Free vibration analysis of functionally graded porous plates based on a new generalized single-variable shear deformation plate theory

IF 2.2 3区工程技术 Q2 MECHANICS Archive of Applied Mechanics Pub Date : 2023-03-10 DOI:10.1007/s00419-023-02396-2

Zhuang-zhuang Wang, Teng Wang, Yan-mei Ding, Lian-sheng Ma

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Abstract

A generalized single-variable shear deformation plate theory (GSSDPT) is proposed. Compared with other single-variable vibration theories, GSSDPT discards the assumption that the shear component has zero effect on the bending moment. This makes the simplification process more reasonable. GSSDPT takes into account the inhomogeneous distribution of material properties, which makes it suitable for many new composite materials, such as functionally graded materials. Compared with higher-order shear deformation plate theories and first-order shear deformation plate theory, GSSDPT has only one governing equation, which significantly simplifies the calculation. GSSDPT takes into account the parabolic distribution of shear stress in the thickness direction. Therefore, it does not require shear correction. In this paper, the free vibration behavior of functionally graded plates under three pore distribution forms is investigated. The convenience and effectiveness of GSSDPT are verified by comparing it with existing literature. In addition, the effects of the porosity parameter, side-to-thickness ratio, aspect ratio, power-law index, and pore distribution forms are investigated based on GSSDPT.

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基于广义单变量剪切变形板理论的功能梯度多孔板自由振动分析

提出广义单变量剪切变形板理论(GSSDPT)。与其他单变量振动理论相比，GSSDPT摒弃了剪切分量对弯矩零影响的假设。这使得简化过程更加合理。GSSDPT考虑到材料性能的非均匀分布，这使得它适用于许多新的复合材料，如功能梯度材料。与高阶剪切变形板理论和一阶剪切变形板理论相比，GSSDPT只有一个控制方程，大大简化了计算。GSSDPT考虑了剪切应力在厚度方向上的抛物线分布。因此，它不需要剪切校正。本文研究了三种孔隙分布形式下功能梯度板的自由振动特性。通过与已有文献的比较，验证了GSSDPT的方便性和有效性。此外，还研究了基于GSSDPT的孔隙度参数、边厚比、纵横比、幂律指数和孔隙分布形式的影响。

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来源期刊

Archive of Applied Mechanics 物理-力学

CiteScore

4.40

自引率

10.70%

发文量

234

审稿时长

4-8 weeks

期刊介绍： Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.