An Inverse Hyperbolic Framework for Deterministic and Uncertain Laminated Composite Structures for Free Vibration Response

Abstract

In the present work, free vibration response of laminated composite spherical and cylindrical shells is carried out with and without material uncertainties. A non-polynomial framework particularly inverse hyperbolic shear deformation theory (IHSDT) is implemented to model the structural behavior of composite shells. The governing equations are obtained by utilizing the principle of virtual work. The linear structural kinematics and Generalised Hooke’s law are also employed to include the material behavior. The coupled differential equations in explicit form are obtained. The coupling of these equations is reduced by assuming the cross ply configuration of composite structures. Further, these explicit coupled differential equations are solved in the exact manner for simply supported boundary conditions by employing a series solution. An Eigen value problem is obtained for the free vibration response. Further, in order to consider the effect of material uncertainties, Monte Carlo simulation (MCS) is implemented. The implementation of MCS enables to predict the second order statistics (mean and variance) of the free vibration response. An in-house MATLAB code is developed based on the developed formulation for deterministic as well as uncertain response. Various numerical studies are carried out to validate the present development. The effect of various parameters such as lamination sequence, material anisotropy, span-thickness ratio, radii of curvature are observed for doubly curved spherical and cylindrical shells. The effect of uncertain material properties on the free vibration response of these structure is also analyzed. It is concluded that IHSDT can be accurately and efficiently applied for the vibration analysis of doubly curved spherical and cylindrical shells. Further, the consideration of uncertain material properties for the optimum design of composite structures for vibration analysis is essential.