Open AccessAccounting for dissipation of the energy of the supple base
Author(s) -
L P Telipko,
V Yu Solod,
A D Romaniuk
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1164/1/012077
Subject(s) - dissipation , inertia , dissipative system , radius , mechanics , rotational symmetry , geometry , shell (structure) , oscillation (cell signaling) , physics , base (topology) , amplitude , classical mechanics , plane (geometry) , mathematics , mathematical analysis , materials science , optics , computer science , thermodynamics , computer security , composite material , genetics , biology
Annotation When calculating the foundations and structures on a compliant basis for the action of dynamic effects, the mathematical model of the base should reflect the real conditions for deformation of the base, due to their lamination, limited by the distribution property, weight and others. This is more, in our opinion, the axisymmetric columnar model of a compliant base is responsible, which takes into account the important properties of the ground base at a dynamic effect, as the extremity of the oscillation distribution zone and its inertia. In this case, the model allows us to determine not only the movement of the boundary plane, but also the stress-strain state of the base. With resonant phenomena, the accounting of energy dissipation during oscillations of the base is essential. The paper discusses the adaptation of the axisymmetric columnar model on a dissipative base, in which the dispersion of energy is carried out according to the complex hypothesis by E.S. Sorokin. The model in question is a cylindrical body in the form of a rod height H and radius R, large enough to believe that the amplitudes of displacements on the cylindrical surface of the rod are zero, when the rod on the outer end is loading within the centrally located circular area with a radius r , much smaller R. The basis, obeying the three-axis linear physical law, is in the conditions of axial symmetry, therefore, only vertical u and radial w movements are observed, which are functions of variables x, r, t . The solution of the dynamic Liame equations described by the deformation of the cylindrical body was carried out by the discrete method of L.V. Vinokurov, according to which the solution was found in an analytical form in the variable x , and in the variable r - in the finite-difference. The use of a method of separation of variables by Fourier, a system of discrete differential equations in private derivatives was reduced to a system of differential equations in ordinary derivatives, the integration of which was carried out using Euler substitutions. Permanent integration was determined from the boundary conditions at the end of the cylindrical rod. The solutions obtained show that energy dissipation accounting causes a phase shift between the perturbing load and the movement of the base and to a significant decrease in the amplitudes of oscillations in the resonance zone.