Vibration and response characteristics of variable stiffness composite plates enveloping piezoelectric panels with arbitrary cutouts: a unified discretization modelling framework

This study proposes a unified discretization dynamic model using a Gauss-Legendre quadrature approach for predicting the vibration and response characteristics of composite plates with arbitrary cutouts. Curvilinear fiber layouts and piezoelectric materials are introduced in the developed model to achieve variable stiffness design and active control. The virtual spring constraint technique is incorporated to allow flexible simulation switching for various boundary conditions. In the formed computational procedures, a theoretical framework is first constructed based on the first-order shear deformation theory and Rayleigh-Ritz method, with variable fiber angles of each laminate being set using the linear path function. The plate plane is subdivided into numerous discrete nodes using the Gaussian-Legendre quadrature idea, and cutout coordinates are described by mathematical mapping. A mass-stiffness assignment algorithm is implemented to characterize the missing solid elements. Forced and free vibration behaviors are obtained using the Newmark-Beta approach and eigen-parameter solvers. Convergence studies and model validations are conducted to verify the robustness and reliability of the model, and alternative parameters are identified to amplify the efficiency. The influences of variable stiffness schemes, cutouts, and electric intensity on the intrinsic characteristics and vibration response are revealed, and some suggestions for enhancing the vibration damping capacity are provided.