Free vibration of laminated composite super-elliptic shells using generalized differential quadrature method

Laminated composite shell structures are extensively utilized in many engineering applications due to their lightweight structure, low cost and satisfactory mechanical properties. This study presents, for the first time, an investigation of free vibrational characteristics of a complex shell structure which will be referred as superelliptic (SE) shell structure made of laminated composite material. Unlike conventional cylindrical and elliptical shell formulations, SE shell formulation is capable of representing both cylindrical, elliptical and quasi rectangular shell structures. First order shear deformation theory (FSDT) and virtual work principle are employed to derive the equation of motion and compute the deformations. Spatial derivatives are computed via generalized differential quadrature (GDQ) method. Standard eigenvalue problem is solved to extract natural frequencies and mode shapes. Effects of ellipticity, ovality of SE shell structure, layer orientation and boundary conditions on free vibrational behavior are examined in detail.