Abstract In this paper we have studied the model for arched beams problem ρ1φtt-k(φx+ψ+lω)x-k0l(ωx-lφ)=0,ρ2ψtt-bψxx+k(φx+ψ+lω)+γθtx=0,ρ1ωtt-k0(ωx-lφ)x+kl(φx+ψ+lω)=0,ρ3θtt-κθxx+β(g?θxx)+γψtx=0,documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$begin{aligned}&rho _{1}varphi _{tt}-k(varphi _{x}+psi +lomega )_{x}-k_{0}l(omega _{x}-lvarphi )=0,&rho _{2}psi _{tt}-bpsi _{xx}+k(varphi _{x}+psi +lomega )+gamma theta _{tx}=0,&rho _{1}omega _{tt}-k_{0}(omega _{x}-lvarphi )_{x}+kl(varphi _{x} +psi +lomega )=0,&rho _{3}theta _{tt}-kappa theta _{xx}+beta (g*theta _{xx})+gamma psi _{tx}=0, end{aligned}$$end{document}which reduces to the classical Timoshenko system when the arch curvature l=0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$l=0$$end{document}, the asymptotic stability of one-dimensional Timoshenko system by thermoelasticity of type III was proved by Djebabla and Tatar in Djebabla (J. Dyn. Control Syst. 16(2):189-210, 2010). The subject of this paper is to supplement these previous results by proving that the Bresse system which is considered a generalization of the Timoshenko system, is also subjected to the same sufficient condition that controls the stability of the Timoshenko system and we have shown that (exponential / polynomial) energy stability is achieved in an (exponential and polynomial) kernel function state.
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