热环境下热电材料圆板的横向自由振动特性

摘要/Abstract

摘要： 为获得热环境作用下热电材料圆板的横向自由振动特性,基于经典板理论和热电材料固有性质,建立热环境下热电材料圆板轴对称自由振动的控制微分方程.采用微分变换法(DTM)对无量纲控制微分方程及边界条件进行变换,分别得到周边简支和固支约束条件下热电材料圆板横向自由振动的无量纲固有频率.退化后与各向同性圆板自由振动的固有频率进行对比,验证研究方法行之有效.讨论不同时刻、不同输入热流和不同外加电流密度对热电圆板瞬态温度场的影响,以及上表面温度和外加电流密度对无量纲固有频率的影响.结果表明:热电材料圆板的无量纲固有频率随上表面温度的升高而减小,随外加电流密度的减小而增大,边界约束条件越强,固有频率越大.

关键词: 热电材料, 圆板, 温度场, 自由振动, 固有频率, 微分变换法

Abstract: In order to obtain the transverse free vibration characteristics of a thermoelectric material circular plate in a thermal environment, based on the classical plate theory and the inherent properties of thermoelectric materials, the governing differential equation of axisymmetric free vibration of thermoelectric material circular plate in thermal environment is established. The dimensionless governing differential equation and its boundary conditions are transformed by differential transformation method (DTM) to obtain the dimensionless natural frequencies of the transverse free vibration of thermoelectric material circular plate under pin-restrained and fixed-restrained conditions, respectively. Compared of the natural frequency of free vibration of isotropic circular plate before and after degradation, the validity of research method is verified. The effects of moments, input heat flux and applied current density on the transient temperature field of thermoelectric circular plate are discussed, as well as the effects of upper surface temperature and the applied current density on the dimensionless natural frequency. The results show that the dimensionless natural frequency of thermoelectric circular plate decreases with the increase of upper surface temperature and increases with the decrease of applied current density. The stronger the boundary constraints, the larger the natural frequency.

Key words: thermoelectric material, circular plate, temperature field, free vibration, natural frequency, differential transformation method

中图分类号:

O343

滕兆春, 杨文秀. 热环境下热电材料圆板的横向自由振动特性[J]. 兰州理工大学学报, 2023, 49(3): 165-172.

TENG Zhao-chun, YANG Wen-xiu. Transverse free vibration characteristics of thermoelectric material circular plate in a thermal environment[J]. Journal of Lanzhou University of Technology, 2023, 49(3): 165-172.

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