基于辛空间波的正交各向异性圆柱壳随机振动分析方法
收稿日期: 2025-05-30
修回日期: 2025-07-28
录用日期: 2025-08-11
网络出版日期: 2025-08-18
基金资助
强度与结构完整性全国重点实验室开放基金(ASSIKFJJ202303003);工业装备结构分析国家重点实验室开放基金(GZ23101)
A symplectic-wave-based method for random vibration analysis of orthotropic cylindrical shells
Received date: 2025-05-30
Revised date: 2025-07-28
Accepted date: 2025-08-11
Online published: 2025-08-18
Supported by
Open Project of the National Key Laboratory of Strength and Structural Integrity(ASSIKFJJ202303003);Optimization and CAE Software for Industrial Equipment(GZ23101);Open Project of the State Key Laboratory of Structural Analysis
针对湍流边界层作用下正交各向异性圆柱壳的随机振动问题，提出基于辛空间波的随机振动分析方法。首先，根据湍流边界层半经验模型，将湍流边界层作用下正交各向异性圆柱壳的随机振动响应转化为简谐位移求解；其次，基于Kirchhoff-Love薄壳理论，并结合Legendre变换，将Lagrange体系下轴压正交各向异性圆柱壳的弹性力学三大方程导入到Hamilton体系，形成统一的控制方程；然后利用辛空间内的波传播分析求解正交各向异性圆柱壳的简谐位移；最后，利用线性微分方程解的叠加原理将状态向量和激励力展开，得到解的周向叠加形式，再结合辛正交关系和一阶线性微分方程的求解方式，求解得到简谐位移。相比于模态叠加法，本方法能够解析地处理任意边界条件，且具有较高的收敛速度和计算精度。通过数值算例验证了本方法的收敛性和有效性，并分析了轴压变化对正交各向异性圆柱壳随机振动响应的影响。
米家琪 , 姜永平 , 高汝鑫 . 基于辛空间波的正交各向异性圆柱壳随机振动分析方法[J]. 航空学报, 2026 , 47(3) : 232322 -232322 . DOI: 10.7527/S1000-6893.2025.32322
A symplectic-wave-based method is proposed for the random vibration analysis of orthotropic cylindrical shells under turbulent boundary layer. Firstly， based on the semi-empirical model of turbulent boundary layer， the random vibration response of orthotropic cylindrical shells under turbulent boundary layer is transformed into harmonic response. Then， according to Kirchhoff-Love theory and Legendre transformation， the unified governing equation is obtained from the fundamental equations for orthotropic cylindrical shells under axial compression in the Lagrangian system transferring into the Hamiltonian system. And， the harmonic response of orthotropic cylindrical shells is solved through wave propagation analysis. Finally， both the state vector and excitation are expanded to obtain circumferential superposition form of the solution by applying the superposition principle of linear differential equation solutions. By combining symplectic orthogonality with the solution for first-order linear differential equations， the harmonic response is obtained. Compared with the modal superposition method， the proposed method can analytically handle arbitrary boundary conditions with higher convergence speed and computational accuracy. Numerical examples validate the convergence and effectiveness of the method， and the influence of axial compression variations on the random vibration response of orthotropic cylindrical shells is analyzed.
