Free Vibrations of Composite Cylindrical Panels with Cutouts of General Shape

Abstract A novel single-domain Ritz method is presented for analyzing the free vibrations of laminated cylindrical panels with cutouts of general shape. The structural model of the panel is based on the first-order shear deformation theory. In this framework, the primary variables—midplane displacements and section rotations—are represented using trial functions, constructed as tensor products of one-dimensional orthogonal Legendre polynomials. The governing equations are derived by enforcing the stationarity of the total potential energy. This leads to a standard eigenvalue problem, the solution of which yields the panel’s free vibration frequencies and modes. To compute the matrices involved in the governing equations, a specialized integration approach is employed, which leverages an implicit cutout representation via level set functions, ensuring accurate integral evaluation over the panel domain. A series of validation results showcasing the method’s accuracy and ability to handle various configurations, including different boundary conditions, laminate layups, cutout geometries and positions, are proposed to demonstrate the effectiveness of the proposed method.