双功能梯度石墨烯片增强金属-陶瓷基圆柱壳的行波振动分析

振动与冲击 ›› 2024, Vol. 43 ›› Issue (3) : 110-119.

论文

徐宏达，王宇，菅泽，李学辉，于晓光

作者信息 +

Traveling wave vibration analysis of dual-functional gradient metal-ceramic matrix rotating cylindrical shell reinforced by graphene sheets

XU Hongda, WANG Yu, JIAN Ze, LI Xuehui, YU Xiaoguang

Author information +

文章历史 +

摘要

采用Halpin-Tsai微观力学模型和传递矩阵方法，开展了旋转态双功能梯度石墨烯片增强复合材料(DFG-GPLRC)圆柱壳体的行波振动特性研究。描述了金属-陶瓷功能梯度基体和五种石墨烯片分布模式的材料属性，基于Love壳理论和传递矩阵方法，考虑转速影响推导了任一截面状态向量的常微分方程和整体传递矩阵关系。以固支-自由(悬臂)边界条件为主，对动力学微分方程进行求解计算，验证了分析方法的合理性。结果表明，低阶模态以轴向半波数为1和周向模态的振动为主，转速引起的科氏力使行波曲线出现分离现象；行波频率随着石墨烯重量分数的增加而增大，分布模式对振型顺序的影响较小，基体体积分数指数对振动特性的影响较大，而石墨烯片层数对振动特性的影响很小，不同倍频激励对共振特性的影响不同。

Abstract

Based on Halpin-Tsai micromechanical model and transfer matrix method, the traveling wave vibration characteristics of a rotating dual-functionally graded graphene platelet reinforced composite(DFG-GPLRC) cylindrical shell were investigated. The material properties of metal-ceramic functionally graded matrix and five types of distribution patterns of graphene platelet were analyzed. Based on the Love’s shell theory and transfer matrix method, the ordinary differential equations and the global transfer matrix relation for any cross section state vector were derived considering the influence of rotational speeds. The dynamic differential equations were solved based on clamped-free (cantilever) boundary condition mainly, which verified the rationality of the analytical method. The research shows that the low-order modes are dominated by the first axial half-wave number and the circumferential mode vibration for the free end, and the coriolis force caused by rotating speeds makes the traveling wave curve separate. The traveling wave frequencies increase with the increase of graphene material weight fraction, and the distribution patterns have little effect on the mode shape order. The volume fraction exponent of the matrix has some obvious effects on the vibration characteristics, while the number of graphene layers has little effect, and different excitation frequencies have different effects on resonance characteristics.

导出引用

徐宏达，王宇，菅泽，李学辉，于晓光. 双功能梯度石墨烯片增强金属-陶瓷基圆柱壳的行波振动分析[J]. 振动与冲击, 2024, 43(3): 110-119

XU Hongda, WANG Yu, JIAN Ze, LI Xuehui, YU Xiaoguang. Traveling wave vibration analysis of dual-functional gradient metal-ceramic matrix rotating cylindrical shell reinforced by graphene sheets[J]. Journal of Vibration and Shock, 2024, 43(3): 110-119

