is 30/30 and the exam is passed with a minimum of 18/30. Up to 6/30 points can be added to a sufficient result if complete and correct reports on numerical and experimental tests are produced and submitted in due time by the student. Also clarity, organisation, synthesis and tidiness of the written texts will be evaluated to assign the final score. A few days after the written test, students are summoned for a review of the written output, in which examiners inform each student on grading criteria, and receive any student appeal if supported by appropriate explanations. Further details on exam rules and regulations are given in class.

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.