**933**

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**Stability of a bar influenced by small and large imperfections**

Náprstek, Jiří; Fischer, Cyril

2020 - English
The geometrical and physical imperfections of systems can drastically reduce their critical loading. These imperfections are usually of stochastic character and, therefore, they act as random parametric perturbations of coefficients of corresponding differential equations. In this paper, the imperfections are introduced as multidimensional statistics on the set of a large number of realizations of the same system. As far as the amount of information is small or the imperfections themselves cannot be considered small, the convex analysis is preferable. The paper compares results obtained by both stochastic and convex analyses for hyperprism and demonstrates when each of them is more convenient to be used. Besides of the hyper-prism, the possibilities and properties of other modifications of convex method are considered, especially those based on the definition of imperfection zone marked as a centric hyper-ellipsoid or as an eccentric hyper-ellipsoid. The analytical background was brought up to the level when only a few configurations of imperfections are sufficient to be evaluated numerically. These configurations are obtained by means of the convex analysis as points of extreme critical loading using the Lagrange method of constrained extremes.
Keywords:
*convex domain method; system stability; hyper-prism and hyper-ellipsoid domains*
Available at various institutes of the ASCR
Stability of a bar influenced by small and large imperfections

The geometrical and physical imperfections of systems can drastically reduce their critical loading. These imperfections are usually of stochastic character and, therefore, they act as random ...

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**Random response of a dynamic system under polynomial of a white noise**

Náprstek, Jiří; Fischer, Cyril

2020 - English
Many types of external additive random excitation of dynamic systems admit to be modelled as a combination of powers of a Gaussian noise. Such a type of excitation produces a non-Gaussian response even if the dynamic system is linear and the excitation is additive only. Although the excitation as a whole is non-Gaussian, the problem can be transformed into the form of a linear system with an additive and multiplicative white noise excitation which _nally produces a non-Gaussian response. The general method of transformation, the respective FPK equation, basic stochastic moments of the response, and a demonstrative example are discussed.
Keywords:
*non-Gaussian excitation; nonlinear filtering; Kronecker algebra*
Available at various institutes of the ASCR
Random response of a dynamic system under polynomial of a white noise

Many types of external additive random excitation of dynamic systems admit to be modelled as a combination of powers of a Gaussian noise. Such a type of excitation produces a non-Gaussian response ...

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**Rukopis lokátorů - rozdíly v triangulaci**

Loits, André; Drdácký, Tomáš; Buzek, Jaroslav; Zadražil, Tomáš

2020 - Czech
Převážná většina současných evropských měst má svůj počátek v období středověku. Na našem území většina měst vznikla od počátku 12. století do poloviny 14. století za doby vlády posledních Přemyslovců. Městské půdorysy jsou originální, a přestože je složité je vizuálně na první pohled porovnat, vykazuje jejich zdánlivá různorodost určitá pravidla a systém. Toto zjištění bylo ověřeno analýzou 29 českých a moravských měst. Příspěvek představuje výsledky rozboru vybraných měst. Při zakládání měst hrál zásadní roli lokátor, pověřený tehdejším investorem zorganizovat osídlení nové lokace. Vzhledem k počtu a těsnému sledu zakládaných měst je pravděpodobné, že města byla vyměřována zkušenými geometry, s teoretickými i praktickými znalostmi geometrie. Složitost úkolu a zároveň doložený fakt, že v rozmezí několika desetiletí vzniklo velké množství měst vede k závěru, že existoval prověřený, do jisté míry rutinní přístup k lokaci, který znamenal jistotu úspěšného vyměření a zrod fungujícího města. Příspěvek představuje rozdílné postupy vyměření půdorysné osnovy měst ve dvou režimech triangulace a jim odpovídajícím čtyřem systémům výchozích základních stanovisek, ze kterých mohlo být město a jeho ohrazení vytyčeno. Práce volně navazuje na text Triangulated medieval cities, publikovaný na konferenci Architektura v perspektivě v roce 2017 a shrnuje výsledky čtyřletého výzkumu. The vast majority of contemporary European cities have their origins in the Middle Ages. ln our territory, most towns were founded from the beginning of the 12th century to the middle of the 14th century during the reign of the last Přemyslids. Urban city layouts are original, and although it is difficult to visually compare them at first glance, their apparent diversity shows certain rules and systems. This finding was verified by an analysis of 29 Czech and Moravian cities. The paper presents the results of the analysis of selected cities. The locator, commissioned by the then investor to organize the settlement of the new location, played a crucial role in the founding of the towns. Due to the number and close sequence of founded cities, it is probable that the cities were measured by experienced surveyors, with theoretical and practical knowledge of geometry. The complexity of the task, as well as the proven fact that a large number of cities have emerged over several decades, leads to the conclusion that there was a proven, somewhat routine approach to the site, which ensured certainty in the survey and the birth of a functioning city. The paper presents identified types of procedures for surveying the city layout in two modes of triangulation and corresponding four systems of initial base stations, from which the city and its boarder was delineated. The work loosely follows the text Triangulated medieval cities, published at the conference Architecture in Perspective in 2017 and summarizes the results of four years of research work.
Keywords:
*historical cities; location; medieval triangulation; urban type; groma*
Available at various institutes of the ASCR
Rukopis lokátorů - rozdíly v triangulaci

