热梯度环境下梁高频振动的能量流模型

doi:10.7527/S1000-6893.2021.25336

材料工程与机械制造

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热梯度环境下梁高频振动的能量流模型

刘知辉¹, 牛军川^1,2, 贾睿昊¹

1. 山东大学机械工程学院, 济南 250061;
2. 山东大学高效洁净机械制造教育部重点实验室, 济南 250061

收稿日期:2021-01-28 修回日期:2021-03-04 发布日期:2021-05-10
通讯作者: 牛军川 E-mail:niujc@sdu.edu.cn
基金资助:
国家自然科学基金（51675306，52075294）；深圳市自然科学基金（JCYJ20190812170811682）

Energy flow model for high-frequency vibration of beams in thermal-gradient environment

LIU Zhihui¹, NIU Junchuan^1,2, JIA Ruihao¹

1. School of Mechanical Engineering, Shandong University, Jinan 250061, China;
2. Key Laboratory of High-Efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education, Jinan 250061, China

Received:2021-01-28 Revised:2021-03-04 Published:2021-05-10
Supported by:
National Natural Science Foundation of China (51675306, 52075294); Natural Science Foundation of Shenzhen (JCYJ20190812170811682)

摘要/Abstract

摘要： 航空航天领域中的结构常由于高速飞行时的气动加热等因素在内外表面形成明显的温度差异，结构内部也常因此存在温度的梯度分布。为分析含有温度梯度的梁在高频激励下的动力学响应，建立了热梯度梁的能量流模型。首先通过求解热传导方程得到了梁内的温度场。然后考虑温度场对材料属性的影响，确定了梁的物理中性层以消除拉伸-弯曲变形耦合。基于哈密顿原理建立了梁的弯曲变形控制方程，进而得到了梁弯曲变形的波动频散关系。进一步推导得到了周期平均与局部空间平均后梁振动能量密度与能量流之间的关系，通过任意微元体内的能量平衡关系得到了热梯度环境下梁的能量流模型。与基准解的对比表明，建立的能量流模型能得到热梯度梁在高频激励下较为准确的振动能量分布情况。

关键词: 能量有限元, 能量流, 功率流有限元, 高频振动, 热环境

Abstract: The structures in aerospace applications are usually exposed in extreme thermal environment due to the aerodynamic heating effect, thereby leading to the significant temperature difference between the internal and external surfaces of structures. As a result, the thermal gradient always exists inside the structures. To analyze the dynamic response of the beam exposed in thermal-gradient environment and subjected to high-frequency excitation, an energy flow model for the beams with thermal gradient is developed. The thermal field in the beam is solved by the thermal conduction equation. Considering the influences of the temperature on material properties, the physical neutral plane of the beam is determined to remove the stretch-bending coupling. The governing equations of deformation of the beam are derived using the Hamilton's principle to obtain the dispersion relation for the bending wave. Furthermore, the relationship between the energy density and energy intensity is deduced after the time-period average and local-space average. The governing equations for the energy density are attained by considering the power balance in any differential element. Compared with the benchmark solutions, the model proposed can give the accurate prediction of the vibrational energy density of the beam under the high-frequency excitation.

Key words: energy finite element method, power flow, power flow finite element method, high-frequency vibration, thermal environment

中图分类号:

V414.3
TB122

刘知辉, 牛军川, 贾睿昊. 热梯度环境下梁高频振动的能量流模型[J]. 航空学报, 2022, 43(5): 425336.

LIU Zhihui, NIU Junchuan, JIA Ruihao. Energy flow model for high-frequency vibration of beams in thermal-gradient environment[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 425336.

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热梯度环境下梁高频振动的能量流模型

Energy flow model for high-frequency vibration of beams in thermal-gradient environment

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