Some deviations from linear dynamics due to more accurate damping models
(2017) In TVSM5000 VSM820 20171Structural Mechanics
Department of Construction Sciences
 Abstract
 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... (More)
 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, steadystate response and the response to sinusshaped pulses are discussed.
In the next chapter linear viscoelastic and nonlinear frictional material models are discussed. An introduction to linear viscoelasticity is followed by a comparison between the KelvinVoigt model and the Standard linear solid model, which are the two most basic linear viscoelastic 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 KelvinVoigtmodel 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 sineshaped 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 viscoelastic. Finally a short introduction to a model which combines both viscoelasticity and friction behavior is given. This model is referred to as the 5parameter model. (Less)  Popular Abstract (Swedish)
 För att förutsäga beteendet hos mekaniska dynamiska system används beräkningsmodeller som utgår ifrån systemens massa, styvhet och dämpningsegenskaper. Dessa modeller kan vara avancerade eller lätthanterliga mycket beroende på hur dämpningsmekanismerna modelleras. Syftet med arbetet var att undersöka hur mer avancerade materialmodeller för beskrivning av dämpningen påverkar systemets dynamik.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8927985
 author
 Sjöstrand, Jakob ^{LU}
 supervisor

 Per Erik Austrell ^{LU}
 organization
 course
 VSM820 20171
 year
 2017
 type
 H3  Professional qualifications (4 Years  )
 subject
 keywords
 Bilinear hysteresis, Standard linear solid, SLS, Linear Dynamics, Nonlinear Dynamics
 publication/series
 TVSM5000
 report number
 TVSM5228
 ISSN
 02816679
 language
 English
 id
 8927985
 alternative location
 http://www.byggmek.lth.se/english/publications#0
 date added to LUP
 20171116 09:31:26
 date last changed
 20171116 09:31:26
@misc{8927985, abstract = {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, steadystate response and the response to sinusshaped pulses are discussed. In the next chapter linear viscoelastic and nonlinear frictional material models are discussed. An introduction to linear viscoelasticity is followed by a comparison between the KelvinVoigt model and the Standard linear solid model, which are the two most basic linear viscoelastic 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 KelvinVoigtmodel 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 sineshaped 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 viscoelastic. Finally a short introduction to a model which combines both viscoelasticity and friction behavior is given. This model is referred to as the 5parameter model.}, author = {Sjöstrand, Jakob}, issn = {02816679}, keyword = {Bilinear hysteresis,Standard linear solid,SLS,Linear Dynamics,Nonlinear Dynamics}, language = {eng}, note = {Student Paper}, series = {TVSM5000}, title = {Some deviations from linear dynamics due to more accurate damping models}, year = {2017}, }