Well-posedness and Stability of Thermoelastic Suspension Bridges with Cattaneo Heat Conduction: The Role of Viscoelastic Memory
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 ρ1/κ = ρ2/b, and that the rate deteriorates to t−1/4 otherwise; moreover, exponential stability fails whenever χ0 ≠ 0, or χ0 = 0 and χ1 = 0, where χ0 and χ1 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.
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BibTeX
@misc{zhou2026wellposedness,
title = {{Well-posedness and Stability of Thermoelastic Suspension Bridges with Cattaneo Heat Conduction: The Role of Viscoelastic Memory}},
author = {Jun Zhou and Jiamin He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.12786},
eprint = {2606.12786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12786},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Well-posedness and Stability of Thermoelastic Suspension Bridges with Cattaneo Heat Conduction: The Role of Viscoelastic Memory
AU - Jun Zhou
AU - Jiamin He
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.12786
UR - https://arxiv.org/abs/2606.12786
AB - 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 ρ_1/κ = ρ_2/b, and that the rate deteriorates to t^−1/4 otherwise; moreover, exponential stability fails whenever χ_0 ≠ 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.
ER -