Civil Engineering

PART I. Dynamic problem formulation. Direct and invers dynamic problem; Principles of Newtonian and Analytical Dynamics; Newton's Laws of Motion; Moment of a Force and Angular Momentum; Work and Energy; Systems of particles and rigid bodies; Generalized Coordinates and Degrees of Freedom; The Principle of Virtual Work; The Generalized Principle of d'Alembert; Hamilton's Principle; Lagrange's Equations of Motion; Linear and nonlinear systems; Rheological models; Methods for Solving the Equations of Motion. PART II. SDOF systems. Free Vibration. Equation of motion; Undamped Free Vibration; Viscously Damped Free Vibration; Energy in Free Vibration; Coulomb-Damped Free Vibration. Forced vibration. Equation of motion; Response to Harmonic excitation; Harmonic Vibration of Undamped Systems; Harmonic Vibration with Viscous Damping; Force Transmission and Vibration Isolation; Response to Ground Motion; Energy Dissipated in Viscous Damping; Equivalent Viscous Damping; Systems with Nonviscous Damping; Harmonic Vibration with Rate-Independent Damping; Response to Periodic, pulse and arbitrary excitation. State Space Representations; Numerical Evaluation of Dynamic Response; Central Difference Method; Newmark’s Method; Stability and Computational Error. PART III. MDOF systems. Free Vibration. Equation of motion; Mass Matrix; Stiffness Matrix; Natural Vibration Frequencies and Modes; Systems without Damping; Natural Vibration Frequencies and Modes; Modal and Spectral Matrices; Orthogonality of Modes; Normalization of Modes; Modal Expansion of Displacements. Damping Matrix; Classical Damping Matrix; Nonclassical Damping Matrix; Solution of Free Vibration Equations: Classically and Nonclassically Damped Systems. Forced vibration. Equation of motion; Response to Harmonic excitation; Harmonic Vibration of Undamped Systems; Harmonic Vibration with Viscous Damping; Force Transmission and Vibration Isolation; Response to Ground Motion; Systems with Nonviscous Damping. Modal Analysis; Modal Equations for Undamped Systems; Modal Equations for Damped Systems. PART IV. Systems with Distributed Mass and Elasticity. Equation of Undamped Motion: Applied Forces. Equation of Undamped Motion: Support Excitation; Vibration Frequencies and Modes; Orthogonality; Modal Expansion of Displacements; Modal Analysis of Forced Dynamic Response. PART V. Structural control: passive, active, semi-active and hybrid control. Passive and semi-active control: isolation, dissipation and Tuned Mass Damper (TMD). Structural identification: Natural Frequency and Damping from free vibration (logarithmic decrement) and Forced Harmonic Tests (half-Power bandwitdth). Experimental dynamic; Response to Vibration Generator; Vibration-Measuring Instruments.

In order to understand the topics of the course and achieve the learning outcomes, no previous knowledge of structural dynamics is required. The necessary background is available through the usual fundamental courses required of civil engineering undergraduates. These include: - Kinematic and static analysis of the structures, including statically indeterminate structures and matrix formulation of analysis procedure; - Rigid-body dynamics; - Mathematics: ordinary and partial differential equations, linear algebra.

Chopra, A. K., Dinamics of Structures – Theory and Applications to Earthquake Engineering, Englewood Cliffs, N.J.: Prentice Hall, 1995. Meirovitch, L., Analytical Methodos in Vibrations, Macmillan, New York, 1967. Ewins, D. J., Modal Testing: Theory and practice, John Wiley & Sons, Inc., 1984. Soong TT, Dargush GF. Passive Energy Dissipation Systems in Structural Engineering, John Wiley & Sons: Chichester, 1997.

Teaching activities are organised in the following way: - frontal classes; - classroom tutorials. Frontal classrooms contribute at achieving the specific learning outcomes related to knowledge and understanding the dynamics behaviour of the linear and nonlinear structural models. Classroom tutorials and homework contribute at achieving the specific learning outcomes related to knowledge applied to real problems. In order to give the final exam the student prepares a monographic work, which was not previously studied within the course.

Presence in the classroom.

The way the exam is conceived allows determining the student actual achievement of learning outcomes, with special emphasis on the applying knowledge and understanding skills. The exam is carried out in a single session at the end of the course and when monographic work is closed. The exam entails written answers (equations, dynamical model, dynamic response, …) and their oral presentation to question given by the lecturer. Questions are related to the monographic work content and the programme of the course. Give the predominantly oral nature of the exam, its duration seldom overcomes an hour. The exam involves usually three questions and the final mark is given as simple mean of the three marks. Some of the elements assessed are: use of a technical language; correct use of symbols and unit of measures; presentation of the process leading to formulate the answer; understanding of the structural behaviour mathematically modelled.

Teaching activities are organised in the following way: - frontal classes; - classroom tutorials. Frontal classrooms contribute at achieving the specific learning outcomes related to knowledge and understanding the dynamics behaviour of the linear and nonlinear structural models. Classroom tutorials and homework contribute at achieving the specific learning outcomes related to knowledge applied to real problems. In order to give the final exam the student prepares a monographic work, which was not previously studied within the course.