Free vibration of FGM Lévy conical panels

Free vibration analysis of open conical panels made of through-the-thickness functionally graded materials (FGMs) is analyzed in this research. Mechanical properties of the shell are distributed across the thickness based on the power law function. First order shear deformation theory of shells accompanied with the Donnell type of kinematic assumptions are used to establish the general motion equations and the associated boundary conditions. Considering the Lévy type of conical shells, which are simply supported on straight edges, a semi-analytical solution based on the trigonometric expansion through the circumferential direction combined with generalized differential quadrature (GDQ) discretization in meridional direction is developed. Due to the special configuration of the conical panel, free vibration of flat rectangular plates, flat annular and circular sectoral plates, and singly curved cylindrical panels may also be studied. Solution method is useful for any arbitrary type of free, clamped, and simply supported boundary conditions along the two other curved edges of the shell. After establishment of eigenvalue problem, a series of comparison studies are conducted to assure the validity and accuracy of the present solution. Afterwards, parametric studies are developed to examine the influences of boundary conditions, semi-vertex angle of the cone, subtended angle of the panel, power law index, and thickness to radius ratio. Influences of the aforementioned parameters on natural frequencies and the associated mode shapes are discussed.