参考文献

[1] LI C F, TANG Q S, XI C Y, et al. Coupling vibration behaviors of drum-disk-shaft structures with elastic connection[J]. International Journal of Mechanical Sciences, 2019, 155: 392-404. [2] LI Z H, WANG L, Li Y, et al. Carbon-based functional nanomaterials: Preparation, properties and applications, Composites Science & Technology, 2019, 179: 10-40. [3] 杜昆,陈麒好,孟宪龙,等. 陶瓷基复合材料在航空发动机热端部件应用及热分析研究进展[J]. 推进技术, 2022, 43(02):113-131. DU Kun, CHEN Qi-hao, MENG Xian-long, et al. Advancement in application and thermal analysis of ceramic matrix composites in aeroengine hot components[J]. Journal of Propulsion Technology. 2022, 43(02):113-131. [4] LI H C, PANG F Z, GONG Qingtao, et al. Free vibration analysis of axisymmetric functionally graded doubly-curved shells with un-uniform thickness distribution based on Ritz method[J]. Composite Structures, 2019, 225: 111145. [5] BAGHBADORANI A A, KIANI Y. Free vibration analysis of functionally graded cylindrical shells reinforced with graphene platelets[J]. Composite Structures, 2021, 276: 114546. [6] LIU D Y, KITIPORNCHAI S, CHEN W Q, et al. Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell, Composite Structures, 2018, 189: 560-569. [7] CHEN Z X, WANG A L, Qin B, et al. Investigation on free vibration and transient response of functionally graded graphene platelets reinforced cylindrical shell resting on elastic foundation[J]. The European Physical Journal Plus, 2020, 135(7): 582. [8] SHEN H S, XIANG Y, FAN Y. Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments[J]. Composite Structures, 2017, 182: 447-456. [9] ZHANG Y, ZHANG L W, LIEW K M, et al. Free vibration analysis of bilayer graphene sheets subjected to in-plane magnetic fields[J]. Composite Structures, 2016, 144: 86-95. [10] YANG S W, HAO Y X, Zhang W, et al. Nonlinear vibration of functionally graded graphene platelet-reinforced com-posite truncated conical shell using first-order shear deformation theory[J]. Applied Mathematics and Mechanics, 2021, 42(7): 981-998. [11] ZHANG Y T, JIN G Y, Chen M F, et al. Isogeometric free vibration of sector cylindrical shells with carbon nanotubes reinforced and functionally graded materials[J]. Results in Physics, 2020, 16: 102889. [12] 韩清凯,王宇,李学军. 旋转薄壁圆柱壳的高节径振动特性以及篦齿结构的影响[J]. 中国科学:物理学力学天文学, 2013, 43(04):436-458. HAN Q K, WANG Y, LI X J. High nodal diameter vibration characteristics of rotating shell and the effects of its sealing teeth[J]. SCIENTIA SINICA Physica, Mechanica & Astronomica, 2013, 43(04):436-458. [13] 罗忠,王宇,孙宁,等. 不同边界条件下旋转薄壁短圆柱壳的强迫振动响应计算[J]. 机械工程学报, 2015, 51(9): 64-72. LUO Zhong, WANG Yu, SUN Ning, et al. Forced vibration response calculation of rotating short thin cylindrical shells for various boundary conditions[J].Chinese Journal of Mechanical Engineering, 2015, 51(9): 64-72. [14] 王宇,谷月,李晖,等. 高速旋转薄壁圆柱壳的行波共振特性研究[J]. 振动与冲击, 2016, 35(05):222-227. WANG Yu, GU Yue, LI Hui, et al. Travelling wave resonance characteristics of a high-speed rotating thin cylindrical shell[J]. Journal of Vibration and Shock, 2016, 35(5): 222-227. [15] SHENG G G, WANG X. The non-linear vibrations of rotating functionally graded cylindrical shells[J]. Nonlinear Dynamics, 2017, 87(2): 1095-1109. [16] 刘超,刘文光,吕志鹏,等. 旋转FGMs层合圆柱壳行波模态频率分析[J]. 航空动力学报, 2022, 37(04): 721-733. LIU Chao, LIU Wen-guang, LÜ Zhi-peng, et al. Analysis on traveling wave modal frequency of a rotating FGMs laminated cylindrical shell[J]. Journal of Aerospace Power, 2022, 37(04):721-733. [17] DONG Y H, LI Y H, CHEN D, et al. Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion[J]. Composites Part B: Engineering, 2018, 145: 1-13. [18] QIN Z Y, SAFAEI B, PANG X, et al. Traveling wave analysis of rotating functionally graded graphene platelet reinforced nanocomposite cylindrical shells with general boundary conditions[J]. Results in Physics, 2019, 15: 102752. [19] HEYDARPOUR Y, MALEKZADEH P. Dynamic stability of rotating FG-CNTRC cylindrical shells under com-bined static and periodic axial loads[J]. International Journal of Structural Stability and Dynamics, 2018, 18(12): 1850151. [20] LIU J, YAN H X, JIANG K. Mechanical properties of graphene platelet-reinforced alumina ceramic compo-sites[J]. Ceramics International, 2013, 39(6): 6215-6221. [21] MIAO X Y, LI C F, JIANG Y L. Free vibration analysis of met-al-ceramic matrix composite laminated cylindrical shell reinforced by CNTs[J]. Composite Structures, 2021, 260: 113262. [22] WANG Y Q, YE C, ZU J W. Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets[J]. Aerospace Science & Technology, 2019, 85(04):359-370. [23] SOBHANIARAGH B, BATRA R C, MANSUR W J, et al. Thermal response of ceramic matrix nanocomposite cylindrical shells using Eshelby-Mori-Tanaka homogenization scheme[J]. Composites Part B: Engineering, 2017, 118: 41-53. [24] PRADHAN S C, LOY C T, LAM K Y, et al. Vibration characteristics of functionally graded cylindrical shells under various boundary conditions[J]. Applied Acoustics, 2000, 61(1): 111-129. [25] XIANG Y, YUAN L Y, HUANG Y Y, et al. A novel matrix method for coupled vibration and damping effect analyses of liquid-filled circular cylindrical shells with partially constrained layer damping under har-monic excitation[J]. Applied mathematical modelling, 2011, 35(5): 2209-2220. [26] LI H, LAM K Y, NG T Y. Rotating shell dynamics[M]. Elsevier, 2005. [27] 钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994, 34(02):131-136. ZHONG Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Dalian University of Technology, 1994, 34(02):131-136. [28] 李波波,宾光富,韩清凯,等. 基于有限元的多转子串联轴系扭转振动特性分析[J]. 湖南科技大学学报(自然科学版), 2014, 29(02): 31-35. LI Bo-bo, BIN Guang-fu, HAN Qing-kai, et al. The method of multi-rotor tandem shafting torsional vibration characteristic analysis based on the finite element[J]. Journal of Hunan University of Science ＆ Technology: Natural Science Editon, 2014, 29(02): 31-35. [29] 李文达,杜敬涛,杨铁军,等.边界条件对旋转薄壁圆柱壳结构自由振动行波特性的影响分析[J]. 振动工程学报, 2016, 29(03):452-464. LI Wen-da, DU Jing-tao, YANG Tie-jun, et al. Influence of boundary conditions on traveling wave characteristics of thin rotating cylindrical shell structure for free vibration[J]. Journal Vibration Engineering, 2016, 29(03):452-464. [30] 孙述鹏. 转动薄壁圆柱壳的动力学特性研究[D]. 哈尔滨工业大学, 2013. SUN Su-peng. Study on the dynamic characteristics of rotat-ing thin cylindrical shell[D]. Harbin Institute of Technology, 2013. [31] QIN B, ZHONG R, WANG T T, et al. A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions[J]. Composite Structures, 2020, 232: 111549.