Wyniki wyszukiwania - BazTech

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Mathematical simulation of the saprapel grinding by means of the shock loads

Didukh V., Polishuuk M., Turchyn I.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2014

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Vol. 3, No 4

3--9

EN

The article discusses the process of grinding of the solid aggregates of the lacustrine sapropel based on the model of mechanics of deformed solid body. As the result of simulation the initially-final problem on theory of elasticity is solved by the method of integral transformations. The research presents a numerical description of the tensed and deformed states of the solid aggregates of sapropel in dependence with the rates of loadings and geometric parameters. It discovered space and time distribution of the main tangent stresses influencing sufficiently the process of destruc-tion and degree of the given material grinding.

2

Application of integral transformations to analytical solution of non-stationary states of stress

Adamek V., Vales F., Las V.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2003

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nr 21

7-12

EN

This work concerns the application of integral transformations U> (fie analytical solution of non-stationary state of stress in a thin homogenous isotropic viscoelastic plate. Owing to the axial symmetry of applied loading and the infinite geometry of the plate, the problem is solved as an axisymmetric one 'md the cylindrical spatial coordinates are used. The theory of thin plates with -1cral corrections is used during the derivation of motion eąuations. After that, the system of two dependent partial integrodifferential equations of the second oidcr is solved using the Laplace and Hankel transformation in the time and spatial domain, respectively. The transforms of unknown functions representing deflection and deflection angle are obtained.

3

O zachowaniu warunku Hӧldera w przekształceniu Hilberta

Grabowski J.

Biuletyn Wojskowej Akademii Technicznej

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2000

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Vol. 49, nr 10

123-149

PL

W pracy tej wykazano następującą własność przekształcenia Hilberta: jeżeli funkcja zespolona zmiennej rzeczywistej spełnia warunek Hӧldera na osi rzeczywistej i jej obraz w przekształceniu Hilberta istnieje w punkcie zero płaszczyzny zespolonej otwartej, to istnieje on również w każdym punkcie tej płaszczyzny i spełnia warunek Holdera na osi rzeczywistej oraz w półpłaszczyznach o nieujemnej i niedodatniej części urojonej, gdy za jego wartości na osi rzeczywistej przyjmiemy odpowiednie wartości graniczne. Podano również stałe występujące w warunku Holdera dla ww. obrazu.

EN

The following property of the Hilbert transformation was found: if a complex function of a real variable satisfies the Hӧlder condition on a real axis and its image in the Hilbert transformation exists at the zero point of the complex open plane, then the image exists also in each point of the plane and satisfies the Holder condition on the real axis as well as in the semiplane of the non negative and non positive complex part, when as its values on the real axis we take the respective boundary values. The constants appearing in the Holder condition are also given for the image.