Dynamics of structures/Computational Mechanics (Dynamics of structures)

The course aims to provide the theoretical principles and practical tools required to address the main topics of structural dynamics. In addition to lectures, the course includes practical classes conducted in the classroom, during which students use their own computers to apply the methodologies and computational tools presented in the lectures. The course also includes selected examples of experimental laboratory tests.

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Knowledge and understanding of structural dynamics analysis methodologies and their use for structural engineering applications.

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Knowledge of Structural Mechanics and Advanced Structural Mechanics. Basic knowledge of programming and numerical computing platforms. Familiarity with MATLAB is desirable.

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Introduction to structural dynamics and basic concepts. Single-degree-of-freedom systems: * Equation of motion and analytical response of free undamped systems. * Analytical response of free damped systems: underdamped, critically damped and overdamped cases. * Analytical response of damped systems under sinusoidal excitation. * Response to periodic excitation, including square, sawtooth and triangular waves. * Response to step and impulse excitations. * General excitation with homogeneous initial conditions and Duhamel’s integral. * Numerical solution under generic forcing using Runge-Kutta methods. * Physical interpretation of resonance, with and without damping. Introduction to Multi-degree-of-freedom systems and modal analysis. Frequency-domain analysis: * Fourier series, Fourier coefficients and Fourier transforms. * Representation of signals in the frequency domain. * Frequency response functions (FRFs). Continuous structural systems: * Transverse vibration of a string: equation of motion, separation of variables, natural frequencies and mode shapes for fixed-fixed boundary conditions, and the role of initial conditions. Application to guitar strings. * Longitudinal vibration of a bar: derivation of the equation of motion, free and forced vibrations, modal orthogonality and Duhamel’s integral. * Free torsional vibration of a shaft: natural frequencies and mode shapes. * Free and forced axial and bending vibrations of Euler-Bernoulli beams. * Euler-Bernoulli beam hypotheses, equations of motion, natural frequencies and mode shapes for different boundary conditions. * Free bending vibrations of Timoshenko beams and comparison with the Euler-Bernoulli model. * Free bending vibrations of cracked Euler-Bernoulli beams using an equivalent rotational spring. Calibration of the spring according to fracture mechanics and analysis of the effect of crack size and position on natural frequencies. * Free vibration of Kirchhoff thin plates. Finite element modelling in structural dynamics: * Stiffness and mass matrices for beam elements. * Comparison between analytical and numerical natural frequencies of a beam in bending. Experimental modal analysis: * Fundamentals of experimental and operational modal analysis. * Sensors for dynamic identification, including piezoelectric and capacitive accelerometers. * Controlled excitation sources: electrodynamic shakers and instrumented hammers. * Experimental procedures: sine sweep, roving hammer and roving sensor tests, and SISO, SIMO and MIMO configurations. * FRF curve fitting and experimental modal parameter estimation. Approximate analytical methods: * Rayleigh’s method. * Rayleigh-Ritz method. Introduction to nonlinear dynamics: * Free vibrations of conservative and dissipative single-degree-of-freedom systems. * Forced vibrations of dissipative single-degree-of-freedom systems. * Nonlinear stiffness and damping. * Generalized power-law formulations. * Pendulum under gravity and the Duffing equation. * Nonlinear viscous damping and the Van der Pol equation. * Limit cycles and Poincaré maps. * Forced nonlinear systems, frequency jumps, quasi-periodicity and chaos. Wave propagation and metamaterials: * Fundamentals of wave shaping with metamaterials. * Engineering applications of mechanical metamaterials.

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Dynamics of structures/Computational Mechanics (Dynamics of structures)

The course consists of lectures, practical classes held in the classroom using students’ own computers, and laboratory classes focused on experimental modal analysis. The practical classes address topics covered during the lectures and provide hands-on experience with the relevant computational tools. Students are also required to complete individual assignments on the different course topics. These assignments contribute to the final grade.

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Notes will be provided during the course. For further consultation: • S.S. Rao Vibration of Continuous Systems John Wiley & Sons, Inc. 2007 • D. J. Ewins, Modal Testing: Theory and Practice. John Wiley & Sons Inc., 1995. • R. W. Clough J. Penzien Dynamics of Structures, McGraw-Hill, 1982. • Carpinteri. Dinamica delle strutture. Pitagora, 1998.

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Dispense;

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Modalita di esame: Prova orale obbligatoria;

Dynamics of structures/Computational Mechanics (Dynamics of structures)

Exam: Compulsory oral exam;

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Dynamics of structures/Computational Mechanics (Dynamics of structures)

The exam is aimed at ascertaining knowledge of the topics listed in the official course program and the ability to apply the theory and related calculation methods to determining the dynamic response of simple structures. The exam consists of an oral test with presentation and discussion of the assignments developed during the course and has the purpose of verifying the level of knowledge and understanding of the topics covered. The evaluations are expressed out of thirty and the exam is passed if the score reported is at least 18/30.

Gli studenti e le studentesse con disabilita 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'Unita Special Needs, al fine di permettere al/la docente la declinazione piu idonea in riferimento alla specifica tipologia di esame.