Abstract

In this paper, the effect of the porosity coefficient and its distribution on the natural frequencies and mode shapes of a thin and thick cylindrical shell made of asymmetric porous materials is investigated analytically. The mechanical properties of the porous shell are non-uniform in the thickness and isotropic in the circumferential directions. The displacement field is assumed based on the first-order Mirsky–Hermann theory by considering the effects of transverse normal strain and rotary inertia. For more accurate stress resultants, the trapezoidal shape factor is considered in the formulation. The constitutive relations follow Biot’s theory for the porous materials and the kinematic of the problem is linear. The governing equations include four coupled partial differential equations that are solved using an analytical method and they are compared with the finite element analysis. By the sensitivity analysis, the effects of porosity distribution and geometry of the cylinder on the natural frequencies and mode shapes are studied. The results show that the largest frequency corresponds to the material which has the maximum density inside of the cylinder.

Abbreviations: FSDT, first-order shear-deformation theory; 2D, two-dimensional; 3D, three-dimensional; FG, functionally graded; FGM, functionally graded materials; DQ, differential quadrature; MDEW, maximum density in outer (external) wall; MDIW, maximum density in inner wall; C.C, complex conjugate (of proceeding terms)

摘要

本文分析研究了孔隙率系数及其分布对非对称多孔材料薄厚圆柱壳的固有频率和振型的影响。. 多孔壳的力学性能在厚度上是不均匀的，在圆周方向上是各向同性的。位移场假设基于一阶 Mirsky-Hermann 理论，考虑了横向法向应变和转动惯量的影响。对于更准确的应力合成，在公式中考虑了梯形形状因子。多孔材料的本构关系遵循Biot的理论，问题的运动学是线性的。控制方程包括四个耦合偏微分方程，它们使用解析方法求解，并与有限元分析进行比较。通过灵敏度分析，研究了孔隙率分布和圆柱几何形状对固有频率和振型的影响。

缩写： FSDT，一阶剪切变形理论；2D，二维；3D，三维；FG，功能分级；FGM，功能分级材料；DQ，差分正交；MDEW，外（外）壁的最大密度；MDIW，内壁最大密度；CC，复共轭（前项）