Well-posedness and Stability of Thermoelastic Suspension Bridges with Cattaneo Heat Conduction: The Role of Viscoelastic Memory
Year: 2026
Type: preprint
Abstract: Thermoelastic suspension bridges operate under strong thermo-mechanical coupling, and the classical Fourier law fails to capture the finite speed of thermal propagation observed in low-conductivity materials such as concrete. This paper investigates a suspension bridge model in which the heat flux is governed by the Cattaneo law with relaxation time $τ$, and in which the bridge deck may or may not possess viscoelastic memory. Using operator semigroup theory, we establish well-posedness and derive sharp decay rates for both regimes. For the memoryless system ($δ=0$), we show that the semigroup is polynomially stable with rate $t^{-1/2}$ when the structural parameters satisfy $\frac{ρ_1}κ = \frac{ρ_2}{b}$, and that the rate deteriorates to $t^{-1/4}$ otherwise; moreover, exponential stability fails whenever $χ_0 \neq 0$, or $χ_0 = 0$ and $χ_1 = 0$, where $χ_0$ and $χ_1$ are parameter-dependent coefficients. In sharp contrast, when viscoelastic memory is present ($δ=1$), the semigroup becomes exponentially stable, regardless of the structural parameter ratio. This reveals a regularizing role of viscoelastic memory: it converts polynomial decay into exponential decay and removes the parameter-ratio obstruction. The results provide a theoretical basis for exploiting inherent viscoelasticity in long-span bridges and for optimizing deck parameters in memoryless structures.
Source: arXiv (Cornell University)
Authors: Zhou, Jun, He, Jiamin
Institution: Southwest University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164527751