TITLE:
Supersonic Flutter of a Spherical Shell Partially Filled with Fluid
AUTHORS:
Mohamed Menaa, Aouni A. Lakis
KEYWORDS:
Vibration, Spherical shell, Flutter, Hybrid FEM
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.3,
May
16,
2014
ABSTRACT:
In the present study, a hybrid ?nite element method is applied to
investigate the dynamic behavior 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
element 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 considered as a velocity potential at each node
of the shell element where its motion is expressed in terms of nodal elastic
displacements at the ?uid-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. Results show that the
spherical shell loses its stability through coupled-mode flutter. This proposed
hybrid finite element method can be used efficiently for analyzing the flutter
of spherical shells employed in aerospace structures at less computational cost
than other commercial FEM software.