Non-Stationary Parametric Responses Of Shear Deformable Orthotropic Plates

Governing non-linear spatial-temporal partial differential equations are derived for rectangular orthotropic plates, taking into account transverse shear deformation-a significant factor in non-metallic structures. The resulting set of dynamic temporal equations of the Mathieu-Hill type has been solved by using an asymptotic method for non-stationary linear and cyclic (fluctuating) variations of the forcing frequency,[formula]and[formula]where α, β, A0 and A1 are constants. Significant new information has been obtained: (1) the effects of large transverse shear deformation on resonance responses; (2) the effects of phase φ (defined in the text) on non-stationary responses; (3) initial disturbance converging to a periodic loop in the case of cyclic frequency; (4) the penetration phenomenon; and (5) the appearance of the separatrices (defined in the text). © 1995 by Academic Press, Inc