Supersonic Flutter of a Spherical Shell Partially Filled with Fluid

Abstract

In the present study, a hybrid finite element method is applied to investigate the dynamic beha-vior of a spherical shell partially filled with fluid and subjected to external supersonic airflow. The structural formulation is a combination of linear spherical shell theory and the classic finite ele-ment method. In this hybrid method, the nodal displacements are derived from exact solution of spherical shell theory rather than approximated by polynomial functions. Therefore, the number of elements is a function of the complexity of the structure and it is not necessary to take a large number of elements to get rapid convergence. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for aerodynamic loading. It is assumed that the fluid is incompressible and has no free surface effect. Fluid is con-sidered as a velocity potential at each node of the shell element where its motion is expressed in terms of nodal elastic displacements at the fluid-structure interface. Numerical simulation is done and vibration frequencies are obtained. The results are validated using numerical and theoretical data available in literature. The investigation is carried out for spherical shells with different boundary conditions, geometries, filling ratios, flow parameters, and radius to thickness ratios