Dynamics of structures: theory and analysis

Description

The fundamental concepts of dynamics are introduced for simple systems with a single degree of freedom. Hereby, aspects such as natural frequencies, damping and resonance are introduced by determining the system’s free vibrations and its forced response to harmonic and transient loading. The foundation of the dynamics of flexible structures is subsequently described by the theory for free beam vibrations, while the connection between this continuous element and its corresponding discrete structural model is illustrated by applying the finite element method to solve the partial differential equation. The dynamic analysis of discrete structures with multiple degrees of freedom is then conducted by modal analysis, based on a series representation by the vibration forms of the structure. Hereby, the influence of the load’s frequency content and its spatial distribution is considered, together with the potential of quasi-static system reduction techniques. For flexible structures, the damping of the system is crucial for the magnitude of the dynamic response, why various naturally occurring damping mechanisms are scrutinized. Furthermore, the effect of external dampers on flexible structures is treated, including the use of tuned mass dampers. For flexible structures with local dampers or advanced loading, the dynamic equations are solved by direct time integration using the Newmark method. The theoretical content of the course is illustrated by simple experiments and treated in exercises, which can be solved in Python. The reports constitute a part of the total course assessment. The first report is handed in individually, while the subsequent two reports are prepared in groups. Not applicable together with: 41214 / 41560 / 41564