On one problem, associated with lateral oscillations of elastic-viscous-relaxating rod

We obtain the solution of the problem about lateral oscillations of elastic-viscous-relaxating rod of finite length, variable profile, and variable momentum of rotation inertia of rod elements about the axis that is perpendicular to oscillation plane.

The inverse problem of recovering an unsteady linear load for an elastic rod of finite length

The main purpose of the paper is to obtain solutions for new non-stationary inverse problems for elastic rods. The objective of this study is to develop and implement new methods, approaches and algorithms for solving non-stationary inverse problems of rod mechanics. The direct non-stationary problem for an elastic rod consists in determining elastic displacements, which satisfies a given equation of non-stationary oscillations in partial derivatives and some given initial and boundary conditions. The solution of inverse retrospective problems with a completely unknown space-time law of load distribution is based on the method of influence functions. With its application, the inverse retrospective problem is reduced to solving a system of integral equations of the Volterra type of the first kind in time with respect to the sought external axial load of the elastic rod. To solve it, the method of mechanical quadratures is used in combination with the Tikhonov regularisation method.

Gallium as a Metrology Substance for Measuring Thermal Conductivity of Metals

In the presented work the effective thermal conductivity of steel was received from the simple experiment in which the change of phase metrology-matter was applied [1]. As the metrology-matter gallium was used.The change of phase process plays role of the heat source. During the change of phase period the temperature is constant. A quasi-stationary temperature fields allows to use the stationary model of heat transfer calculations. The model is a cylindrical rod of finite length losing heat out one face to melting-substance and by radiation from surface, respectively. All process measurement was carried out in vacuum. Measurement of thermal conductivity quasi-stationery method is practiced at the Department of Thermodynamics at Rzeszow University of Technology. This method has application in measurement of thermal conductivity of good conductors.

GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS

The Kirchhoff elastic rod is one of the mathematical models of equilibrium configurations of thin elastic rods, and is defined to be a solution of the Euler–Lagrange equations associated to the energy with the effect of bending and twisting. In this paper, we consider Kirchhoff elastic rods in a space form. In particular, we give the existence and uniqueness of global solutions of the initial-value problem for the Euler–Lagrange equations. This implies that an arbitrary Kirchhoff elastic rod of finite length extends to that of infinite length.

Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods

We discuss thermodynamical restrictions for a linear constitutive equation containing fractional derivatives of stress and strain of different orders. Such an equation generalizes several known models. The restrictions on coefficients are derived by using entropy inequality for isothermal processes. In addition, we study waves in a rod of finite length modelled by a linear fractional constitutive equation. In particular, we examine stress relaxation and creep and compare results with the quasistatic analysis.

On solution of initial-boundary problem, connected with longitudinal impact of elastic-viscous rod

We conduct the solution, by Fourier method, of the problem about longitudinal oscillations caused by impact to one end of elastic-viscous rod of finite length with variable lateral section in the case when the condition of fixation of another end of the rod is represented by linear equation in displacement and deformation.