Free vibration of joined spherical-Cylindrical panel and shells using the 2D GDQ method

In this study, free vibrations of isotropic cylindrical-spherical shell panels connected to each other were investigated. Shells and panels are created by a curve around the central symmetry axis, with a rotation of 360 degrees or less. Equations were extracted using the first-order shear deformation theory, which models the effects of shear deformation and rotational inertia well. Then, assuming Donnell kinematic and Hamilton's principle, the equations of motion for the panels were extracted. The equations were discretized in both x, θ and φ, θ directions, which correspond to cylindrical and spherical sections, respectively, using the extended differential squares method. After equating the derivatives in the equations with a polynomial expansion using the method described, the differential equations were transformed into algebraic equations. In the next step, the natural frequencies of the combined cylindrical-spherical shell panels with different boundary conditions were obtained, and the accuracy of the extracted solutions was verified using Abaqus software and reputable articles. Finally, the effects of parameters such as thickness, length of the cylindrical section, and radius of the spherical section on the natural frequencies of the desired model were investigated.