变曲率均质梁结构的振动特性研究

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摘要曲梁结构具有外形美观、力学性能好和承载能力强等一系列优点，在建筑、桥梁、船舶和航空航天等领域得到广泛应用。首先，基于一阶剪切变形梁理论和哈密尔顿原理建立四种典型曲梁结构（即圆弧曲梁、椭圆曲梁、抛物曲梁和双曲曲梁）在复杂边界条件下的统一动力学分析模型。其次，对上述曲梁结构模型进行收敛性验证并确定最佳截断数和边界弹簧刚度的取值。再次，对已建立曲梁结构模型进行准确性验证并证明其可以快速求解复杂边界条件下曲梁结构的振动特性。最后，研究结构参数、边界条件和脉冲载荷类型对曲梁结构振动特性的影响。分析结果表明，曲梁结构厚度、弹性边界条件以及脉冲载荷类型对曲梁结构的振动特性具有不同程度的影响。

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	于春蕾1
	冀浩杰2
	孟忠良1
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	卢纪丽1
	徐伟1
	C.Chiu1

关键词 ：曲梁结构, 一阶剪切变形梁理论, 稳态响应, 瞬态响应

Abstract：The curved beam structure has a series of advantages including beautiful appearance, good mechanical properties and strong bearing capacity etc and it has been widely used in construction, bridge, ship, aerospace and other fields due to the above advantages. Firstly, a unified dynamic analysis model of curved beams with complex boundary conditions is established by using Hamilton's principle based on the theory of first-order shear deformed beams. Four typical curved beam structures including circular curved beam, elliptic curved beam, parabolic curved beam and hyperbolic curved beam are taken into accounted in this study. Secondly, the convergence of the established curved beam model is verified and the optimal truncation number and boundary spring stiffness are determined according to the above verification. Then, the accuracy of the established curved beam model is verified and it is validated that the established model can quickly solve the vibration characteristics of the curved beam model with complex boundary conditions. Finally, the effects of structural parameters, boundary conditions and pulse load types on the vibration characteristics are investigated and the results show that the thickness, elastic boundary conditions and pulse load types of the curved beam have different degrees of influence on the structure of the curved beam.

Key words： curved beam structure first-order shear deformed beam theory steady-state response transient response

收稿日期: 2021-10-21 出版日期: 2023-01-28

引用本文:

于春蕾1，冀浩杰2，孟忠良1,3，卢纪丽1，徐伟1，C.Chiu1. 变曲率均质梁结构的振动特性研究[J]. 振动与冲击, 2023, 42(2): 216-224.
YU Chunlei1,JI Haojie2,MENG Zhongliang1,3,LU Jili1,XU Wei1,C.Chiu1 . Vibration characteristics of homogeneous curved beam structures with variable curvatures. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(2): 216-224.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I2/216

