<p style='text-indent:20px;'>In this paper we consider star-shaped viscoelastic networks, and study the large-time behaviour of these networks by proving polynomial decay rates. The energy decay rate depends on the irrationality properties of the lengths of the rods.</p>

We deal with N 0 + N 1 mixed elastic strings bounded and unbounded with Kelvin-Voigt damping. We show that the energy decays polynomially if and only if the lengths satisfy the irrationality condition KEYWORDSKelvin-Voigt damping, network of strings, strong stability, the rates of decay