含焊接残余应力薄圆板结构自由振动近似解

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (5) : 119-125.

论文

含焊接残余应力薄圆板结构自由振动近似解

陈炉云，易宏

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Approximate solutionto free vibration of thin circular plate structure with welding residual stress

CHEN Luyun, YI Hong

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文章历史 +

摘要

研究焊接残余应力对薄圆板结构振动特性的影响，解决薄圆板结构振动中存在非均匀分布预应力问题。根据含预应力结构的应变-应力方程，建立含预应力薄圆板结构的运动控制方程。基于Rayleigh-Ritz 法构造Lagrange能量泛函方程。将预应力和位移试函数展开成三角级数形式，对含预应力薄圆板结构的自由振动问题进行求解。以周边简支边界薄圆板结构为例，对比焊接残余应力的不同分布形式对薄圆板结构固有频率及振型的影响。数值计算结果验证了所提方法的有效性，可应用于解决任意分布预应力问题。

Abstract

The influence of welding residual stress on the vibration characteristics of circular thin plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain-stress relationship equations, the differential formula of thin circular plate with pre-stress distribution is derived. Based on the Rayleigh-Ritz method, the Lagrange energy formulation is constructed. The pre-stress distribution function and vibration displacement trial function are expanded into the cosine trigonometric series, and the approximate solutions of structural free vibration for circular plate is proposed. The thin circular plate with simply-support boundary for example, the influence of different type’s distribution of welding residual stress on the natural frequency and mode shape are compared. The effectiveness and convergence of the proposed method are verified through numerical calculations; and the proposed approach can be used to deal with the arbitrary pre-stress distribution problem.

关键词

自由振动 / 薄圆板 / Rayleigh-Ritz法 / 固有频率 / 焊接残余应力

Key words

free vibration

/ circular thin plate / Rayleigh-Ritz method / natural frequency / welding residual stress

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导出引用

陈炉云，易宏. 含焊接残余应力薄圆板结构自由振动近似解[J]. 振动与冲击, 2021, 40(5): 119-125

CHEN Luyun, YI Hong. Approximate solutionto free vibration of thin circular plate structure with welding residual stress[J]. Journal of Vibration and Shock, 2021, 40(5): 119-125

参考文献

[1] Wu TY, Liu GR. Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule [J]. International Journal of Solids and Structures, 2001, 38(44): 7967-7980.
[2] Wu TY, Wang YY, Liu GR. Free vibration analysis of circular plates using generalized differential quadrature rule [J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(46): 5365-5380.
[3] Yalcin HS, Arikoglu A, Ozkol I. Free vibration analysis of circular plates by differential transformation method [J]. Applied Mathematics and Computation, 2009, 212(2): 377-386.
[4] Bauer HF, Eidel W. Determination of the lower natural frequencies of circular plate with mixed boundary conditions [J]. Journal of Sound and Vibration, 2006, 292(3): 742-764.
[5] 侯朝胜, 李磊. 环形薄圆板的非线性振动分析[J]. 天津大学学报, 2005, 38(6): 538-542.
    Hou Chaosheng, Li Lei. Nonlinear Vibration of an Annular Thin Plate [J]. Journal of Tianjin University, 2005, 38(6): 538-542.
[6] 郝君宇, 张小凤, 张光斌. 液体中薄圆板弯曲振动特性的分析[J]. 陕西师范大学学报(自然科学版), 2005, 38(6): 538-542.
    Hao Junyu, Zhang Xiaofeng, Zhang Guangbin. Analysis of the flexural vibration of the thin circular plates in the fluid [J]. Journal of Shangxi Normal University (Natural Science Edition), 2005, 38(6): 538-542.
[7] 鲍四元, 邓子辰. 薄板弯曲自由振动问题的高精度近似解析解及改进研究[J]. 应用数学和力学, 2016, 37(11): 1169-1180.
    Bao Siyuan, Deng Zichen. High-precision approximate analytical solutions for free bending vibrations of thin plates and an improvement [J]. Applied Mathematics and Mechanics, 2016, 37(11): 1169-1180.
[8] 齐红元, 张增杰, 陈科山, 等. 多集中质量离散固支弹性板基波频率解析[J]. 工程力学, 2015, 32(8): 22-28.
    Qi Hongyuan, Zhang Zengjie, Chen Keshan, et al. Fundamental frequency analysis of discrete-clamped elastic plate with multi-concentrated mass [J]. Engineering Mechanics, 2015, 32(8): 22-28.
[9] 石先杰, 李春丽, 史冬岩. 环板结构面内自由振动特性分析[J]. 振动工程学报, 2016, 29(3): 465-471.
    Shi Xianjie, Li Chunli, Shi Dongyan. Free in-plane vibration analysis of annular plates [J]. Journal of vibration engineering, 2016, 29(3): 465-471.
[10] 李秋红, 刘广明, 薛开, 等. 圆柱型正交各向异性圆板的自由振动分析[J]. 哈尔滨工程大学学报, 2015, 36(7): 981-986.
    Li Qiuhong, Liu Guangming, Xue Kai, et al. Free vibration analysis of cylindrical orthotropic circular plates [J]. Journal of Harbin Engineering University, 2015, 36(7): 981-986.
[11] 李秋红, 刘广明, 薛开, 等. 圆形薄板在任意弹性边界条件下的自由振动分析[J]. 船舶力学, 2015, 19(1-2): 162-168.
    Li Qiuhong, Liu Guangming, Xue Kai, et al. Free vibration analysis of circular plates with general elastic boundary support [J]. Journal of Ship Mechanics, 2015, 19(1-2): 162-168.
[12] Chen CS, Cheng WS, Tan AH. Non-linear vibration of initially stressed plates with initial imperfections [J]. Thin-Walled Structures, 2005, 43(1): 33-45.
[13] Yang N, Chen LY, Yi H, et al. A unified solution for vibration analysis of plates with general structural stress distributions [J]. International Journal of Naval Architecture and Ocean Engineering, 2016, 8(6): 615-630.
[14] 陈炉云, 李磊鑫, 张裕芳. 含局部预应力的圆柱壳结构声辐射特性研究[J]. 上海交通大学学报, 2014, 48(8): 772-777.
    Chen Luyun, Li Leixin, Zhang Yufang. The influence of acoustic radiation property for cylindrical shell with prestress in local areas [J]. Journal of Shanghai Jiaotong University, 2014, 48(8): 772-777.
[15] 羌凯, 陈炉云, 张裕芳. 焊接残余应力对环肋圆柱壳振动特性影响分析[J]. 中国造船, 2016, 57(1): 38-49.
    Qian Kai, Chen Luyun, Zhang Yufang. Influence of Welding Residual Stress on Vibration of Circularly Ring-Stiffened Cylindrical Shell [J]. Shipbuilding of China, 2016, 57(1): 38-49.
[16] 高永毅, 唐果, 万文. 具有焊接残余应力的矩形薄板固有频率计算方法研究[J]. 振动与冲击, 2014, 33(9): 165-167.
    Gao Yongyi，Tang Guo，Wan Wen. Natural frequencies calculation of a quadrate thin plate with welding residual stress [J]. Journal of Vibration and Shock, 2013, 32(22): 95-98.
[17] 陈章兰, 叶家玮. 焊接热效应对结构动力学性能影响的非线性分析[J]. 焊接学报, 2014, 35(4): 79-82.
    Chen Zhanglan, Ye Jiawei. Non-linear influence of welding thermal effect on dynamic performance of structure [J]. Transactions of the China Welding Institution, 2014, 35(4): 79-82.