Analysis of Higher-Order Shear Deformable Porous Orthotropic Laminated Doubly-Curved Shallow Shells with Non-Uniformly Distributed Porosity: Nonlinear Free Vibration Response

Abstract

The present study proposes a nonlinear vibration analysis model incorporating non-uniform porosity distributions, various lamination sequences, and orientation angles. This study investigates the nonlinear free vibration behavior and natural frequency variations of porous orthotropic laminated shallow shells (OLSSs) subjected to various geometrical and material parameters, including porosity distribution, vibration amplitude, and lamination sequences. The equations of motion are derived based on Hamilton's principle and higher-order shear deformation theory (HSDT), containing von-Karman nonlinear relations. Galerkin's method is employed to solve the equations and obtain nonlinear vibration frequency formulations. The results reveal that the vibration amplitude significantly influences the natural frequency, with specific trends depending on the shell type, lamination sequence, and porosity pattern. It is observed that as the vibration amplitude increases, the influence of the non-uniform porosity patterns becomes more pronounced. Additionally, changes in the lamination sequence and aspect ratio significantly affect the frequency difference between the two shell types. This study highlights the complex inter-dependencies between the material properties, geometrical configurations, and porosity distribution patterns, providing valuable insights into the dynamic behavior of porous orthotropic shells for engineering applications.