Modeling and Free Vibration Analysis of Variable Stiffness System for Sandwich Conical Shell Structures with Variable Thickness

This paper presents modeling and free vibration analysis of variable stiffness system for the truncated sandwich conical shell made of porous aluminum foam core with variable thickness and carbon fiber face sheets under the simply supported boundary condition. The thickness of the core layer varies along the longitudinal direction. Five different types of porosity distribution of the aluminum foam core, which contains Type-X, Type-O, Type-U, Type-V and Type-lambda along the direction of thickness, are considered. Considering the effect of thermal environment, we derive the nonlinear dynamic equations based on first-order shear deformation theory and Hamilton's principle, and obtain the natural frequencies of the system by employing the Galerkin method. The comparison and validation are conducted by contrast with the determined results of the literature. The influences of porosity distribution pattern, porosity coefficient, the total number of layers, temperature increment, semi-vertex angle, the exponent of thickness function, the minimum radius-thickness and length-thickness ratio of the core layer on the natural frequencies, modal and mode shapes are studied comprehensively.