Nonlinear dynamics and resonance analysis of multilayer porous FG shallow shells reinforced with FG oblique stiffeners under two-term excitation

Abstract

The present research examines the nonlinear dynamic behaviors of multilayer porous functionally graded (MPFG) shallow shells reinforced with FG oblique stiffeners (FGOS), under two-term excitation and combination resonances, utilizing a semi-analytical method. The shallow shells have three layers consisting of ceramic, porous FG (PFG), and metal. The oblique stiffeners are made of FG material and also reinforce the shell internally. In addition, two types of PFG layers, including evenly and unevenly distributed porosities, are examined in the current study. The technique of Lekhnitskii's smeared stiffeners is employed to simulate the stiffeners. Employing a semi-analytical approach, the research introduces a nonlinear model formulated using the first-order shear deformation theory (FSDT) combined with stress functions. Furthermore, the Galerkin method is utilized to discretize the nonlinear governing equations (NGEs). Eventually, the method of multiple scales (MMS) is employed to derive the necessary theoretical relations for examining combination resonance, and P-T method is employed to analyze the vibration responses. To validate the findings of this study, comparisons are made with prior studies as well as with P-T method. The analysis reveals significant impacts of stiffener angles and material parameters on the vibration responses, demonstrating enhanced dynamic performance and resonance management capabilities of the proposed shell configurations. Key findings include the identification of optimal stiffener configurations that minimize resonance amplitudes. The outcomes of this study can serve as reference points for engineers and researchers involved in the design and analysis of MPFG shallow shells reinforced with FGOS.