# 151-0505-00L  Mechanics III for Civil Engineers

 Semester Autumn Semester 2013 Lecturers G. Haller Periodicity yearly course Language of instruction English (lecture), German (exercise)

 Abstract Contents: basic concepts: planar dynamics with (principle of) linear and angular momentum, moment of inertia, kinetic energy. - linear vibration systems: (higher-order) eigenvectors, modal decoupling. - wave equation: normal form, characteristics, reflection. Objective This lecture gives the student a well-founded basic education in the technical theory of oscillations. The focus of the lecture lies - in addition to directly applicable methods - in the methodical introduction to the theory of vibrations. This should enable the student to work independently in the praxis-oriented area of oscillation analysis and to study further at a high level. The material used in the lectures is mathematically oriented and strictly causally structured and makes use of vector and matrix calculus. Particular importance is given to demanding and practice-oriented exercises. Content 1. Fundamental concepts: Planar systems: Position, velocity, acceleration, linear momentum, angular momentum, principle of linear momentum, principle of angular momentum, moment of inertia, Steiner's formula, elementary force laws, kinetic and potential energy, equations of motion.2. Linear oscillations - 1 degree of freedom: force and kinematic excitation, state space, damped and undamped free oscillations, Lehr's damping, phase space portraits, eigenvalue plots, harmonic excitation, amplitude and phase responses, power consumption, beat frequencies, resonance.3. Linear oscillation - f degrees of freedom: MDGKN system, representation in configuration and state space, eigenvalues, eigenvectors, higher order eigenvectors, undamped and damped systems, Rayleigh damping, modal decoupling.4. Wave equation: String under tension, longitudinal dynamics of rods, torsional vibrations of circular cylindrical rods, boundary conditions in space and time, canonical transformation, normal form of the wave equation, d'Alembert solution, characteristics, left and right waves, reflection at free and restrained ends, standing waves and oscillations. Lecture notes Es gibt kein offizielles Vorlesungsskript. Den Studenten wird empfohlen, eine eigene Mitschrift der Vorlesung anzufertigen. Eine elektronische Mitschrift der Vorlesung kann aber auf der Mechanik III-Homepage heruntergeladen werden. Vorlesungsbegleitende Arbeitsunterlagen sowie ein Katalog mit Übungsaufgaben werden ausgegeben. Die zugehörigen Musterlösungen werden nach Bearbeitung auf der Homepage zugänglich gemacht. Literature Als Zusatzliteratur wird empfohlen: Mechanik 3, Dynamik, M.B. Sayir, Eigenverlag (CHF 32.-)