Calculation of natural frequencies of doubly curved laminated shells using a modified higher order zigzag theory

Abstract

In this study, the analysis of free vibrations for doubly curved laminated shells has been performed with modified higher order zigzag theory (MHOZT). This approach incorporates higher order displacement kinematics and considers both transverse normal and shear strains. The model assumes that the displacement fields within the plane are a combination of a global cubicly varying field and a locally zigzag linearly varying field. On the other hand, the out-of-plane displacement field varies quadratically with shell thickness coordinates. This formulation considers extended thickness criteria, ensuring the inclusion of the ratio of thickness to the radius of curvature (z/R) in strain displacement relations. Additionally, this model guarantees that there is no transverse shear stress at the extreme surfaces of the shell and that inter-laminar shear stress at interfaces is continuous. To implement this formulation effectively, a C° finite element is used. The outcomes are compared against a three-dimensional (3D) elasticity solution, as well as other pertinent results available in the literature. The suggested model accurately predicts the vibration characteristics of laminated shells, showing good agreement with the 3D elasticity solutions.