Analysis of vibration and critical buckling load of porous functionally graded material rectangular nanoplates under thermo‐mechanical loading

IF 2.3 4区工程技术 Q1 MATHEMATICS, APPLIED

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-08-31 DOI:10.1002/zamm.202200073

Weibin Wang, Zhaochun Teng

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引用次数: 0

Abstract

Based on Eringen's nonlocal elastic theory, the vibration characteristics and critical buckling load of porous functionally graded rectangular nanoplates under thermomechanical load are studied. The material properties of porous FGM nanoplates are characterized by Voigt mixing power rate and arbitrarily distributed porous model, and the correlation between material and temperature is further considered, the temperature distribution along with the thickness direction is uniform. The numerical solution of the vibration and critical buckling loads of porous functionally graded material (FGM) rectangular nanoplates under thermo‐mechanical loading are investigated using the numerical solution method‐differential transformation method (DTM), and the governing differential equations are established in the classical plate theory and Hamilton system. The effects of boundary conditions, nonlocal parameters, gradient index, temperature rise, porosity, compression load, and aspect ratio on the vibration and critical buckling load of porous FGM nanoplates under thermo‐mechanical loading effects are mainly investigated utilizing arithmetic examples.

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热机械载荷下多孔功能梯度材料矩形纳米板的振动和临界屈曲载荷分析

基于Eringen非局部弹性理论，研究了热载荷作用下多孔功能梯度矩形纳米板的振动特性和临界屈曲载荷。采用Voigt混合功率率和任意分布多孔模型表征多孔FGM纳米板的材料性能，并进一步考虑材料与温度的相关性，温度沿厚度方向的分布是均匀的。采用数值解法-微分变换法(DTM)研究了热机械载荷作用下多孔功能梯度材料(FGM)矩形纳米板的振动和临界屈曲载荷的数值解，并在经典板理论和Hamilton系统中建立了控制微分方程。通过算例研究了边界条件、非局部参数、梯度指数、温升、孔隙率、压缩载荷和长径比对热机械载荷作用下多孔FGM纳米板振动和临界屈曲载荷的影响。

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来源期刊

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik 数学-力学

CiteScore

3.30

自引率

8.70%

发文量

199

审稿时长

3.0 months

期刊介绍： ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.