A unified dynamic modeling for FGM sandwich conical shell built-in reinforcing plate in airflow environment

In this paper, a unified dynamic modeling for investigating the free and forced vibration of the functionally graded material (FGM) sandwich conical shell built-in reinforcing plate structures with arbitrary curve coupled boundaries is established. The structure is split into three structures by the intercept b and slope k of the relative position intersection curve which include hyperbola, parabola etc. The subshell is FGM sandwich shell and subjected to a temperature distribution field and airflow environment. Theoretical model of the substructure is expressed by using the Jacobian differential quadrature method (JDQM). Thereinto, the governing equations are derived from the Hamilton principle based on the first-order shear theory. To solve the coupling problem of curve boundaries in modeling process, a general penalty function is used to describe it. On this basis, a novel coupling method of spatial curve integral penalty function is developed by the coordinate transformation of the curve boundary displacement function. After comparing with the finite element method (FEM) results and verifying the effectiveness of the theoretical model, a series of numerical cases of the effects of geometry, material distribution, temperature field and incoming airflow velocity on the free and forced vibration characteristics are presented, which provides a reliable framework for studying the dynamic behavior of the FGM sandwich conical shell built-in reinforcing plate exposed in the airflow. In the parametric study, it was observed that increasing the intercept b, while keeping the slope k constant, can enhance the performance of the structure.