Second-order resonance of a plate containing long defects of integrity

We study the problem of forced transverse vibration of rectangular plate of constant thickness containing a finite number of surface latitudinal nonintersecting defects of integrity, such as blunt cracks. Based on the Ostrogradsky-Hamilton principle and the Ritz method, we constructed a system of ordinary nonlinear differential equations of the second order that describes forced vibration of the system at the subharmonical resonance of the second order. We propose an approximate trinomial expression for the vibration rule for one type of plate configuration that corresponds to the balance rule for the energies spent and dissipated at forced vibration. We present results of the numerical simulation of the second-order resonance.