Abstract
The vibrations of flexible structures in practice are described by nonlinear models of strings, beams, plates, and so on. This paper is concerned with longitudinal vibrations of a thermoelastic beam equation. Our main result is the general decay of the system. Using the multiplier method and some properties of the convex functions, we establish the general decay of energy.
Highlights
Speaking, the vibrations of flexible structures in practice are described by nonlinear models of strings, beams, plates, and so on
The linearized vibrations of flexible structures are usually governed by partial differential equations, in particular, by the second-order wave equation and the fourth-order Euler-Bernoulli beam equation [ ]
Proof We prove this lemma by using the method developed by Guesmia [ ]
Summary
The vibrations of flexible structures in practice are described by nonlinear models of strings, beams, plates, and so on. If we assume that the heat flux satisfies a different thermal law, we can obtain flexible structures with different thermal effects. Taking into account all considerations mentioned, in this paper, we consider the following longitudinal vibrations of a thermoelastic beam equation with past history: m(x)utt – p(x)ux + δ(x)uxt x + κθxt = ,
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