纤维增强FGM梁的自由振动和临界屈曲载荷分析

滕兆春; 王伟斌; 马铃权

doi:10.13433/j.cnki.1003-8728.20200529

纤维增强FGM梁的自由振动和临界屈曲载荷分析

doi: 10.13433/j.cnki.1003-8728.20200529

兰州理工大学理学院，兰州　730050

基金项目: 国家自然科学基金项目（11662008）

详细信息

作者简介:
滕兆春（1969− ），副教授，研究方向为结构动力学和复合材料结构力学研究，tengzc@lut.edu.cn

中图分类号: O343
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- 文章访问数: 120
- HTML全文浏览量: 67
- PDF下载量: 21
- 被引次数: 0
出版历程
- 收稿日期: 2020-12-08
- 网络出版日期: 2023-02-18
- 刊出日期: 2022-12-05

Analysis of Free Vibration and Critical Buckling Load of Fiber Reinforced FGM Beams

School of Science, Lanzhou University of Technology, Lanzhou 730050, China

摘要

摘要: 基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程，并应用微分变换法（DTM）对控制微分方程及边界条件进行变换，计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁，并与已有文献结果进行对比，验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。
- 功能梯度材料梁 /
- 自由振动 /
- 固有频率 /
- 临界屈曲载荷 /
- 微分变换法（DTM）
Abstract: Based on the classical beam theory (CBT), the transverse free vibration and critical buckling load of fiber reinforced functionally graded material (FGM) beams subjected to axial force are studied. Firstly, the mixing law model is considered to characterize the material properties of the fiber reinforced FGM beam. Secondly, the governing differential equations of transverse free vibration and critical buckling load of the fiber reinforced FGM beam subjected to axial force are derived by Hamilton principle, and the governing differential equations and boundary conditions are transformed by differential transformation method (DTM). The dimensional natural frequencies for transverse free vibration and dimensionless critical buckling loads of the fiber reinforced FGM beam are calculated under three boundary conditions of clamped-clamped (C-C), clamped-simply supported (C-S) and simply supported-simply supported (S-S). The problem is reduced to homogeneous material beams and FGM beams and compared with the existing literatures to verify its effectiveness. Finally, the effects of stiffness ratio, fiber volume fraction and dimensionless compressive load on the dimensionless natural frequency and all parameters on the dimensionless critical buckling load of the fiber reinforced FGM beam under different boundary conditions are discussed.
- functionally graded material beams /
- free vibration /
- natural frequency /
- critical buckling load /
- differential transformation method (DTM)

HTML全文

图 1 纤维增强FGM梁的几何描述

下载: 全尺寸图片幻灯片

图 2 不同边界条件下刚度比$ {P_c}/{P_m} $对纤维增强FGM梁前5阶固有频率的影响

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图 3 不同边界条件下纤维体积分数V_f对纤维增强FGM梁前3阶无量纲固有频率的影响

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图 4 不同边界下刚度比$ {P_c}/{P_m} $对无量纲临界屈曲载荷的影响

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图 5 不同边界条件下纤维体积分数和无量纲临界屈曲载荷的关系曲线

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图 6 不同边界条件和不同纤维体积分数下无量纲压载荷对一阶无量纲固有频率的影响

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表 1 不同边界条件各向同性材料梁的无量纲固有频率

边界		Ω₁	Ω₂	Ω₃	Ω₄	Ω₅
C-C	本文解	22.3733	61.6728	120.9034	199.8588	298.663
C-C	文献[21]	22.3733	61.6728	120.903	199.859	298.556
C-S	本文解	15.4182	49.9649	104.2477	178.2696	274.1436
C-S	文献[21]	15.4182	49.9649	104.248	178.270	272.031
S-S	本文解	9.8696	39.4784	88.8264	157.9136	247.3156
S-S	文献[21]	9.8696	39.4784	88.8264	157.914	246.740

下载: 导出CSV

表 2 不同边界条件下FGM梁无量纲固有频率

P_c/P_m	Ω	C-C		C-S		C-S
P_c/P_m	Ω	本文解	文献[21]	本文解	文献[21]	本文解	文献[21]
	Ω₁	22.1080	22.108	15.2354	15.235	9.7526	9.7525
2	Ω₂	60.9416	60.942	49.3725	49.373	39.0113	39.010
	Ω₃	119.4699	119.47	103.0117	103.01	87.7733	87.773
	Ω₁	21.7197	21.720	14.9678	14.968	9.5813	9.5813
3	Ω₂	59.8711	59.871	48.5052	48.505	38.3251	38.325
	Ω₃	117.3713	117.37	101.2022	101.20	86.2315	86.231
	Ω₁	21.3518	21.352	14.7143	14.714	9.4190	9.4190
4	Ω₂	58.8571	58.857	47.6837	47.684	37.676	37.676
	Ω₃	115.3834	115.38	99.4882	99.488	84.7710	84.771
	Ω₁	21.0199	21.020	14.4856	14.486	9.2726	9.2726
5	Ω₂	57.9424	57.941	46.9427	46.942	37.0905	37.090
	Ω₃	113.5903	113.59	97.9421	97.942	83.4536	83.454

下载: 导出CSV

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