Building engineering and architecture

PART I. Dynamic problem formulation. Direct and invers dynamic problem; Principles of Newtonian 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; 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. Numerical Evaluation of Dynamic Response. 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; Response to Ground Motion. PART IV. Structural control: passive, active, semi-active and hybrid 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.

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.

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. 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.

Chopra, A. K., Dinamics of Structures – Theory and Applications to Earthquake Engineering, Englewood Cliffs, N.J.: Prentice Hall, 1995.

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.