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Aeroelastic stability of a two-degrees of freedom system with additive and multiplicative narrow band random noises
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Naprstek, JiriMon, 24 Jul 2017 12:46:57 GMT/record/22615l'Association pour l'Ingénierie du VentCOMPARISON OF NUMERICAL AND SEMI-ANALYTICAL SOLUTION OF A SIMPLE NON-LINEAR SYSTEM IN STATE OF THE STOCHASTIC RESONANCE
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Stochastic resonance (SR) is a phenomenon which can be observed at some nonlinear dynamic systems under combined excitation including deterministic harmonic force and random noise. The Duffing single degree of freedom oscillator is treated and the Gaussian white noise as the random excitation component is considered. Mathematical basis of this phenomenon follows from properties of the Duffing system with negative linear part of the stiffness. Under certain combinations of the system and excitation parameters the SR can emerge. It manifests by stable periodic hopping between two nearly constant limits perturbed by random noises. SR is observed and practically used in a number of disciplines in physics, biophysics, chemistry, etc. However it seems to be promising as a theoretical model of several aeroelastic post-critical effects arising at a prismatic beam in a cross flow. Three independent theoretical solution methods have been addressed and tested in order to compare results of the system response. The first kind is semi-analytic dealing with the relevant Fokker-Planck Equation (FP). It is solved by means of the stochastic moment procedure. The multiharmonic non-stationary solution of the Probability Density Function (PDF) is expected. The Galerkin approach is adopted. The second way is based on the FEM solution of the FP equation. It is analyzed in an original evolutionary form which enables an analysis of transition effects starting the Dirac type initial conditions. The last procedure represents simulation regarding the original Duffing or relevant Ito stochastic system. Comparison of results provided by the above three methods has revealed appropriate domains of their application to particular problems regarding a preliminary analysis or careful detailed inspection in specific small domains in final stage of an engineering system design.
Náprstek, JiříThu, 22 Jun 2017 13:00:10 GMT/record/22372National Technical University of Athens, 2015ANALYTICAL APPROACH OF SLENDER STRUCTURE VIBRATION DUE TO RANDOM COMPONENT OF THE WIND VELOCITY
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Along wind random vibration of slender structures represents one of the most important aeroelastic effects resulting from wind - structure interaction. The theoretical model being based on one-dimensional elements with continuously distributed mass and stiffness has been introduced in this paper. The system has been considered to be linear self-adjoint with strongly non-proportional linear damping due to both material of the structure and presence of vibration dampers. The additive random excitation continuously distributed in time and space is Gaussian, therefore the response is Gaussian as well. Consequently, mathematical mean value and correlation function are satisfactory for the full description of the generalized solution of the respective PDE in the stochastic meaning. The general results have been obtained mostly in the form of analytical formulae for important cases of input spectral densities. A numerical example dealing with real structure is presented.
Náprstek, JiříThu, 22 Jun 2017 11:12:51 GMT/record/21546National Technical University of Athens, 2017Planar Compress Wave Scattering and Energy Diminution Due To Random In-Homogeneity of Material Density
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Slender engineering structures are endangered by a surface seismic wave. Subsoil parameters include a significant random inhomogeneity, which strongly influences character, spectral composition and intensity of such waves. Therefore, the seismic shock in a certain distance from the epicenter changes its degree and type, depending on a random character of the subsoil parameters in the positive but also in the negative meaning of the term. The paper investigates the compress wave propagation in two-dimensional continuum, the density of which is a continuous random function of x,y coordinates. This basic concept refers materials with in-homogeneity, which are encountered in subsoil being attacked by seismic wave. The random in-homogeneity influences significantly the wave structure and energy diffusion due to scatter at in-homogeneities. The density consists of a constant mean value and density fluctuations. Relevant centered two-dimensional random process is considered to be Gaussian, stochastically homogeneous and ergodic in x,y coordinates. The integral spectral decomposition in space is employed to derive the governing integro-differential system. It includes unknown deterministic component of the response and functions characterizing its random part. An approximate supposition that Gaussian imperfections lead to non-centered Gaussian response is adopted. There is shown a steep drop of the response deterministic part and a simultaneous increase of the response uncertainty (stochastic part) with raising distance from the point of excitation. These processes don't represent any mechanical energy loss, but only changes of its form. An upper limit of the excitation frequency (critical frequency) depending predominantly on the mean correlation length of imperfections has been found. Some ideas of application in earthquake engineering are given.
