Vibration in multi-coupled functionally graded porous shells by a generalized variational method

Functionally graded porous shell structures with multi-component coupling have gained increasing prominence in advanced engineering applications due to their superior performance and tunable dynamic characteristics. This study investigates the vibration behavior of a coupled shell system consisting of a conical shell and cylindrical shell interconnected through multiple annular plates, establishing a comprehensive theoretical framework for vibration analysis. Based on the first-order shear deformation theory, unified kinematic formulations are developed to describe annular plate, cylindrical shell, and conical shell. A modified variational method incorporating interface potential is proposed to rigorously satisfy continuity conditions at multi-component junctions, effectively addressing the interface compatibility challenge in hybrid shell structures. Two types of functional gradient porosity distributions are comparatively analyzed: power law governed and trigonometric function modulated material configurations. The validity of the theoretical model is confirmed through numerical verification and published studies. Parametric investigations demonstrate that porosity distribution design can manipulate the fundamental frequencies of the coupled system, which provide critical insights for the vibration optimization of functionally graded porous shell systems in aerospace and marine engineering applications.