初始几何缺陷对含裂纹的双向功能梯度梁振动特性研究

史迎辉; 唐怀平; 赵英治

doi:10.21656/1000-0887.450213

初始几何缺陷对含裂纹的双向功能梯度梁振动特性研究

doi: 10.21656/1000-0887.450213

西南交通大学力学与航空航天学院，成都 610031

基金项目:

国家自然科学基金（51778548）

详细信息

作者简介:
史迎辉（1999—），男，硕士生（E-mail: syhui@my.swjtu.edu.cn）;

唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

通讯作者:
唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

中图分类号: O342
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- 被引次数: 0
出版历程
- 收稿日期: 2024-07-15
- 修回日期: 2025-06-07
- 网络出版日期: 2025-10-17

Study on Natural Vibration Characteristics of Bidirectional Functionally Graded Material Beams With Cracks and Geometric Imperfections

School of Mechanics and Aerospace Engineering, Southwest Jiaotong University,Chengdu 610031, P.R.China

Funds:

The National Science Foundation of China(51778548)

摘要

摘要: 基于Timoshenko梁理论，考虑初始几何缺陷与裂纹，利用Hamilton原理推导了含初始几何缺陷与裂纹的双向功能梯度梁的振动控制方程，使用无质量扭转弹簧模型模拟裂纹，采用微分求积法对结构控制方程求解.探究了初始几何缺陷类型、几何缺陷的无量纲振幅、裂纹深度等因素对梁结构自由振动无量纲频率的影响.结果表明：在一定轴向功能梯度指标下，无量纲基频随初始几何缺陷无量纲振幅增大而增大，随裂纹深度的增加而减小，且全局缺陷对无量纲基频的影响要大于正弦缺陷.
- 双向功能梯度梁 /
- 初始几何缺陷 /
- 裂纹 /
- 无质量扭转弹簧 /
- 微分求积法
Abstract: Based on the Timoshenko beam theory, in view of geometric imperfections and cracks, the governing equations for bidirectional functionally graded beams were derived under the Hamiltonian principle. The cracked section was modeled with a massless elastic rotational spring, and the governing equations were solved with the differential quadrature method. The effects of geometric imperfection types, geometric imperfection dimensionless vibration amplitudes, crack depths, and other factors on the dimensionless frequencies were explored. The results show that, for a certain axial functional gradient index value, the dimensionless fundamental frequency increases with the dimensionless amplitude of the geometric imperfection, and decreases with the of crack depth. Moreover, the influence of the global imperfection on the dimensionless fundamental frequency is greater than the sine imperfection.
- bi-directional functionally graded beam /
- geometric imperfection /
- crack /
- massless elastic rotational spring /
- differential quadrature method

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参考文献(26)

[2]ZHANG B, JAISWAL P, RAI R, et al. Additive manufacturing of functionally graded material objects: a review[J].Journal of Computing and Information Science in Engineering,2018,18(4): 041002.

LOH G H, PEI E, HARRISON D, et al. An overview of functionally graded additive manufacturing[J].Additive Manufacturing,2018,23: 34-44.

[3]DUBEY A, JAISWAL S, HALDAR S, et al. Functionally gradient magnesium-based composite for temporary orthopaedic implant with improved corrosion resistance and osteogenic properties[J].Biomedical Materials,2021,16(1): 015017.

[4]陈琦, 马连生, 郭章新. 功能梯度材料梁自由振动的线性与非线性振动[J]. 力学与实践, 2023,45(3): 520-525. (CHEN Qi, MA Liansheng, GUO Zhangxin. Linear and nonlinear vibration of free vibration of functional gradient material beams[J].Mechanics in Engineering,2023,45(3): 520-525. (in Chinese))

[5]滕兆春, 马铃权, 付小华. 多孔功能梯度材料Timoshenko梁的非线性自由振动分析[J]. 西北工业大学学报, 2022,40(5): 1145-1154.(TENG Zhaochun, MA Lingquan, FU Xiaohua. Nonlinear free vibration analysis of Timoshenko beams with porous functionally graded materials[J].Journal of Northwestern Polytechnical University,2022,40(5): 1145-1154. (in Chinese))

[6]GHAZARYAN D, BURLAYENKO V N, AVETISYAN A, et al. Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method[J].Journal of Engineering Mathematics,2018,110(1): 97-121.

[7]SHAHBA A, RAJASEKARAN S. Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials[J].Applied Mathematical Modelling,2012,36(7): 3094-3111.

[8]葛仁余, 张金轮, 姜忠宇, 等. 轴向功能梯度变截面Timoshenko梁自由振动的研究[J]. 振动与冲击, 2017,36(22): 158-165. (GE Renyu, ZHANG Jinlun, JIANG Zhongyu, et al. Free vibration analysis of axially functionally Timoshenko beams with a non-uniform cross-section[J].Journal of Vibration and Shock,2017,36(22): 158-165. (in Chinese))

[9]杜运兴, 程鹏, 周芬. 变截面功能梯度Timoshenko梁的自由振动分析[J]. 湖南大学学报(自然科学版), 2021,48(5): 55-62. (DU Yunxing, CHENG Peng, ZHOU Fen. Free vibration analysis of functionally graded Timoshenko beams with variable section[J].Journal of Hunan University(Natural Sciences), 2021,48(5): 55-62. (in Chinese))

[10]KE L L, YANG J, KITIPORNCHAI S. An analytical study on the nonlinear vibration offunctionally graded beams[J].Meccanica,2010,45(6): 743-752.

