Control of resonant oscillations of viscoelastic systems
Ismoil Safarov and Muhsin Teshaev
Available online 14 September 2023

Abstract
Structures in the form of cylindrical ribbed shells and panels are widely used in engineering and construction. The problem of the action of moving loads on an infinitely long cylindrical shell, reinforced along the outer surface with longitudinal stiffeners and containing a viscoelastic inertial filler, is considered. The moving load is transferred to the shell only through the ribs, and there is no load outside the ribs. The discreteness of the location of the ribs is taken into account by writing the equations of motion of the beams, followed by the satisfaction of the conjugation conditions. The influence of the number and stiffness of ribs on the nature of the distribution of shell displacements and contact pressure at the boundary of a viscoelastic filler is shown. The movement of the shell is described by classic equations based on the Kirchhoff--Love hypothesis; for the filler, dynamic equations of the theory of visco-elasticity are used. It has been established that the reinforcement of shells with longitudinal ribs (oscillations of a cantilevered cylindrical shell) leads to a decrease in natural frequencies and damping coefficients in some shells, an increase in the density of the spectrum of natural frequencies, and the appearance of intermediate forms and forms with the same wave numbers, but with different frequencies. External forces increase natural frequencies and damping coefficients. It is found that the frequencies for the inner edges are lower than for the outer edges. In the high-frequency zone, any efforts reduce the natural frequencies and the damping coefficient. This means that additional mass plays a more significant role than additional rigidity. Consequently, the longitudinal strengthening of the shell worsens its dynamic properties.

Mathematics Subject Classification
73E60

Keywords
moving load, shell, filler, rib stiffness, mating conditions, contact pressure

DOI
https://doi.org/10.2298/TAM220510007S

Synchronization conditions for stochastic landslide chain model with delayed coupling
Nebojša Vasović, Srdan Kostić, Kristina Todorović, and Dragoslav Kuzmanović
Available online 15 January 2024

Abstract
We examine the conditions for synchronization of landslide stochastic chain model with delayed coupling. Firstly, a new chain model for landslide dynamics is proposed, with the included effect of delayed coupling and background noise. The model is of the microscopic type, where the state of each block in the chain is influenced by the previous state of the same block and its neighbors as well as by noise. Secondly, we examine the stochastic synchronization of such a system of stochastic delay-differential equations. A sufficient condition for the exponential mean square stability of the synchronization is obtained. The sufficient condition indicates that the uni-directional asymmetric coupling induces the synchronization much more efficiently than the bi-directionally symmetric one. From the practical viewpoint, the results obtained confirm that different parts of the large unstable slope could exhibit synchronized activity under certain conditions, which indicates their possible larger influence on the structures (and generation of corresponding deformation) compared to the individual effect of unsynchronized activities.

Mathematics Subject Classification
37N99

Keywords
synchronization, time delay, noise, landslides

DOI
https://doi.org/10.2298/TAM230927001V

Investigating interfacial cracks in bi-materials through a 4-point bending model analysis
Abdeljelil Mankour and Bachir B. Belabbes
Available online 15 April 2024

Abstract
This study focuses on examining the failure behavior of interfacial cracks in bimaterial structures. Bimaterials present a unique challenge due to their composition, consisting of two materials that can be homogeneous and isotropic, with a specific emphasis on the ceramics/metal combination. The disparity in elastic and physical properties between these materials leads to stress singularities and embrittlement of the interface. In order to investigate the behavior of an interfacial crack without propagating into the individual materials, numerical simulations of a 4-point bending model were conducted. The stress intensity factors were computed at the crack tip to determine the energy release rate, which is a crucial parameter in evaluating interfacial crack behavior. The energy release rate, along with the mixed mode angle (G, ψ), provides insights into the crack's response. The findings demonstrate that an increase in the thickness ratio (H₁/H₂) of the assembled materials, as well as a reduction in the Young's modulus ratio (E₁/E₂), result in higher energy release rates for interfacial cracks in bimaterials. This indicates that the properties of the assembled materials play a significant role in determining the dominant mode of crack propagation tendency.

Mathematics Subject Classification
74B05; 74E30; 74Rxx; 74S05

Keywords
bimaterials, interfacial crack, energy release rate, mixed mode, finite element method

DOI
https://doi.org/10.2298/TAM230523002M