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基于光谱几何方法的功能梯度材料（FGM）双层舱体状结构的振动分析

Vibration Analysis of Functionally Graded Material (FGM) Double-Layered Cabin-like Structure by the Spectro-Geometric Method.

作者信息

He Dongze, Zhong Rui, Wang Qingshan, Qin Bin

机构信息

School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China.

Hebei Innovation Center for Equipment Lightweight Design and Manufacturing, Yanshan University, Qinhuangdao 066004, China.

出版信息

Materials (Basel). 2025 Mar 10;18(6):1231. doi: 10.3390/ma18061231.

DOI:10.3390/ma18061231
PMID:40141513
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11943642/
Abstract

This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation of arbitrary boundary and coupling conditions by varying the elastic spring stiffness coefficients. The spectral geometry method is employed to represent the displacement variables of the FGM substructure, overcoming the discontinuity phenomenon commonly observed when traditional Fourier series are used. The dynamic equations of the FGM cylindrical double-walled shell with an internal structure are derived using the first-order shear deformation assumption and the Rayleigh-Ritz method, and the corresponding vibration solutions are computed. The model's reliability and prediction accuracy are confirmed through convergence checks and numerical comparisons. Additionally, parametric studies are conducted to examine the influence of material constants, position parameters, and geometric parameters on the shell's inherent characteristics and steady-state response.

摘要

本研究提出了一种光谱几何振动模型，用于分析具有内部结构的功能梯度材料（FGM）圆柱双壁壳的自由振动和强迫振动特性。使用人工虚拟弹簧方法对边界条件和耦合效应进行建模，通过改变弹性弹簧刚度系数，可以模拟任意边界和耦合条件。采用光谱几何方法来表示FGM子结构的位移变量，克服了使用传统傅里叶级数时常见的不连续现象。基于一阶剪切变形假设和瑞利-里兹法推导了具有内部结构的FGM圆柱双壁壳的动力学方程，并计算了相应的振动解。通过收敛性检查和数值比较，验证了该模型的可靠性和预测精度。此外，还进行了参数研究，以考察材料常数、位置参数和几何参数对壳体固有特性和稳态响应的影响。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/323a/11943642/61c613e53886/materials-18-01231-g018.jpg
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本文引用的文献

1
Vibration analysis of coupled conical-cylindrical-spherical shells using a Fourier spectral element method.基于傅里叶谱元法的圆锥-圆柱-球壳耦合振动分析
J Acoust Soc Am. 2016 Nov;140(5):3925. doi: 10.1121/1.4967853.