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We consider an inhomogeneous Euler-Bernoulli (EB) beam of length $L$ clampedat both ends and subject to : an external frictional damping and a thermaleffect (Fourier law). We prove the well-posedness of the model and analyze thebehavior of the solution as $t \rightarrow + \infty.$ The existence is provedusing semigroup theory, and the exponential stabilization of solutions isobtained considering multiplier technique. A numerical illustration of theenergy decay is given, based on initial data close to a real physicalexperiment.

Stabilization of transverse vibrations of an inhomogeneous Euler- Bernoulli beam with a thermal effect