Naprstek, JiriWed, 18 Jan 2017 17:23:48 GMT/record/19955Gibbs-Appel Formulation of Non-Holonomic Motion of a Ball on a Spherical Surface
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A new type of a passive vibration absorber is proposed and investigated as a non-linear non-holonomic system. It consists of Wherical horizontal cavity in which a ball of a smaller diameter is rolling. The system of six degrees of freedom with three non- holonomic constraints is investigated. Instead of conventional way via Hamiltonian functional and Lagrangian procedure, the respective differential system is derived using the Gibbs-Appel function and related steps. Comparison of both approaches has been done. The system has an auto-parametric character and hence the semi-trivial solution and dynamic stability is investigated. Some principal post-critical regimes are outlined and qualitatively evaluated in the resonance neighborhood. Numerical experiments are performed and physically interpreted.
Naprstek, JiriTue, 15 Nov 2016 09:02:08 GMT/record/14987International Union of Theoretical and Applied Mechanics, 2016Non-Linear Auto-Parametric Stability Loss of a Slender Structure due to Random Non-Stationary Seismic Excitation
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Slender structures exposed to a strong vertical component of an earthquake excitation are endangered by autoThe first section of the paperThis highlya single paragraph abstract outlining the aims, scope and conclusion of parametric resonance effect. should be non-linear dynamic process caused heavy damages or collapses of towers, the paper, and the structures thethe past. should be limited between 100 and 250 words. The response components bridges and other length of in abstract In sub-critical linear regime vertical and horizontal words of ‘Abstract’ and independent are set in bold andhorizontal The full paper length including abstract shall not exceedthepages. are ‘Keywords’ and therefore no full caps. response component is observed. If an amplitude of 8 vertical excitation in a structure foundation exceeds a certain limit, a vertical response component looses stability and 3-6 components arise. This post-critical regime (auto-parametric resonance) follows
Naprstek, JiriFri, 05 Dec 2014 14:58:40 GMT/record/11136Engineering Mechanics 2012
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The objective of the 18th conference is to provide a forum for researchers to discuss the state-of-the-art in Mechanics of Solids, Fluids and Thermomechanics, this particularly in connection with problems under investigation in the Czech Republic. Problems of Engineering Mechanics related to the contemplated topics can be discussed, and their solutions presented, during the sessions of the Conference, held at the Hotel of the ŽĎAS, a.s., situated in the beautiful countryside of the Žďár Highlands. EM2012 aims to provide an forum for researchers, industry practitioners, engineers and postgraduate scholars to promote, exchange and disseminate knowledge and experiences of the most recent results and advances in a wide range of topics in Engineering Mechanics.Náprstek, JiříThu, 04 Dec 2014 08:08:48 GMT/record/8924Institute of Theoretical and Applied Mechanics, AS CRAuto-Parametric Stability and Post-Critical Behavior of a Non-Linear Continuous System Under Random Seismic Excitation
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Náprstek, JiříWed, 03 Dec 2014 08:20:14 GMT/record/5249NON-LINEAR BEHAVIOUR AND DYNAMIC STABILITY OF A VIBRATION SPHERICAL ABSORBER
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Wind excited vibrations of slender structures such as towers, masts or certain types of bridges can be reduced using passive or active vibration absorbers. If there is available only a limited vertical space to install such a device, a spherical type of absorber can be recommended. In general, it is a semi-spherical horizontal dish in which a sphere of a smaller diameter is rolling. Ratio of both diameters, mass of the rolling sphere, quality of contact surfaces and other parameters should correspond with characteristics of the structure. The spherical absorber is modelled as a holonomous system. Using Lagrange equations of the second type, governing nonlinear differential system is derived. The solution procedure combines analytical and numerical processes. As the main tool for dynamic stability investigation the 2nd Lyapunov method is used. The function and effectiveness of the absorber identical with those installed at the existing TV towers was examined in the laboratory of the Institute of Theoretical and Applied Mechanics. The response spectrum demonstrates a strongly non-linear character of the absorber. The response amplitudes at the top of a TV tower with spherical absorber were reduced to 15-40% of their original values.
