Nonlinear group and phase velocity analysis and architectural design of functionally graded tapered plates under supersonic airflow

In this research, we study the nonlinear group of phase velocity and the architectural design of functionally graded plates with variable thickness in the presence of supersonic airflow. The plates are modeled as three-directional functionally graded materials (TD-FGMs) using a quasi-3D refined theory (Q3D-RT) to capture a full representation of the interactions between the materials' properties, geometry, and loading conditions. The nonlinearities of the system are described via Von-Karman's geometric nonlinearity, subject to the constitutive equations that are modified for viscoelastic solids, where the time derivative of strain is explicitly included. The analysis encompasses several forms of aerodynamic pressure to model the supersonic flow field, including dynamic unsteady Bernoulli-type pressure, nonlinear dynamic pressure including strain coupling, krumhaar’s modified supersonic piston theory, and the viscoelastic dynamic lag model. The neural network-nerodynamic hybrid pressure model is evaluated as the most accurate model for supersonic airflow conditions. The research utilizes Hamilton’s principle to derive the governing equations before they are solved using the harmonic balance technique, along with a numerical iterative method to achieve good accuracy of the results. As part of the examination of the accuracy of the current work, the results will also be compared with the results from finite element simulations. The results analyze the effect of different material gradation, plate thickness, and supersonic airflow conditions on the dynamic response and stability of the structure. The results add new knowledge in the design and functional performance of functionally graded plates in aerospace applications, where considerations of both material nonlinearity and complex aerodynamic interactions must be taken into account. The method also provides a practically applicable framework for both analysis and design of advanced structural components, experienced with unique multi-physics situations, subject to supersonic environments. The method has potential applications in advanced aerospace vehicle development.