The subject aims at giving an analytical, numerical and experimental survey of the various topics related to the study of vibrating structures. Signal processing, oriented at a correct use of the practical and numerical tools for modal analysis and system identification, is therefore treated both at a theoretical and applicative level.

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 the methods provided in the subject; the capability of dealing with the fundamentals of signal processing, both in time and frequency domains; 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 hysteretical 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, carried out in the classroom. 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 familiarize with the experimental procedures of modal analysis.
Numerical examples are weekly solved (in one of the computer rooms of PoliTo) 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 but the knowledge of the explained numerical techniques is compulsory.
Students, split in small groups, will take part to lab demonstrations and hands-on lab examples to familiarize with the instrumentation and the basic procedures of sound and vibration tests. No homework is given and no report is required about the experimental tests, but the active participation to these classes is a viable method to link practice and theory.
The lecturer and the tutor are available weekly (contact them by e-mail) during the teaching period 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 semester.

Achieved learning outcomes will be assessed by means of a final closed-book, written only test, with a duration of 90 minutes.
Questions on three 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.
The final mark only depends on this text and the grade is proportional to the correctness and completeness of the answers. The maximum obtainable mark is 30/30 cum laude.
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.
An example of exam is thoroughly discussed during the subject, with examples and comments on typical errors and hints on evaluation criteria.
Further details on exam rules are given on the official subject website.