Stochastic stability of gyroscopic viscoelastic systems and applications in axially moving bands
Jian Deng and Wei-Chau Xie
Available online 08 May 2026

Abstract
This paper investigates the stochastic stability of gyroscopic viscoelastic systems subjected to parametric wide-band noise excitation. The analysis focuses on both moment stability, using moment Lyapunov exponents, and almost-sure stability, via the largest Lyapunov exponent. The wide-band noises considered include Gaussian white noise and Ornstein-Uhlenbeck noise. The Stratonovich stochastic differential equations governing the system with small damping and weak excitation are first converted to Itô stochastic differential equations through stochastic averaging techniques. An elegant mathematical framework is then introduced to approximate the moment Lyapunov exponents through stochastic transformations and an eigenvalue problem. The largest Lyapunov exponent is subsequently derived based on its relationship with the moment Lyapunov exponents. An application example involves deriving the stochastic equations of motion for an axially moving band system with fluctuating tension, analyzing its stochastic stability. The analytical approximations are validated via Monte Carlo simulations and compared with results from the literature. The study also discusses the influence of various parameters on the system’s stability, with potential applications in engineering fields.

Mathematics Subject Classification
37C75, 37N15

Keywords
stochastic stability, wide-band noise, viscoelasticity, axially moving band, moment Lyapunov exponents, largest Lyapunov exponent

DOI
https://doi.org/10.2298/TAM251127003D

Dimension reduction in elasticity
Reinhold Kienzler
Available online 03 June 2026

Abstract
From the three-dimensional linear theory of elasticity, two- and one-dimensional descriptions are derived by involving the consistent-approximation approach. The pseudo-reduction technique yields well-known and higher-order theories for quasi two-dimensional and quasi one-dimensional structural members.

Mathematics Subject Classification
74K20; 74K10

Keywords
dimension reduction, plates and discs, bars, beams and shafts, consistent approximation, pseudo reduction

DOI
https://doi.org/10.2298/TAM251115004K

Dual-mesh control-domain analysis of nonlinear problems in mechanics
Tanmaye Yashodan Heblekar, J. N. Reddy, and Arun R. Srinivasa
Available online 28 July 2026

Abstract
The dual mesh control domain method, introduced by Reddy [23], is a hybrid numerical technique that combines features of the finite element and finite volume methods. It uses integral balance statements of governing principles, as in the finite volume method, together with systematic finite element interpolation of the dependent unknown functions, as in the finite element method. This combination provides a convenient and locally conservative framework for the spatial discretization of boundary-value problems. In this article, we present dual mesh control domain formulations for nonlinear problems arising in applied mechanics. The focus is on two representative classes of problems: the finite deformation of hyperelastic solids and the flow of viscous incompressible fluids in domains with moving boundaries. For the hyperelasticity problem, the governing equations are written in the reference configuration and solved using Newton linearization. For the moving-boundary flow problem, an Arbitrary Lagrangian--Eulerian formulation is used to account for the motion of the computational mesh. Numerical examples are presented to illustrate the implementation of the method and to assess the proposed formulations.

Mathematics Subject Classification
65N30; 74B20, 76D05, 74F10

Keywords
dual mesh control domain method; nonlinear continuum mechanics; finite-deformation hyperelasticity; viscous incompressible flow; Arbitrary Lagrangian-Eulerian formulation

DOI
https://doi.org/10.2298/TAM260601007H

Classification of the geodesic curves of a sub-Riemannian LR system on the Heisenberg group in dimension 5
Milan Pavlović
Available online 19 October 2026

Abstract
The corresponding Hamiltonian system is completely integrable and we study its solutions in this paper. We obtain a complete classification of the geodesic curves by studying the reduced Hamiltonian system. Moreover, we compute $r\left(t\right)$ as the first step of the quadrature in the reduced system in the hyper-spherical coordinates and present numerical examples that illustrate the theoretical results.

Mathematics Subject Classification
53C17, 22E25, 37J35

Keywords
Heisenberg group, left-invariant metrics, sub-Riemannian metric, right-invariant distributions, completely integrable Hamiltonian system

DOI
https://doi.org/10.2298/TAM260212008P