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