General stability of memory-type model for double-wall carbon nanotubes

Source abstract

We study the general stability of solutions for a doublewall carbon nanotubes (DWCNTs), modeled as coupled Timoshenko beams with viscoelastic damping acting on the transverse displacements. First, we establish the well-posedness via the Faedo-Galerkin approximation method. Then, with general decay assumption on the memory functions, the Multiplier method is used to prove a general stability of the solution energy. The viscoelastic dissipation on the transverse displacements and linear frictional damping on the longitudinal displacements are strong enough to achieve our results without imposing the equal-wave speed condition on the coefficient parameters.