[11]ZHAO Y, TANG H, ZHANG B, et al. Effect of hygrothermal loads on the nonlinear vibration of porous bi-directional functionally graded beams placed on an elastic foundation[J].International Journal of Structural Stability and Dynamics,2024,24(11): 2450114.

[12]赵英治, 唐怀平, 赖泽东, 等. 弹性地基上多孔二维功能梯度材料微梁自由振动研究[J]. 应用数学和力学, 2023,44(11): 1354-1365. (ZHAO Yingzhi, TANG Huaiping, LAI Zedong, et al. Free vibration analysis of porous 2D functionally graded material microbeams on winkler’s foundation[J].Applied Mathematics and Mechanics,2023,44(11): 1354-1365. (in Chinese))

[13]雷剑, 谢宇阳, 姚明格, 等. 变截面二维功能梯度微梁的振动和屈曲特性[J]. 应用数学和力学, 2022,43(10): 1133-1145. (LEI Jian, XIE Yuyang, YAO Mingge, et al. Vibration and buckling characteristics of 2D functionally graded microbeams with variable cross sections[J].Applied Mathematics and Mechanics,2022,43(10): 1133-1145. (in Chinese))

[14]YOUCEF T, RABIA B, DAOUADJI T H. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity[J].Structural Engineering and Mechanics,2021,77(2): 217-229.

[15]马明辉, 郑玉芳, 陈昌萍. 含裂纹功能梯度材料Timoshenko梁的非线性静力分析[J]. 贵州大学学报(自然科学版), 2021,38(6): 98-103. (MA Minghui, ZHENG Yufang, CHEN Changping. Nonlinear static analysis of cracked functionally graded material Timoshenko beam[J].Journal of Guizhou University(Natural Sciences), 2021,38(6): 98-103. (in Chinese))

[16]衡星, 朱翔, 李天匀, 等. 含裂纹功能梯度材料梁结构的振动功率流特性分析[J]. 噪声与振动控制, 2017,37(4): 40-46. (HENG Xing, ZHU Xiang, LI Tianyun, et al. Vibrational power flow analysis of the functionally graded beam with an open crack[J].Noise and Vibration Control,2017,37(4): 40-46. (in Chinese))

[17]YAYLACI M, YAYLACI E U, OZDEMIR M E, et al. Vibration and buckling analyses of FGM beam with edge crack: Finite element and multilayer perceptron methods[J].Steel and Composite Structures,2023,46(4): 565-575.

[18]LIU H, WU H, LYU Z. Nonlinear resonance of FG multilayer beam-type nanocomposites: effects of graphene nanoplatelet-reinforcement and geometric imperfection[J].Aerospace Science and Technology,2020,98: 105702.

[19]田婷婷, 王忠民, 王清波. 初始几何缺陷的功能梯度梁振动特性分析[J]. 力学与实践, 2022,44(5): 1151-1158. (TIAN Tingting, WANG Zhongmin, WANG Qingbo. Vibration characteristics analysis of functionally graded beams with initial geometric defect[J].Mechanics in Engineering,2022,44(5): 1151-1158. (in Chinese))

[20]GUO L J, MAO J J, ZHANG W, et al. Modeling and analyze of behaviors of functionally graded graphene reinforced composite beam with geometric imperfection in multiphysics[J].Aerospace Science and Technology,2022,127: 107722.

[21]ZHANG W, GUO L J, WANG Y, et al. Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads[J].Nonlinear Dynamics,2022,110(4): 3255-3272.

[22]KITIPORNCHAI S, KE L L, YANG J, et al. Nonlinear vibration of edge cracked functionally graded Timoshenko beams[J].Journal of Sound and Vibration,2009,324(3/4/5): 962-982.

[23]KE L L, YANG J, KITIPORNCHAI S, et al. Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials[J].Mechanics of Advanced Materials and Structures,2009,16(6): 488-502.

[24]石兴东, 程鹏, 张宇飞. 带裂纹石墨烯增强金属泡沫梁的振动特性研究[J]. 动力学与控制学报, 2024,22(3): 48-55. (SHI Xingdong, CHENG Peng, ZHANG Yufei. Study on vibration characteristics of cracked metal foam beams reinforced with graphene[J].Journal of Dynamics and Control,2024,22(3): 48-55. (in Chinese))

[25]DIMAROGONAS A D. Vibration of cracked structures: a state of the art review[J].Engineering Fracture Mechanics,1996,55(5): 831-857.

[26]CHONDROS T G, DIMAROGONAS A D, YAO J.A continuous cracked beam vibration theory[J].Journal of Sound and Vibration,1998,215(1): 17-34.

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初始几何缺陷对含裂纹的双向功能梯度梁振动特性研究

doi: 10.21656/1000-0887.450213

作者简介:
史迎辉（1999—），男，硕士生（E-mail: syhui@my.swjtu.edu.cn）;

唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

通讯作者:
唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

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Study on Natural Vibration Characteristics of Bidirectional Functionally Graded Material Beams With Cracks and Geometric Imperfections

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留言板

初始几何缺陷对含裂纹的双向功能梯度梁振动特性研究

doi: 10.21656/1000-0887.450213

作者简介: 史迎辉（1999—），男，硕士生（E-mail: syhui@my.swjtu.edu.cn）; 唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

通讯作者: 唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

计量

出版历程

Study on Natural Vibration Characteristics of Bidirectional Functionally Graded Material Beams With Cracks and Geometric Imperfections

计量

出版历程

目录

作者简介:
史迎辉（1999—），男，硕士生（E-mail: syhui@my.swjtu.edu.cn）;

唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.

通讯作者:
唐怀平（1967—），男，副教授，博士（通讯作者. E-mail: thp_vib@163.com）.