Course program
1) Introductory notions: Basic concepts of mechanics, physical quantities, dimensional equations, vectors, matrices, elements of linear algebra (eigenvalues and eigenvectors), kinematics, and dynamics of a material point.
2) The elementary oscillator and discrete mechanical systems with multiple degrees of freedom:
- Homogeneous problem;
- Undamped forced problem;
- Damped forced problem.
3) Continuous systems and Euler-Bernoulli beam:
- Compatibility, constitutive relation, and equilibrium;
- Dynamic eigenvalue problem with various boundary conditions;
- Dynamic problem with discrete masses.
4) Techniques for analysing dynamic response:
- Fourier Transform;
- Frequency response curve and function;
- Experimental modal analysis.
5) Contact and non-contact acquisition tools:
- Accelerometers and displacement transducers;
- Point triangulation lasers for displacement acquisition;
- Laser Doppler vibrometers for velocity field acquisition;
- Digital Image Correlation for displacement and strain field acquisition.
6) Calculation and experimental acquisition of Frequency Response Functions (FRF) and Frequency Response Curves (FRC):
- Numerical calculation of FRFs and FRCs for discrete mechanical systems using Matlab or Python or Mathematica;
- Experimental acquisition of FRFs and FRCs through Frequency Sweep using electromechanical shakers;
- Identification of dynamic responses using phenomenological models and genetic algorithms.
7) Computational and experimental modal analysis of small beams subject to different constraint conditions:
- Numerical calculation of frequencies and vibration modes using Matlab or Python or Mathematica;
- Application of experimental modal analysis for calculating modes, frequencies, and damping: FFT, Half-Power Peak Method, Complex Mode Indicator Function (CMIF).
Prerequisites
Knowledge of the topics covered in courses on mathematical analysis, linear algebra, and preferably mechanical physics and signal theory is required. Specifically, solid knowledge is required in the following areas: matrices and vectors, operations with matrices and vectors, elements of linear algebra, systems of linear equations, eigenvalue problems, derivatives and integrals, Fourier and Laplace transforms.
Books
After each lesson, students will be provided with study materials covering the topics discussed.
Frequency
Attendance is not mandatory. However, maximum participation is required, especially for group projects.
Exam mode
Assessment will take place in two phases: after the completion of the theoretical module and at the end of the course. In the first phase, participants will have to complete a written assignment containing exercises and theoretical questions. Those who score at least 18/30 on this first test will be admitted to the second test at the end of the course. The latter will consist of a discussion of a report carried out in groups of 2-3 people aimed at verifying the acquisition of practical and operational skills. The final grade will be a weighted average of the two assessments. Those who do not achieve a score of at least 18/30 on the first test, or do not take it during the course, will have to complete it at the end of the course. Passing the first test is necessary to access the second.
Lesson mode
The lessons will be held in person, while online consultations will be available.
