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Root-finding methods for solving dispersion equations
Hora, Petr
Contribution deals with the methods of rootfinding in a plate and cylindrical waveguide. The methods are based on: classic root-finding, interval arithmetics, Chebyshev interpolation, marching squares and marching triangles. All methods have been implemented both in Matlab (ChebFun toolbox) and Julia (ApproxFun module).
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Numerical modeling of magnetostrictive materials
Kholmetska, I. ; Chleboun, J. ; Krejčí, Pavel
An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density function. The uncertainty is modeled through a fuzzy set approach. In galfenol, an alloy of gallium and iron, however, the hysteresis phenomenon is present only weakly. This allows to propose a simpler, but computationally faster model without hysteresis. The new, simpler model has been identified from the measured magnetic and magnetostrictive cycles. The amount of harvested energy is of the same order in both models. Again, an uncertainty in the identified model can be considered and its impact on the amount of the harvested energy calculated.
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Experiment E7/0,3-displacement processes in non cohesive sand mass during active translative motion of retaining wall
Koudelka, Petr
The first part of information on the new experiment denominated as E7/0,3 with active pressure of non-cohesive quartz sand on time behaviour of the mass was presented at the last Conference (P. Koudelka, 2015). The second part is object of this Paper. The experiment was performed at the Institute of Theoretical and Applied Mechanics in 2014. The moved rigid front wall of the experimental equipment was translatively moved towards active direction (out of the mass) at a position of supposed acting of active pressure value, then the wall motion was stopped and time pressure stability was monitored. After more than three months the wall was moved at the last position of 100 mm from original position before the experiment. The experiment ran four and a half months. The paper presents firstly results on the deforming mass through the course of the wall movement at a supposed position for active pressure mobilization of 1.357 mm and after the further movement. The experiment was repeated to be the results proved (Experiment E8/0,3). New results are analysed.
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Health monitoring of building structures: preliminary considerations on a case study
Bayer, Jan ; Urushadze, Shota ; Zíma, Pavel
Ageing, erosion, local damage or increase of the operating loads can decrease the reliability and load bearing capacity of building structures. Vibration monitoring may provide a promising solution of this problem, however robust health monitoring techniques are needed before wider practical applications. The presented analytical and experimental case study on a simple supported steel beam is an introductory practical investigation into this topic. It shows the sensitivity of chosen parameters to artificially induced damage and outlines possible directions or further research in conclusions. Special attention is paid to simultaneous monitoring of deformations and strains which can provide us with a useful information about the stress redistribution in monitored or tested structures.
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Non-linear normal modes in dynamics-continuous systems
Náprstek, Jiří ; Fischer, Cyril
The paper presents a continuation of an effort started last year, when the authors briefly informed about the Non-linear normal modes (NNM) concerning the version dealing with discrete systems. Although many features of the continuous formulation from the mathematical viewpoint are similar to the discrete case, a couple of specifics should be highlighted from the viewpoint of a real applicability of this tool to investigate particular dynamic systems. Three approaches are mentioned in the paper and the Galerkin-Petrov based procedure is outlined in more details. As a particular subject the cantilever prismatic beam is discussed. Non-linear normal modes for several amplitudes are shown to demonstrate the dependence of their shapes on the actual effective amplitude. Comparison with adequate linear counterpart is done.
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Approximation of the movement of the spherical pendulum
Fischer, Cyril ; Náprstek, Jiří
The horizontally driven two-degrees of freedom spherical pendulum is an auto-parametric system which exhibits a wide variety of response types. Depending on the amplitude and frequency of the excitation the response can vary from stationary to chaotic regime. It has been already shown that the response can be described using time variable parameters of an inscribed ellipse. Such a description has a potential to close the gap between description of stationary, quasi-periodic and chaotic types of response. This study presents methodology and results of an analysis of the experimentally measured data providing the time dependent parameters of a twisting ellipse. The obtained results are discussed and some open problems are indicated.
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Invariants of simple nozzles
Tesař, Václav
Paper presents a new concept: invariance of second order. The idea bypasses the necessity geometric similarity (known as allowing only a scaling up or down) in derivation of dimensionless criterial parameters. The approach is demonstrated on the case of family of simple nozzles, the members of the family differing in their lengths of exit channel. While each nozzle is characterised by its primary invariant, characterisation of the whole family leads to two secondary invariants.
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Stability analysis of the lateral oscillations of a flexibly supported viscoelastic Jeffcott rotor
Ferfecki, P. ; Zapoměl, Jaroslav ; Kozánek, Jan ; Dekýš, V.
Material damping has a significant influence on vibrations of flexible rotors and can induce their self excited oscillations. The squeeze film dampers inserted in the rotor supports are frequently used to suppress occurrence of these undesirable operating conditions. Modelling the shaft by means of a Kelvin- Voigt material can arrive at the overestimation of the effect of internal damping on the rotor movement. This was a motivation to develop a procedure based on utilization of the Zener material (standard solid theoretical material) to represent the shaft of a Jeffcott rotor supported by squeeze film dampers. The development and testing of this procedure, the experimental determination of the appropriate material constants, and learning more on the influence of material damping on the stability and vibration attenuation of flexible rotors are the principal contributions of the presented article.
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The effect of the pitch support elasticity on the NACA0015 profile aeroelastic properties
Vlček, Václav ; Zolotarev, Igor ; Kozánek, Jan
The aeroelastic experiments realized in wind tunnel of the Institute of Thermomechanics with Mach numbers M ~ 0.20-0.22 and with the interval of Reynolds numbers Re = (2.4-2.6).105, are presented. These results correspond to the self-excited vibration of the profile NACA0015 with two degrees of freedom allowing the profile rotation in 1/3-chord axis and allowing the vertical displacement of the profile. The dependence of vibration frequency on the wind-flow velocity has been obtained. Comparing with the previous experiments the influence of the pitch support elasticity on the profile aeroelastic properties was determined.
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Experimental analysis of torsion vibration of hard rubbers under large deformation
Šulc, Petr ; Pešek, Luděk ; Bula, Vítězslav ; Cibulka, Jan ; Košina, Jan
The paper deals with a stress analysis of hard rubber under large torsion deformations. This study was motivated by effort to enhance the theoretical background for experimental evaluation of material behaviour of hard rubbers on our test rig. First the Mooney Rivlin model (MRM) for shear case of loading was developed and then MRM constants were attained by fitting of the MRM to the experimental torsiondeformation curve. Then the tuned MRM cylindrical model was tested under torsion loading for evaluation of stress state. Besides the radial distribution of shear stress and strain the attention was paid to evaluation of axial stresses. It could help to assess the influence of the tension stresses on the tangential deformations of the test sample during large torsion.
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