Převážná většina současných evropských měst má svůj počátek v období středověku. Na našem území většina měst vznikla od počátku 12. století do poloviny 14. století za doby vlády posledních ...

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**Damage detection using a cogwheel load - numerical case study**

Bayer, Jan

2020 - English
A moving impulse load generated by a heavy cogwheel (CW) can be used as a testing excitation for bridges. This proposed type of dynamic load acts along the entire driving path, its intensity is adjustable, and it can be very efficient in the case of resonance. However, higher harmonic components are an inevitable effect of this type of loading, complicating the vibration analysis. The present study investigates suitable procedures to detect and locate damage in structures using a cogwheel load and only one or a few transducers mounted on the bridge. This arrangement seems to be sensitive to early damage indication. Damage localization is also possible, but further research will be required to increase its credibility.
Keywords:
*bridge testing; damage detection; impulse loading; vibration analysis; bridge health monitoring*
Available at various institutes of the ASCR
Damage detection using a cogwheel load - numerical case study

A moving impulse load generated by a heavy cogwheel (CW) can be used as a testing excitation for bridges. This proposed type of dynamic load acts along the entire driving path, its intensity is ...

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**Multifold stationary solutions of an auto-parametric non-linear 2DOF system**

Fischer, Cyril; Náprstek, Jiří

2020 - English
A non-linear 2DOF model of a bridge girder with a bluff cross-section under wind loading is used to describe the heave and pitch self-excited motion. Existence conditions of stationary auto-parametric response for both the self-excited case and an assumption of a harmonic load form a non-linear algebraic system of equations. Number of distinct solutions to this algebraic system depends on the frequencies of two principal aero-elastic modes and other system parameters. Thus, the system may possess none, one, or several stationary solutions, whose stability has to be checked using the Routh-Hurwitz conditions. If all quantities entering the system are continuous functions, individual solutions may exhibit (piecewise) continuous dependence on selected system parameters. Thus, multiple identified solutions to the system for a given set of parameters may actually belong to a single solution branch and their values can be determined from the knowledge of the solution branch. Such a situation may significantly simplify assessment of stability of the particular solutions and/or provides an applicable overall description of the system response.
Keywords:
*multifold solution; algebraic system; aero-elastic system; stationary vibration*
Available at various institutes of the ASCR
Multifold stationary solutions of an auto-parametric non-linear 2DOF system

A non-linear 2DOF model of a bridge girder with a bluff cross-section under wind loading is used to describe the heave and pitch self-excited motion. Existence conditions of stationary auto-parametric ...

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**Distribution of hydration products in the microstructure of cement pastes**

Hlobil, Michal

2020 - English
This case study focuses on the quantification of the amorphous hydrate distribution in the microstructure of hardened cement paste. Microtomographic scans of the hardenend cement paste were thresholded based on histogram image analysis combined with microstructural composition obtained from CEMHYD3D hydration model, to separate unhydrated cement grains, crystalline and amorphous hydrates, and capillary pores. The observed spatial distribution of the amorphous hydrate exhibited a strong spatial gradient as the amorphous gel tended to concentrate around dissolving cement grains rather than precipitate uniformly in the available space. A comparative numerical study was carried out to highlight the effect of the spatially (non)uniform hydrate distribution on the compressive strength of the hardened cement paste.
Keywords:
*cement paste; hydration products; microstructure; modelling*
Available at various institutes of the ASCR
Distribution of hydration products in the microstructure of cement pastes

This case study focuses on the quantification of the amorphous hydrate distribution in the microstructure of hardened cement paste. Microtomographic scans of the hardenend cement paste were ...

