Free vibration of laminated cylindrical shells with a circular cutout

A semi-analytical solution method is presented for determining the natural frequencies and mode shapes of laminated cylindrical shells containing a circular cutout. The method utilizes Hamilton's principle to obtain the governing equations for the vibration response of the shell. In the derivation of governing equations, Lagrange multipliers are employed to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. The natural frequencies and the corresponding modes of the shell are determined by transforming the governing equations into a matrix eigenvalue problem. The present semi-analytical solution method accurately predicts the natural frequency and vibration modes of the shells with a cutout. The focus of this study is to investigate the effects of varying cutout size, shell radius, and laminate layup, as well as the effects of two types of boundary conditions on the shell vibration response. Selected results of the parametric studies are presented for several geometric parameters to demonstrate that this semi-analytical approach is a powerful means for optimizing design parameters.