Náprstek, JiříWed, 19 Nov 2014 13:45:43 GMT/record/4674Columbia University in the City of New YorkFlutter stability condition of bluff body with respect to stochastic approach
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This article analyses the conditions of aeroelastic stability of a beam with rectangular cross-section also with consideration of random noises. The aeroelastic parameters and stability conditions are presented as functions of the wind velocity. Random noises are shown to have not only destabilizing but also stabilizing effects. The geometrical forms of their stability domains are identified in frequency plane. Critical wind velocity for flutter and other instabilities is calculated using Routh-Hurwitz criterion applied on the characteristic polynomial of the set of differential equations. Theoretical results are compared with those obtained by experimental measurements in a wind tunnel.
Hračov, StanislavTue, 18 Nov 2014 17:57:59 GMT/record/4325American Association for Wind Engineering, 2005Engineering Mechanics 2009
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Náprstek, JiříFri, 14 Nov 2014 08:59:20 GMT/record/3852Institute of Theoretical and Applied Mechanics, AS CR, v.v.i., PragueEngineering Mechanics 2006
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Náprstek, JiříWed, 12 Nov 2014 10:17:18 GMT/record/3410Institute of Theoretical and Applied Mechanics, AS CR, v.v.i., PragueEngineering Mechanics 2003
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Náprstek, JiříFri, 24 Oct 2014 06:16:51 GMT/record/971Institute of Theoretical and Applied Mechanics AS CR, PragueINSTABILITY ONSET OF RECTANGULAR PRISMATIC BEAMS IN THE WIND FLOW
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Abstrakt: This paper describes a part of theoretical and experimental research dealing with the problem of the aeroelastic instability onset of slender rectangular beams in the air stream. The fluid-structure interaction response is modeled using two degrees-of-freedom system oscillating in the potential flow. The coupling of the translation and rotation is due to nonconservative and gyroscopic forces. The linearized differential equations of motion are solved qualitatively and the solution is analyzed in the frequency plane. Numerical solution of four examples is based on the aerodynamics lift and moments that are expressed by means of Theodorsen's circulatory function. Solution is given in the form of frequencies of the aeroelastic modes and the critical flutter velocity. A mechanical model of a structure with adjustable parameters has been designed in order to compare the theoretical results with forthcoming experiments in the wind tunnel. Abstract: This paper describes a part of theoretical and experimental research dealing with the problem of the aeroelastic instability onset of slender rectangular beams in the air stream. The fluid-structure interaction response is modeled using two degrees-of-freedom system oscillating in the potential flow. The coupling of the translation and rotation is due to nonconservative and gyroscopic forces. The linearized differential equations of motion are solved qualitatively and the solution is analyzed in the frequency plane. Numerical solution of four examples is based on the aerodynamics lift and moments that are expressed by means of Theodorsen's circulatory function. Solution is given in the form of frequencies of the aeroelastic modes and the critical flutter velocity. A mechanical model of a structure with adjustable parameters has been designed in order to compare the theoretical results with forthcoming experiments in the wind tunnel.Pospíšil, StanislavThu, 23 Oct 2014 15:39:42 GMT/record/922Institute of Mechanics and Solids, FME, TU BrnoINTERACTION OF A PVC-BEARING WITH A BRIDGE STRUCTURE
