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Dynamic analysis of tall slender structure equipped with passive absorber and founded on various subsoils using simplified model
Hračov, Stanislav
The paper is focused on the investigation of dynamic behavior of tall slender structures taking into account the soil-structure interaction effect (SSI) and a presence of a tuned mass damper (absorber). The main aim is to qualitatively and quantitatively assess effects of both phenomena on changes in basic dynamic properties and response of the structure. The real tower equipped with absorber is chosen and analyzed. Analytical and numerical analysis of modal properties and of the response of a simple discrete model are performed. The structure and absorber are represented by one degree of freedom, the interaction interface by spring-dashpot system. This simplified model together with multi degree of freedom discrete model is analyzed parametrically for different dynamic properties of subsoil to cover all possible dynamic effects. The influence of neglecting of both phenomena is quantified and suggestions for assessments of such a type of structures are proposed.
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Dynamic response of a heavy ball rolling inside a spherical dish under external excitation
Náprstek, Jiří ; Fischer, Cyril
The set of a heavy metallic ball which is rolling freely inside a semispherical dish with larger diameter, being fixed to structure, is frequently used as tuned mass damper of vibration. Ratio of both diameters, mass of the rolling ball, quality of contact surfaces and other parameters should correspond with characteristics of the structure. The ball damper is modelled as a non-holonomic system. Hamiltonian functional including an adequate form of the Rayleigh function is formulated in moving coordinates using Euler angles and completed by ancillary constraints via Lagrangian multipliers. Subsequently Lagrangian differential system is carried out. Together with rolling conditions the governing system of seven equations is formulated. Later Lagrangian multipliers character is analysed and redundant motion components are eliminated. First integrals are derived and main energy balances evaluated together with their physical interpretation. Discussion of basic dynamic properties of the system is provided.
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Experimental verification of resonance behaviour of a damped spherical pendulum
Fischer, Cyril ; Pospíšil, Stanislav ; Náprstek, Jiří
Theoretical, experimental and numerical analysis of a spherical pendulum is carried out. The stability of the response in a vertical plane is analysed in the theoretically predicted resonance region. Mathematical model respects the non-linear character of the pendulum and allows to introduce asymmetrical damping. Experimental pendulum is hanging from the Cardan joint and placed to carriage. Uni-directional harmonic excitation is applied to the system. The pendulum is damped by two magnetic units. These units are able to reproduce linear viscous damping independently in both principal response components. Response in in-plane and out-of-plane directions is measured and analyzed.
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Massive parallel implementation of ODE solvers
Fischer, Cyril
The paper maps the possibilities of exploitation of the massive parallel computational hardware (namely GPU) for solution of the initial value problems of ordinary differential equations. Two cases are discussed: parallel solution of a single ODE and parallel execution of scalar ODE solvers. Whereas the advantages of the special architecture in the case of a single ODE are problematic, repeated solution of a single ODE for different data can prot from the parallel architecture. However, special algorithms have to be used even in the latter case to avoid code divergence be- tween individual computational threads. The topic is illustrated on several examples.
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Analytic model of a ball rolling on a spherical surface under harmonic kinematic excitation
Náprstek, Jiří ; Fischer, Cyril
The set of a heavy metallic ball which is rolling freely inside a semi-spherical dish with larger diameter, being fixed to structure, is frequently used as tuned mass damper of vibration. Ratio of both diameters, mass of the rolling ball, quality of contact surfaces and other parameters should correspond with characteristics of the structure. The ball damper is modeled as a non-holonomic system. Hamiltonian functional including an adequate form of the Rayleigh function is formulated in moving coordinates using Euler angles and completed by ancillary constraints via Lagrangian multipliers. Subsequently Lagrangian differential system is carried out. Together with rolling conditions the governing system of seven equations is formulated. Later Lagrangian multipliers character is analyzed and redundant motion components are eliminated. First integrals are derived and main energy balances evaluated together with their physical interpretation.
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Resonance behaviour of spherical pendulum – influence of damping
Fischer, Cyril ; Náprstek, Jiří ; Pospíšil, Stanislav
Experimental and numerical model of a uni-directionally driven pendulum-based tuned mass damper is presented in the paper. Stability of the motion in a vertical plane is analysed in the theoretically predicted resonance region. For the experimental part, special experimental frame is used, allowing independent change of linear viscous damping in the both perpendicular directions. Mathematical model respects the non-linear character of the pendulum and allows to introduce asymmetrical damping. Sensitivity of the resonance behaviour on the change of damping in both directions is studied and commented in the paper. The stability of the system is analysed experimentally and compared with numerical and theoretical results.
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Experimental and numerical verification of vortex-induced vibration of hangers on the footbridge
Urushadze, Shota ; Pirner, Miroš ; Pospíšil, Stanislav ; Král, Radomil
The paper deals with vortex-induced oscillations of footbridge hangers at a very low wind speed. The two-spans (2x50m) reinforced concrete structure with the central pylon (25m height) is designed as the harp system of hangers with circular cross-section. The oscillations were observed at the low wind speed and the high double amplitudes has been measured. The wind-excited deformation shape corresponded to the 6th, 7th and 8th natural modes of a hanger. The individual hanger as well as thein group were analysed to estimate the dynamic response, possible aeroelastic vibration and special interference or coupling effects. It also includes proposal for the elimination of the extensive vibration. The analysis is complemented by numerical investigation using Computational Fluid Dynamics methods.
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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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