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Applicability of existing indexes of non-proportionality of damping in case of theoretical model of slender structure with installed TMD
Hračov, Stanislav ; Pospíšil, Stanislav ; Náprstek, Jiří
The paper analyzes an applicability of to date published indexes of non-proportionality in the case of a linear viscously damped numerical model of slender structure equipped with tuned mass damper (TMD). The installation of TMD into the structure not only reduces the level of undesired vibration, but it can also cause due to damping element of TMD a significant increase of damping nonproportionality. The paper recommends the most suitable indexes for such a type of structure and points out to impropriety of the others. The point of view of is also focus on the validity of the existing criterions for neglecting of non-diagonal terms of a modal damping matrix. Only indexes and criterions based on the properties of the modal damping matrix were taking into account.
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Relation of flutter derivatives and indicial functions in linear aero-elastic models
Náprstek, Jiří ; Pospíšil, Stanislav
Double degree of freedom (DDOF) linear systems are frequently used to model the aero-elastic response of slender prismatic systems until the first critical state is reached. Relevant mathematical models appearing in literature differ in principle by way of composition of aero-elastic forces. This criterion enables to sort them roughly in three groups: (i) neutral models - aero-elastic forces are introduced as suitable constants independent from excitation frequency and time; (ii) flutter derivatives - they respect the frequency dependence of aero-elastic forces; (iii) indicial functions - they are defined as kernels of convolution integrals formulating aero-elastic forces as functions of time. The paper tries to put all three groups together on one common basis to demonstrate their linkage and to eliminate gaps in mathematical formulations between them.
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Analysis of eigen-values of viscously damped two degrees of freedom system due to changes of parameters of secondary subsystem
Hračov, Stanislav ; Náprstek, Jiří ; Pospíšil, Stanislav
The paper deals with an analysis of non-classically damped two degrees of freedom system from the point of view of eigen-values. The theoretical relations between the system parameters for the case of multiple complex eigen-values were derived. The parametric problem was carried out analytically and graphically. The influence of the relative frequency tuning on the overdamping of individual eigen-values with increasing of the secondary damping was studied. The overdamping intervals were defined with respect to the mass ratio and the frequency tuning. The boundaries between respective overdamping intervals represent among others the frequency tuning of system with multiple complex eigen-values. The phase between components of eigen-modes and its relation to the eigen-values were examined with respect to the secondary damping increase.
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Multipurpose experimental rig for aeroelastic tests of bridge girders and slender beams
Pospíšil, Stanislav ; Král, Radomil ; Náprstek, Jiří
The bridges, footbridges and broadcast towers create an important subset of infrastructure subjected to dynamic loading of various origins. Especially, exposed to wind, they are susceptible to vibrations under certain circumstances due to pure load action or aero-elastic effects. This means that once an element or a structure starts to vibrate, a complex interaction between the moving boundary and the airflow takes place. Because of the complexity, the research has been in progress for several decades in both theoretical and experimental way. The article describes an original and multi-purpose experimental frame for the analysis of complex linear and non-linear aspects of aero-elastic behavior of the slender beams. The apparatus meets the rigorous theoretical assumptions and allows very precise and quick adjustment of the stiffness and mass of the structure, which is not always possible with a traditional "parallel spring-supported bridge" approach used by many researchers.
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Experimental and theoretical stability analysis of damped auto-parametric pendulum
Pospíšil, Stanislav ; Fischer, Cyril ; Náprstek, Jiří
The article describes an experimental and theoretical treatment of the auto-parametric pendulum damper modelled as a double-degree-of-freedom (DDOF) system. It is strongly non-linear, with the harmonic excitation being applied in the suspension point and interpreted for instance as an excitation by wind. The stability of the motion in a vertical plane is analysed in the meaning of semi-trivial vibration. This effect of stability loss and possible stability regain is very important from practical point of view, because the motion of an damper beyond the stability limits may act negatively and thus endanger the structure itself. Special experimental frame was developed.The stability of the system is analysed experimentally and compared with theoretical results.
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