Ing - Civ (Mag.)(ord. 270) - LC (437) CIVIL ENGINEERING FOR RISK MITIGATION
053449 - STRUCTURAL DYNAMICS
088905 - STRUCTURAL ANALYSIS
The course objective is the ability to study the response of a complex structural system, subjected to a time varying load, in a neighborhood of the position the equilibrium, using appropriate mathematical models of both the structure and the loading process.
Most of the relevant analytical methods are introduced with reference to simple, single degree of freedom models, and are then generalized to multiple degrees of freedom systems.
Most of our attention will be devoted to models derived using the Finite Element Method, with a discrete number of degrees of freedom, but we are going to study also the response of a simple continuous model of a beam, characterized by an infinite number of degrees of freedom.
Eventually Earthquake Response of Building Structures is analyzed, using the methods that we have developed in the main part of the course and introducing new, simplified methods for the analysis of peak response.
Risultati di apprendimento attesi
The expected results of the course are the students' knowledge of the theoretical basis of dynamical models and their ability to correctly model different types of structures and dynamic loads, as well as their capability in presenting their results. With reference to the European descriptors:
Knowledge and understanding: equations of dynamic equilibrium for SDOF and MDOF systems, canonical forms, modal analysis, numerical methods.
Applying knowledge and understanding: know how to develop a dynamic model of a structure and of the loading process.
Making judgments: ability to use the most appropriate set of modelling techniques and computational algorithms for at least a set of common problems.
Communication skills: ability to clearly expose an analytical procedure.
Learning skills: ability to autonomously increase knowledge in comparison with what has been taught during classes
Single Degree of Freedom Systems (SDOF)
Definition of Structural Dynamics, Dynamic Loadings. The Linearized Equation of Motion for a Single Degree of Freedom System. Free Vibrations of a SDOF System. Forced Response of a SDOF System: Harmonic, Periodic, Impulsive and Arbitrary Loadings. Forced Response of a SDOF System: Harmonic, Periodic, Impulsive and Arbitrary Loadings. Response in Frequency Domain: Fourier Series, Fourier Transform, Discrete Fourier Transform, Fast Fourier Transform. Numerical Methods for Response Analysis in Time and Frequency Domains. Numerical Methods for Non-Linear SDOF Systems. Modeling Simple Structures as SDOF systems: Generalized Coordinates, Rayleigh's Quotient Method for Vibration Analysis.
Multi Degree of Freedom Systems (MDOF)
Multi DOF Systems: Equations of Motion, Free Vibrations, Eigenvalues and Eigenvectors, Modal Analysis. Modeling Building Structures as MDOF Systems, Dynamic Degrees of Freedom and Static Condensation. MDOF Response to External Loadings, the Modal Superposition Method, Earthquake Response, General Support Motion. Extension of Numerical Methods to MDOF Systems. Numerical Methods for the Modal Analysis of MDOF Systems, Ritz Vectors.
Equations of dynamic equilibrium for an Euler beam. Free Vibrations, Eigenvalues and Eigenfunctions, Modal Analysis of a uniform Euler beam. Response of Continuous Systems Using the Modal Superposition Method.
Earthquake Strong Motion, Effects on Structures. Earthquake Spectra for Linear and Non Linear SDOF Systems. Response Spectrum Analysis of MDOF Systems.
Newton's Laws of Motion, De Saint Venant's theory of beams, Matrix Algebra.
Modalità di valutazione
Grades will be assigned on the merits of a written test, intended to check the candidate's ability to develop and study a simple structural model and to apply the analytical procedures discussed in the course to easy problems, and of an oral exam, intended to test the candidate's understanding of the subject and their ability in presenting and discussing the procedures and the results characteristic of structural dynamics.
Anil K. Chopra, Dynamics of Structures --- theory and applications to earthquake engineering, 5th Ed., Editore: Prentice Hall, Anno edizione: 2016, ISBN: 0134555120 Note:
The 5th edition is really new. The material discussed in the course can be found in the 2nd edition (the one I have...) or maybe in the 1st one. If you want to make an investment for your future career go 5, if you want to save (possibly a lot of) money, go with a previous edition.
Ray W. Clough and Joseph Penzien, Dynamics of Structures, 2nd ed., Editore: McGraw-Hill, Anno edizione: 1993, ISBN: 0-07-113241-4
Slides (as shown in classes), additional exercises, computer programs, homeworks' solutions, etchttps://boffi.github.io/
Tipo Forma Didattica
Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Di Progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese