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EN
In this paper, the effect of the fractional order of the Caputo time-derivative occurring in heat conduction models on the temperature distribution in a finite cylinder consisting of an inner solid cylinder and an outer concentric layer is investigated. The inner cylinder (core) and the cylindrical layer are in perfect thermal contact. The Robin boundary condition on the outer surface and the Neumann conditions on the ends of the cylinder are assumed. An internal heat source is represented in the mathematical model by taking into account in the heat conduction equation of a function which depends on the space and time variable. An analytical solution of the problem is derived in the form of the double series of eigenfunctions. Numerical examples are presented.
EN
The paper deals with relation between inner structure of the machine and the composite material used in it and macroscopic dynamic response. It presents the experimental results of testing the relation between inner composite material structure and damping properties presented by logarithmic decrement quantity. Moreover, the paper provides the case study of application the composite material layered structure to the flexographic printing machine and results of that applications presented by printing speed.
PL
W artykule omówiono zależność między wewnętrzną budową maszyny i wykorzystanego w niej materiału kompozytowego a makroskopową odpowiedzią dynamiczną układu. Przedstawiono wyniki badań zależności między wewnętrzną strukturą materiału kompozytowego a właściwościami tłumiącymi wyrażonymi przez logarytmiczny dekrement tłumienia. Ponadto zaprezentowano studium przypadku – zastosowanie kompozytu warstwowego w konstrukcji drukarki fleksograficznej oraz wpływ tego rozwiązana na uzyskiwaną prędkość druku.
EN
In this paper, an elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends subjected to uniformly distributed internal energy generation within an inner cylinder is studied using Tresca’s yield condition and its associated flow rule. Stress, strain and displacement distributions in the composite cylinder made of elastic-perfectly plastic material are derived considering the influence of geometric parameters as well as material properties such as yield strength, modulus of elasticity, Poisson’s ratio, coefficient of thermal conduction and coefficient of thermal expansion. Yielding starts at the outer boundary or at the axis corresponding to an ‘edge regime’ of Tresca’s prism in both cases. Propagations of the plastic regions are studied due to an increase of a heat generation.
EN
In this paper, the Green’s functions which are used in solving the heat conduction problem in a composite cylinder are derived. The functions are obtained by the solution of one dimensional eigenproblems and are presented in the form of eigenfunction series. The temperature in the cylinder as a function of time and space coordinates are expressed by the Green’s functions. A numerical example is presented.
6
Content available remote Axially symmetric vibrations of finite composite poroelastic cylinders
EN
Axially symmetric vibrations of a finite composite poroelastic circular cylinder are investigated employing Biot's theory of wave propagation in poroelastic media. The composite poroelastic cylinder consists of two poroelastic cylinders of different materials bonded at the plane ends. Frequency equations for such vibrations are derived both for pervious and impervious surfaces. Let the finite composite poroelastic cylinder be homogeneous and isotropic and the boundaries free from stress. Non-dimensional phase velocity for propagating modes is computed as a function of ratio of length of cylinders in the absence of dissipation. The results are presented graphically for two types of composite poroelastic cylinders and then discussed. In general, the phase velocity of composite cylinder-I is higher than that of composite cylinder-II both for a pervious and an impervious surface.
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