Dynamic instability of viscoelastic orthotropic laminated plates

The dynamic instability of viscoelastic specially orthotropic laminated plates, subjected to in-plane parametric excitation, is investigated. The viscoelastic behavior is caused by the polymeric matrix of the fiber-reinforced material, and a micromechanics analysis is employed in order to obtain the time-dependent relaxation functions of the unidirectional lamina. The Boltzmann representation involved in the stress-strain relation of the laminated plate leads to an integrodifferential equation of motion. The stability boundaries of this equation are determined analytically by using the multiple-scales method. Time-dependent instability regions and minimum load parameter are derived, together with an expression for the critical time at which the system, with a given load amplitude, will turn unstable.