Some deviations from linear dynamics due to more accurate damping models

Damping is present in all dynamic systems. In one way or another energy is being dissipated in the system. To capture this aspect of reality in a computational model is a difficult task. A common simplification is to assume that the damping is of a linear viscous nature. This assumption provides an equation of motion (linear dynamics) which is easy to handle mathematically. However, the simplicity of linear dynamics can in turn result in a poor representation of the physical reality. Perhaps the material is not viscous, perhaps friction is present either inside the material or at the boundaries? Different material models can take different damping phenomena into account, and it could be wise to work with a model or a combination of models that represent the physical properties of the material in the best way possible. This thesis starts with an introduction to linear dynamics of single degree of freedom systems, where the structure is modeled as a spring and viscous damper in parallel. Free vibration response, steady-state response and the response to sinus-shaped pulses are discussed. In the next chapter linear visco-elastic and non-linear frictional material models are discussed. An introduction to linear visco-elasticity is followed by a comparison between the Kelvin-Voigt model and the Standard linear solid model, which are the two most basic linear visco-elastic models, describing solid materials. This section is followed by a comparison between the two most basic frictional models. These are 1) a model based on Coulomb friction and 2) a more refined friction model referred to as the SFS model. In the following chapter a comparative study of the dynamic behavior of the Kelvin-Voigtmodel and the Standard linear solid model (SLS)is conducted. The models are given a structural formulation and a mass is attached. The main idea is to study if the behavior of the SLS model could be represented by a Kelvin model. Free vibration response, steady state response and response to sine-shaped pulses are investigated. In the last chapter the steady state response of the frictional SFS model is studied. This model has bilinear hysteresis. The idea is to show the number of physical phenomenas that goes missing if a system is described as purely linear visco-elastic. Finally a short introduction to a model which combines both visco-elasticity and friction behavior is given. This model is referred to as the 5-parameter model.För att förutsäga beteendet hos mekaniska dynamiska system används beräknings-modeller som utgår ifrån systemens massa, styvhet och dämpningsegenskaper. Dessa modeller kan vara avancerade eller lätthanterliga mycket beroende på hur dämpnings-mekanismerna modelleras. Syftet med arbetet var att undersöka hur mer avancerade materialmodeller för beskrivning av dämpningen påverkar systemets dynamik