Shearing Viscoelasticity in Partially Dissipative Timoshenko–Boltzmann Systems

We investigate both the mathematical modeling and stability methods for a new integro-differential system referred to as the viscoelastic Timoshenko–Boltzmann model. The modeling is developed for materials with hereditary memory under the creation time scenario whose foundation goes back to Boltzmann’s superposition principle in linear viscoelasticity, complemented by Timoshenko’s assumptions concerning shearing in certain beam vibrations. The mathematical methodology provides a comprehensive characterization of the uniform stability for the partially damped Timoshenko–Boltzmann system through the identity of wave speeds on the structural coefficients and a pointwise dissipative condition on the memory kernel that does not require differential inequalities.