Rao–Nakra sandwich beam with second sound

In this manuscript, we prove the well-posedness and exponential stability for a thermoelastic structure given by a Rao–Nakra sandwich beam. The system consists of two wave equations for the longitudinal displacements of the top and bottom layers, and one Euler–Bernoulli beam equation for the transversal displacement, where, the thermal disturbances are modeled by the propagation of wave-like pulses traveling at a finite speed, that is, we remove the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law by using Cattaneo's law for heat conduction.