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<p>This paper studies the free vibration of functionally graded triply periodic minimal surface (FG-TPMS) cylindrical shells with elastic boundary restraints. The shells are made from FG-TPMS materials with three TPMS types: Gyroid (G), Primitive (P), and I-graph and Wrapped Package-Graph (IWP); each is examined with different mass-density patterns. Elastic supports at both shell ends are modeled using the artificial spring technique (AST). The governing equations of the shell are developed based on the first-order shear deformation theory (FSDT) and solved by the Rayleigh–Ritz method using modified Chebyshev trial functions. The key contribution of this work is the development of free vibration formulations for FG-TPMS cylindrical shells incorporating elastic boundary restraints—an aspect not previously reported in the literature. A detailed parametric study is carried out to assess how different TPMS geometries, mass–density gradation patterns, boundary conditions, circumferential mode numbers, geometric characteristics and spring stiffness levels influence the shell’s natural frequencies. The findings provided in this study offer reliable reference data for numerical verification and support future efforts in the design and optimization of FG-TPMS cylindrical shell structures.</p>

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Free Vibration of Functionally Graded Triply Periodic Minimal Surface Cylindrical Shells with Elastic Boundary Constraints

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Van-Loi Nguyen

摘要

This paper studies the free vibration of functionally graded triply periodic minimal surface (FG-TPMS) cylindrical shells with elastic boundary restraints. The shells are made from FG-TPMS materials with three TPMS types: Gyroid (G), Primitive (P), and I-graph and Wrapped Package-Graph (IWP); each is examined with different mass-density patterns. Elastic supports at both shell ends are modeled using the artificial spring technique (AST). The governing equations of the shell are developed based on the first-order shear deformation theory (FSDT) and solved by the Rayleigh–Ritz method using modified Chebyshev trial functions. The key contribution of this work is the development of free vibration formulations for FG-TPMS cylindrical shells incorporating elastic boundary restraints—an aspect not previously reported in the literature. A detailed parametric study is carried out to assess how different TPMS geometries, mass–density gradation patterns, boundary conditions, circumferential mode numbers, geometric characteristics and spring stiffness levels influence the shell’s natural frequencies. The findings provided in this study offer reliable reference data for numerical verification and support future efforts in the design and optimization of FG-TPMS cylindrical shell structures.