Jacobi–Ritz method for free vibration analysis of medium-thickness sandwich cylindrical shells utilizing the layerwise theory and domain decomposition method

Abstract

This study establishes the core theoretical foundation by coupling the Layerwise Theory (LWT) and First-Order Shear Deformation Theory (FSDT). Then, the Jacobi-Ritz method and Domain Decomposition Method (DDM) are integrated into this foundation to construct a four-layer synergistic coupled analysis framework. This framework solves the technical challenges in vibration analysis of medium-thickness sandwich cylindrical shells (with a thickness-to-radius ratio $h/R=0.05-0.2$). Exclusive DDM connection energy formulas and matrices are derived to adapt to the LWT-FSDT framework, ensuring interlayer displacement continuity and mechanical consistency between subdomains. Global displacement functions are constructed within this framework using Jacobi polynomials. Moreover, the cylindrical shell is discretized into subdomains connected by virtual springs via DDM. This design suppresses high-order oscillations in non-segmented models, reduces the sensitivity of Jacobi parameters by two orders of magnitude, and eliminates the need for complex parameter optimization. According to the numerical result validation, when the core material modulus is ≥ 100 MPa, the maximum error between the theoretical results and finite element method (FEM) results is ≤ 2.16 %. The framework accurately captures the interfacial behavior of heterogeneous materials (with an error of 1.34 %) and quantifies its applicable boundary (the error is approximately 10 % when the core modulus is 10 MPa). Lastly, the proposed framework provides a robust and efficient analytical tool for the engineering design of medium-thickness sandwich cylindrical shells, especially those with heterogeneous material configurations.