Nonlinear vibrations in the stability region of axially functionally graded composite plates excited by periodic in-plane loads

This study discusses the parametric resonance and the nonlinear vibration response of an axially functionally graded (AFG) composite plate subjected to a harmonic in-plane load. The effective material properties of the plate are modeled using the rule-of-mixture, and the axial gradation of the material is designed with a power-law coefficient. The plate is constrained by simply supported movable edges and is modeled using a higher-order shear deformation theory. Using Hamilton’s variational principle, the governing equations, in the form of partial differential equations, are derived and discretized using the Galerkin method. The discretized equations allow for determining the region of instability under periodic in-plane loading using Bolotin’s method. The bounded region is associated with an unstable solution, and the unbounded region with a stable solution. Further, the nonlinear vibration response of the plate is obtained using the Incremental Harmonic Balance method along with the arc-length continuation method. Time-history responses are obtained in the stable and unstable regions using the Newmark-β and the Newton-Raphson methods. The influence of material properties, dynamic load, and static pre-load on the nonlinear vibration response of the plate is discussed in detail.