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Proposal of hyperelastic proportional damping as dissipated energy model of hard rubbers
Šulc, Petr ; Pešek, Luděk ; Bula, Vítězslav ; Košina, Jan ; Cibulka, Jan
The paper deals with a stress analysis of hard rubber under large torsion deformations. This study was motivated by effort to find the dependency the dissipated energy on the deformation energy. Based on the results of an experiment, a function of dissipation energy of hard rubbers for finite strains using the theory hyperelasticity was proposed herein analogically as a proportional damping for elastic theory. Samples of hard rubber of different hardness (EPDM, Silicone) were dynamically tested on the developed torsional test-rig at different frequencies, amplitudes. First the Mooney Rivlin model (MRM) for a shear case of loading was analytically developed and then MRM constants were attained by fitting of the MRM to the experimental torsion-deformation curve. These constants were used to obtain the deformation energy of the MRM models. The coefficients of hyperelastic proportional damping relating a dissipated energy to a strain energy were evaluated for tested rubbers on the basis of experimental results.
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Running flutter waves in blades cascade
Půst, Ladislav ; Pešek, Luděk
The simplified mathematical model of dynamic properties of bladed cascade excited by wakes of flowing steam from the stationary cascade is derived. Interaction of this kind of forced excitation with aero-elastic self-excitation described by Van der Pol formula causes origin of flutter and its. running waves. It is shown that the velocity, direction of flutter running waves and mode of vibration depend on the blades’ number ratio and on kind of self-excitation forces on individual blade or on inter-blade distance.
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Concentration distribution and slip velocity of coarse-particle-water mixture in horizontal and inclined pipe sections
Vlasák, Pavel ; Chára, Zdeněk ; Konfršt, Jiří
Narrow particle size distribution basalt pebbles of mean particle size 11.5 mm conveyed by water in the pipe sections of different inclination were investigated on an experimental pipe loop of inner diameter D = 100 mm. Mixture flow-behaviour and the concentration distribution were studied in a pipe viewing section and with the application of a gamma-ray densitometer. The study refers to the effect of mixture velocity, overall concentration, and angle of pipe inclination on chord-averaged concentration profiles and local concentration maps. The study revealed that the coarse particle-water mixtures in the inclined pipe sections were significantly stratified, the solid particles moved principally close to the pipe invert, and for higher and moderate flow velocities particle saltation becomes the dominant mode of particle conveying.
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Lyapunov exponents – practical computation
Fischer, Cyril ; Náprstek, Jiří
The Lyapunov exponents serve as numerical characteristics of dynamical systems, which measure possible divergence of nearby trajectories of the solution. In this way they express dependence of the dynamical system on initial conditions. However, the value of Lyapunov exponents consists in their ability to characterise deterministic chaos. The limiting process intrinsic in the definition of Lyapunov exponents, unfortunately, seriously complicates their computation. The short paper presents an overview of difficulties in numerical approaches to enumeration of Lyapunov exponents or at least the largest one and shows a promising method based on QR decomposition of the system Jacobian.
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A concept for testing and monitoring of building structures – theoretical case study
Bayer, Jan
A mere comparison of measured and analytical deformations, natural frequencies and mode\nshapes provides us with just a small part of the information contained in the data, especially when component- level damage prevention is needed. The presented analysis studies in detail a few criteria for evaluation of measured data, with the example of simulated plane trusses in respect to the ultimate limit state. It demonstrates the high potential of a systematic approach, while combining several criteria, particularly when using simultaneous strain and deformation measurements, as it documents the proposed Relative Mode Difference (RMD) criterion. On the other hand, the study points out the major limitation of practical applications that is caused by unknown inherent uncertainties of various kinds, providing us with the incentive for further experimental research.
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Non-holonomic planar and spatial model of a ball-type tuned mass damping device
Náprstek, Jiří ; Fischer, Cyril
The area of tuned mass dampers is a wide field of inspiration for theoretical studies in non-linear dynamics and dynamic stability. The studies attempt to estimate behaviour of diverse damping devices and their reliability. The current paper deals with the response of a heavy ball rolling inside a spherical cavity under horizontal kinematic excitation. The non-linear system consists of six degrees of freedom with three non-holonomic constraints. The contact between the ball and the cavity surface is supposed to be perfect without any sliding. The mathematical model using the Appell-Gibbs function of acceleration energy is developed and discussed. Comparison with previous planar (SDOF) model which is based on the Lagrangian procedure is given. The system has an auto-parametric character and therefore semi-trivial solutions and their dynamic stability can be analysed. The most important post-critical regimes are outlined and qualitatively evaluated in resonance domain. Numerical experiments were performed when excitation frequency is slowly swept up and down to identify different modes of response. Some applications in civil engineering as a tuned mass damper, which can be used on slender structures, are mentioned. The proposed device is compared with a conventional pendulum damper. Strengths and weaknesses of both absorbers types are discussed.
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