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Abstrakt: Long-term observation of bridges supported by bearings made of synthetic materials reveals a steady horizontal deformation increase of these elements. This process can be very dangerous for the bridge as a whole. Therefore an applicable theoretical model should be developed and implemented to predict the level of these deformations and to give adequate recommendations to design practice. While a short-term response corresponds rather with the Voigt model, the long-term records have a trend of a non-uniform increase of deformations respecting the Maxwell model. Therefore influences of horizontal time variable loading can accumulate successively. The process of an increase can be either stabilized approaching to horizontal asymptotic line or it can lose the stability in a certain moment and starts to rise beyond any limits. The mathematical model of the system is composed ofVoigt and Maxwell elements in a form of a system of linear differential equations. The system is solved either directly or in an integro-differential form using the Laplace transformation. The general and several special cases of external excitation are investigated in details. Closed form results are presented for impulse and Heaviside types of the loading. Experimental measurement in a laboratory and approximative analyses have been done and compared with results obtained by theoretical investigation. Abstract: Long-term observation of bridges supported by bearings made of synthetic materials reveals a steady horizontal deformation increase of these elements. This process can be very dangerous for the bridge as a whole. Therefore an applicable theoretical model should be developed and implemented to predict the level of these deformations and to give adequate recommendations to design practice. While a short-term response corresponds rather with the Voigt model, the long-term records have a trend of a non-uniform increase of deformations respecting the Maxwell model. Therefore influences of horizontal time variable loading can accumulate successively. The process of an increase can be either stabilized approaching to horizontal asymptotic line or it can lose the stability in a certain moment and starts to rise beyond any limits. The mathematical model of the system is composed ofVoigt and Maxwell elements in a form of a system of linear differential equations. The system is solved either directly or in an integro-differential form using the Laplace transformation. The general and several special cases of external excitation are investigated in details. Closed form results are presented for impulse and Heaviside types of the loading. Experimental measurement in a laboratory and approximative analyses have been done and compared with results obtained by theoretical investigation.Náprstek, JiříThu, 23 Oct 2014 15:39:40 GMT/record/900Institute of Mechanics and Solids, FME, TU BrnoNumerické řešení úloh stochastické mechaniky: Numerical solution of problems of stochastic mechanics.
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Práce popisuje některé nové numerické metody řešení stochastických diferenciálních rovnic s aplikací v seismickém inženýrství. The text brings some modified methods for solution of stochastic differential equations with applications in the earthquake engineering.Thu, 10 Jul 2014 13:37:33 GMT/record/81Ústav teoretické a aplikované mechaniky AV ČR, v.v.i. Vlastní čísla řídkých, pozitivně definitních matic s hyperprvkovou strukturou: The eigenvalues of sparse SPD block matrices with
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Čtvercová matice je rozdělena na hyperprvky. Diagonální hyperprvky jsou vždy čtvercové, mohou však mít obecně různé řády. imodiagonální hyperprvky jsou tedy obecně obdélníkové. Nenulových mimodiagonálních hyperprvků je v matici velmi málo, a proto je účelné při zpracování matice vycházet z její řídké struktury. Cílem diplomové práce bylo posoudit vhodnost uvedeného přístupu při hledání několika extrémních vlastních čísel zobecněného problému Ax = Bx; kde A je symetrická, B je pozitivně definitní a je možno provést její Choleského rozklad. V první části se práce zabývá metodou simultánních iterací, v druhé iterační metodou založenou na konsrukci iteračních podprostorů Lanczosovým algoritmem se selektivní reortogonalizací. V závěru práce je uvedena dokumentace k přiloženému programu GEISO, vytvořeného pro testování zmíněných metod. The thesis deals with determination of several dominant eigen-values of large sparse block matrices. Generalized eigen-value problem Ax=Bx is assumed, where A is SPD matrix.Wed, 09 Jul 2014 17:47:26 GMT/record/78Matematicko-fyzikální fakulta UK, Praha