Experimental observation of stabilization of tippe top spinning on a vibrating plane
Alexander A. Kilin and Yury L. Karavaev
Available online 10 January 2025

Abstract
This paper presents an experimental study of the motion of a spherical body with a displaced center of mass on a surface undergoing oscillations in the vertical plane. The phenomenon of vibrostabilization of an unstable position in which the center of mass of the body is above the geometric center of the sphere is revealed. The influence of the frequency and amplitude of oscillations of the surface on the stabilization of the unstable position of the motion of the spherical body is analyzed.

Mathematics Subject Classification
74H45; 70-05, 70E50

Keywords
spherical top, vibrating plane, stabilization, experiment

DOI
https://doi.org/10.2298/TAM241204001K

Erratum to: Symmetries and stability of motions in the Newtonian and the Hookean potentials (Theor. Appl. Mech. 49(1) (2022), 61--69) DOI: https://doi.org/10.2298/TAM220213005C
Christian Carimalo
Available online 28 February 2025

Abstract

Mathematics Subject Classification

Keywords

DOI
https://doi.org/10.2298/TAM231221002E

Viscous dissipation effects in a vertical annulus filled with fluid-saturated porous medium
Eduard Marušić-Paloka and Igor Pažanin
Available online 05 June 2025

Abstract
The investigation of heat transfer within porous medium has attracted considerable interest because of its growing practical importance. The present paper is devoted to the study of a steady-state non-isothermal fluid flow through a vertical cylindrical annulus filled with sparsely packed porous medium. The governing system is given by the Darcy-Brinkman-Boussinesq model where the heat equation includes the viscous dissipation term. The side walls are maintained at uniform temperatures, while the flow is driven by the axial pressure gradient. Introducing the thickness of the annular region as the small parameter of the problem, the goal is to derive the approximation of the flow via asymptotic analysis. Although the governing problem is coupled and nonlinear, the asymptotic solution is proposed in the explicit form and that represents our main contribution. As such, it clearly displays the effects of porous structure and viscous dissipation on the temperature and velocity distribution. Due to the viscous dissipation, we observe the increase in the heat generation leading to a raise in the temperature and velocity profile within the annulus. Moreover, it is deduced that reducing the thickness of the annular region may be employed to strengthen the seepage velocity of the working fluid.

Mathematics Subject Classification
35B40, 35Q35, 76S05

Keywords
cylindrical annulus, viscous dissipation, porous medium, asymptotic analysis

DOI
https://doi.org/10.2298/TAM250311009M