Technical Mechanics - Supplementary Course

On the basis of continuum mechanical considerations the solution methods gained during the basic course will be developed and placed into a common context. By applying these solution methods the broad field of mechanics will be explained to the students so that they can expand it at a later date during their Master or PhD studies. After passing this course the student will be able to identify the limits of assumptions, e.g. those made within Technical Mechanics for the beam-theory, and develop a deep understanding for possible solutions. The students will learn how to calculate dynamic systems' internal forces and how to determine the vibration characteristics of multi body systems and elastic, mass distributed structures by applying the theory of single-degree-of-freedom systems (SDOF).

In continuum mechanics the focus is laid on the development of selected continuum mechanical solutions by means of energy methods, principle of virtual work and weighted residuum methods. Basic methods for structural dynamics are refined for structural engineers. Knowledge of structural dynamic effects is evident for the examination of loads induced by wind, earthquakes, pedestrians, vehicles etc. Approximative methods, which are useful practical engineering tasks e.g. for the determination of eigenfrequencies are offered. The relevant structural dynamical load cases for practical problems like vibrations caused by pedestrians, wind, earthquakes or church bells are discussed. In addition dynamical loads of moving systems are explained. Thematic outline: - Newtons law, d'Alembert's principle - Energy methods - Free damped vibrations - Forced damped vibrations - Damped vibrations caused by ground movement - Vibration of an Euler-Bernoulli-beam - Approximation of eigenfrequencies - Linear displacement - Plane displacement of a mass - Plane displacement of a disc - Rolling and slipping - Impulse and energy considerations - Ideal central collision of compact bodies - Angular momentum - Internal forces caused by displacement