Abstract: In this paper, using the method of differential inequalities, we study the existence of solutions and their asymptotic behavior, as e->0⁺ > ofDirichlt problem for second order quasttinear systems. Depending on whether the reduced solution U(t) has or does not have a continuous first-derivative in (a, b), we study two types of asymptotic behaviour, thus leading to the phenomena of boundary and angular layers.

Key words: viscoelastic material, cylindrical shell, sandwich shell, free vibration, constrained layer damping