Abstract
In this paper, we investigate the decay properties of the thermoelastic suspension bridges model. We prove that the energy is decaying exponentially. To our knowledge, our result is new and our method of proof is based on the energy method to build the appropriate Lyapunov functional.
Highlights
In recent years, increasing attention has been turned to the analysis of some classical engineering structures describing the dynamics of linear and nonlinear vibrations of suspension bridges
We prove that the coupling with the two temperatures is strong in a way that the solutions of System (1.1) decay exponentially
Our aim in this paper is to prove the uniform decay of the energy using the multipliers techniques
Summary
In recent years, increasing attention has been turned to the analysis of some classical engineering structures describing the dynamics of linear and nonlinear vibrations of suspension bridges. We consider the following coupled system of partial differential equations, given by:. The given system models a one-dimensional suspension bridge with thermal effects, where u is the vertical displacement, v is the torsional angle, and the couple (θ, φ) is the two temperatures. We need to mention here that the modeling for the first two coupled equations in (1.1) was considered in [7] with intermediate piers, and the authors proved the well-posedness of the problem and investigated the stability of the solutions. The analysis and the stability of various nonlinear suspension bridge models have been attracting many researchers (see [1,2,3,4,5,6,7,8,9,10]) and the references therein.
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