[1] 权凌霄,孔祥东,俞滨,白欢欢.液压管路流固耦合振动机理及控制研究现状与发展[J].机械工程学报, 2015, 51(18): 175-183.
Quan Xuao-lin, Kong Xiang-dong, Xu Bin, Bai Huan-huan. Research status and trends on fluid-structure interaction vibration mechanism and control of hydraulic pipeline[J]. Journal of Mechanical Engineering, 2015, 51(18): 175-183.
[2] 叶康生, 姚葛亮. 平面曲梁有限元静力分析的p型超收敛算法[J]. 工程力学, 2017, 34(11): 26-33+58.
YE Kang-sheng, YAO Ge-liang. A p-type superconvergent recovery method for FE static analysis of planar curved beams[J]. Engineering Mechanics, 2017, 34(11): 26-33+58.
[3] 殷振炜. 平面曲梁和旋转壳自由振动有限元超收敛算法研究[D]. 清华大学, 2018.
YIN Zhen-wei. Research on superconvergent recovery algorithm for FE analysis of free vibration of planar curved beams and shells of revolution[D]. Tsinghua University, 2018.
[4] 武兰河, 刘淑红, 周敏娟. 圆弧曲梁面内自由振动的微分容积解法[J]. 振动与冲击, 2004, 23(1): 118-121.
WU Lan-he, LIU Shu-hong, ZHOU Min-juan. Differential cubature method for in-plane vibration analysis of shear deformable curved beams[J]. Journal of Vibration and Shock, 2004, 23(1): 118-121.
[5] 宋郁民, 吴定俊, 李奇.圆弧曲梁振动微分方程推导及振动特性分析[J]. 沈阳建筑大学学报(自然科学版), 2012, 28(03): 400-404.
SONG Yu-min, WU Ding-jun, LI Qi. Derivation of vibration differential equation and analysis of vibration properties about ARC-Curved beam[J]. Journal of Shenyang Jianzhu University (Natural Science), 2012, 28(03): 400-404.
[6] 叶康生, 赵雪健. 动力刚度法求解平面曲梁面外自由振动问题[J]. 工程力学, 2012, 29(03): 1-8.
YE Kang-sheng, ZHAO Xue-jian. Dynamic stiffness method for out-of-plane free vibration analysis of planar curved beams[J]. Engineering Mechanics, 2012, 29(03): 1-8.
[7] 许杠. 几何非线性曲梁结构的求积元法分析[D]. 重庆大学, 2019.
XU Gang. Quadrature element analysis of geometrically nonlinear curved beam structures[D]. Chongqing University, 2019.
[8] 赵翔, 周扬, 邵永波, 等. 基于Green函数法的Timoshenko曲梁强迫振动分析[J]. 工程力学, 2020, 37(11): 12-27.
ZHAO Xiang, ZHOU Yang, SHAO Yong-bo, et al. Analytical solutions for forced vibrations of Timoshenko curved beam by means of Green’s functions[J]. Engineering Mechanics, 2020, 37(11): 12-27.
[9] 孙广俊, 李鸿晶, 王通, 等. 基于DQM的曲梁平面外固有振动特性及参数分析[J]. 工程力学, 2013, 30(12): 220-227.
SUN Guang-jun, LI Hong-jing, WANG Tong, et al. Out-of-plane natural vibration characteristic and parameter analysis of curved girders based on DQM[J]. Engineering Mechanics, 2020, 37(11): 12-27.
[10] 陈明飞, 靳国永, 张艳涛, 等. 弹性约束的功能梯度曲梁等几何振动分析[J]. 振动工程学报, 2020, 33(05): 930-939.
CHEN Ming-fei, JIN Guo-yong, ZHANG Yan-tao, et al. Isogeometric vibration analysis of functionally graded curved beams with elastic restraints[J]. Journal of Vibration Engineering, 2020, 33(05): 930-939.
[11] 张建书, 芮筱亭, 陈刚利. 计及应力刚化效应的空间大运动曲梁动力学建模与分析[J]. 振动与冲击, 2016, 35(14): 27-33.
ZHANG Jian-shu, RUI Xiao-ting, CHEN Gang-li. Dynamics modeling and analysis of a spatial curved beam with stress stiffening[J]. Journal of Vibration and Shock, 2016, 35(14): 27-33.
[12] CORRÊA R M, ARNDT M,MACHADO R D. Free in-plane vibration analysis of curved beams by the generalized/extended finite element method[J]. European Journal of Mechanics - A/Solids, 2021, 88: 104244.
[13] Jockovic M, Radenkovic G, Nefovska-Danilovic M, et al. Free vibration analysis of spatial Bernoulli-Euler and Rayleigh curved beams using isogeometric approach[J]. Applied Mathematical Modelling, 2019, 71:152-172.
[14] Luu A T, Lee J. Non-linear buckling of elliptical curved beams[J]. International journal of non-linear mechanics, 2016, 82: 132-143.
[15] Lee J K, Jeong S. Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundations[J]. Applied Mathematical Modelling, 2016, 40(3): 2242-2256.
[16] Luu A T, Kim N I, Lee J. NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature[J]. Composite Structures, 2015, 119: 150-165.
[17] Chen M, Chen H, Ma X, et al. The isogeometric free vibration and transient response of functionally graded piezoelectric curved beam with elastic restraints[J]. Results in Physics, 2018, 11: 712-725.
[18] Beg M S, Yasin M Y. Bending, free and forced vibration of functionally graded deep curved beams in thermal environment using an efficient layerwise theory[J]. Mechanics of Materials, 2021, 159: 103919.
[19] Ye T, Jin G, Su Z. A spectral-sampling surface method for the vibration of 2-D laminated curved beams with variable curvatures and general restraints[J]. International Journal of Mechanical Sciences, 2016, 110: 170-189.
[20] Tseng Y P, Huang C S, Kao M S. In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis[J]. Composite structure, 2000, 50(2): 103-114.
[21] Ye S, Mao X, Ding H, et al. Nonlinear vibrations of a slightly curved beam with nonlinear boundary conditions[J]. International Journal of Mechanical Sciences, 2020, 168(15):105294.
[22] Su J, Qu Y, Zhang Knm, et al. Vibration analysis of functionally graded porous piezoelectric deep curved beams resting on discrete elastic supports[J]. Thin-Walled Structures, 2021, 164(5771):107838.
[23] Sun K, Nie X, Tan T, et al. Coupled vortex-induced modeling for spatially large-curved beam with elastic support[J]. International Journal of Mechanical Sciences, 2022, 214: 106903.
[24] Zhao J, Wang Q S, Deng X W, et al. A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams[J]. Composites Part B: Engineering 2019, 165(15): 155-166.
[25] Li Z, Zhong R, Wang Q, et al. The thermal vibration characteristics of the functionally graded porous stepped cylindrical shell by using characteristic orthogonal polynomials[J]. Journal of Mechanical Sciences, 2020, 182: 105779.