length Vibration analysis and critical speeds of a rotating functionally graded conical shell stiffened with Anisogrid lattice structure based on FSDT

The present study explores the frequency characteristics and critical speeds of rotating functionally graded truncated conical shells stiffened by anisogrid lattice structures. The shell and stiffener structures are transformed into an equivalent conical shell with variable stiffness and density using the smeared method. A dynamic model of the rotating equivalent structure is developed based on the first-order shear deformation theory in order to account for the effects of shear deformation and rotational inertia. By taking centrifugal and Coriolis accelerations and initial hoop tension into account, the motion equations with variable coefficients are derived using Hamilton's principle and then are solved numerically using the generalized differential quadrature method. The obtained results under different conditions are validated by comparing them with existing data in the literature, and reliable precision is observed. A comprehensive parametric study is conducted on the frequencies of backward and forward travelling waves, with a special focus on critical speeds of the proposed conical structure.