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**Probability density determination by means of Gibbs entropy probability density**

Náprstek, Jiří; Fischer, Cyril

2019 - English
A method of random response investigation of a nonlinear dynam-ical system is discussed. In particular, the solution of the probability density of a single/multi-degree of freedom (SDOF/MDOF) system response is investigated. Multiple stable equilibrium states with possible jumps of the snap-through type among them are considered. The system is Hamiltonian with weak damping excited by a set of non-stationary Gaussian white noises. The solution, which is based on the Gibbs principle of the maximum entropy of probability, can be employed in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker-Planck equation (FPE) for the system considered or from the system of ordinary di_erential equations for the stochastic moments of the response derived from the relevant FPE
Keywords:
*Fokker-Planck equation; Gibbs entropy functional; maximum entropy; probability density principle*
Available at various institutes of the ASCR
Probability density determination by means of Gibbs entropy probability density

A method of random response investigation of a nonlinear dynam-ical system is discussed. In particular, the solution of the probability density of a single/multi-degree of freedom (SDOF/MDOF) system ...

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**Moving dynamic test loads for road bridges - a case study**

Bayer, Jan; Urushadze, Shota

2019 - English
Two types of dynamic testing load for bridges - driving sprung mass and driving impulse load - areexamined from the drive-by identification point of view. Numerical studies in ANSYS using contact elements and in MATLAB using a modal solution together with coupling force were performed. Equations for the estimation of the impulse load caused by a rolling cogwheel were suggested. The experiments confirmed that a driving impulse load is more efficient in exciting bridge vibrations. This, together with the fact that impulse loading is not sensitive to surface roughness, leads to the conclusion that, as a method for bridge health monitoring, impulse loading is more promising than using a driving sprung mass
Keywords:
*drive-by identification; bridge testing; moving sprung mass; impulse loading; vibration measurements; laboratory experiments*
Available at various institutes of the ASCR
Moving dynamic test loads for road bridges - a case study

Two types of dynamic testing load for bridges - driving sprung mass and driving impulse load - areexamined from the drive-by identification point of view. Numerical studies in ANSYS using contact ...

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**System response with random imperfections in coefficients on the space of realizations**

Náprstek, Jiří; Fischer, Cyril

2019 - English
The contribution is concerned with the analysis of the simultaneous effect of a random perturbation and a white noise in the coefficient of the system. The excitation of the system of the 1-st order is described by the sum of a deterministic signal and an additive white noise which is partly correlated with the parametric noise. The random perturbation in the parameter is considered as a statistics in a set of realizations. It reveals that the density of probability of perturbations must be limited in the phase space, otherwise the system would lose the stochastic stability in probability. The width of the permissible zone depends heavily on the intensity of the parametric noise, the extent of correlation with the additive excitation noise and the type of probability density. The general explanation is demonstrated on cases of normal, uniform and truncated normal densities of probability.
Keywords:
*noisy signal; filtration; random imperfections*
Available at various institutes of the ASCR
System response with random imperfections in coefficients on the space of realizations

The contribution is concerned with the analysis of the simultaneous effect of a random perturbation and a white noise in the coefficient of the system. The excitation of the system of the 1-st order ...

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**Deformation response of polydimethylsiloxane substrates subjected to uniaxial quasi-static loading**

Vinařský, V.; Martino, F.; Forte, G.; Šleichrt, Jan; Rada, Václav; Kytýř, Daniel

2019 - English
To investigate cellular response of cardiomyocytes to substrate mechanics, biocompatible material with stiffness in physiological range is needed. PDMS based material is used for construction of microfluidic organ on chip devices for cell culture due to ease of device preparation, bonding, and possibility of surface functionalization. However it has stiffness orders of magnitude out of physiological range. Therefore, we adapted recently available protocol aiming to prepare substrates which offer stiffness in physiological range 5−100 kPa using various mixtures of Sylgard. An in-house developer loading device with single micron position tracking accuracy and sub-micron position sensitivity was adapted for this experimental campaign. All batches of the samples were subjected to uniaxial loading. During quasi-static experiment the samples were compressed to minimally 40% deformation. The results are represented in the form of stress-strain curves calculated from the acquired force and displacement data and elastic moduli are estimated.
Keywords:
*quasi-static loading; hyperelasticity; polydimethylsiloxane substrates; in-situ loading device*
Available at various institutes of the ASCR
Deformation response of polydimethylsiloxane substrates subjected to uniaxial quasi-static loading

To investigate cellular response of cardiomyocytes to substrate mechanics, biocompatible material with stiffness in physiological range is needed. PDMS based material is used for construction of ...

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