| [1] | CORCOS G M. The structure of the turbulent pressure field in boundary-layer flows［J］. Journal of Fluid Mechanics， 1964， 18（3）： 353-378. |
| [2] | ESMAILZADEH M， LAKIS A A， THOMAS M， et al. Prediction of the response of a thin structure subjected to a turbulent boundary-layer-induced random pressure field［J］. Journal of Sound and Vibration， 2009， 328（1/2）： 109-128. |
| [3] | MONTGOMERY J. Modeling of aircraft structural-acoustic response to complex sources using coupled FEM/BEM analyses［C］∥10th AIAA/CEAS Aeroacoustics Conference. Reston： AIAA， 2004. |
| [4] | BONNESS W K， FAHNLINE J B， LYSAK P D， et al. Modal forcing functions for structural vibration from turbulent boundary layer flow［J］. Journal of Sound and Vibration， 2017， 395： 224-239. |
| [5] | BIRGERSSON F， FINNVEDEN S， ROBERT G. Modelling turbulence-induced vibration of pipes with a spectral finite element method［J］. Journal of Sound and Vibration， 2004， 278（4/5）： 749-772. |
| [6] | 陈美霞， 魏建辉， 乔志， 等. 湍流激励下结构振动特性的半解析半数值算法研究［J］. 振动工程学报， 2011， 24（6）： 689-695. |
| CHEN M X， WEI J H， QIAO Z， et al. Semi-analytical and semi-numerical method for calculating the vibration characteristics of structure excited by turbulent boundary layer［J］. Journal of Vibration Engineering， 2011， 24（6）： 689-695 （in Chinese）. | |
| [7] | TRAFNY N， SERRE G， COTTé B， et al. A stochastic volume approach based on tailored Green’s functions for airfoil noise prediction at low Mach number［J］. Journal of Sound and Vibration， 2023， 551： 117603. |
| [8] | 李祖荟， 陈美霞. 湍流边界层激励下平板辐射噪声数值计算方法［J］. 中国舰船研究， 2017， 12（4）： 76-82. |
| LI Z H， CHEN M X. Numerical method for calculating sound radiation characteristics of plate structure excited by turbulent boundary layer［J］. Chinese Journal of Ship Research， 2017， 12（4）： 76-82 （in Chinese）. | |
| [9] | 徐嘉启， 梅志远， 李华东， 等. 湍流边界层激励下加筋平板振声响应特性研究［J］. 振动与冲击， 2020， 39（14）： 156-163. |
| XU J Q， MEI Z Y， LI H D， et al. Vibration & acoustic response characteristics of a stiffened plate stimulated by turbulent boundary layer wall pressure fluctuation［J］. Journal of Vibration and Shock， 2020， 39（14）： 156-163 （in Chinese）. | |
| [10] | DURANT C， ROBERT G， FILIPPI P J T， et al. Vibroacoustic response of a thin cylindrical shell excited by a turbulent internal flow： comparison between numerical prediction and experimentation［J］. Journal of Sound and Vibration， 2000， 229： 1115-1155. |
| [11] | EFIMTSOV B M， LAZAREV L A. Sound pressure in cylindrical shells with regular orthogonal system of stiffeners excited by a random fields of forces［J］. Journal of Sound and Vibration， 2011， 330： 3684-3697. |
| [12] | ZHANG Q L， MAO Y J， QI D T. Effect of perforation on the sound transmission through a double-walled cylindrical shell［J］. Journal of Sound and Vibration， 2017， 410： 344-363. |
| [13] | ZHOU J， BHASKAR A， ZHANG X. Sound transmission through double cylindrical shells lined with porous material under turbulent boundary layer excitation［J］. Journal of Sound and Vibration， 2015， 357： 253-268. |
| [14] | HUO H， ZHOU Z， CHEN G H， et al. Exact benchmark solutions of random vibration responses for thin-walled orthotropic cylindrical shells［J］. International Journal of Mechanical Sciences， 2021， 207： 106644. |
| [15] | MAXIT L， GUASCH O， MEYER V， et al. Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer［J］. Journal of Sound and Vibration， 2020， 466： 115016. |
| [16] | MAXIT L， KARIMI M， GUASCH O. Spatial coherence of pipe vibrations induced by an internal turbulent flow［J］. Journal of Sound and Vibration， 2021， 493： 115841. |
| [17] | DAVIES H G. Sound from turbulent-boundary-layer-excited panels［J］. The Journal of the Acoustical Society of America， 1971， 49（3B）： 878-889. |
| [18] | ZHONG W X. Plane elasticity in sectorial domain and the Hamiltonian system［J］. Applied Mathematics and Mechanics， 1994， 15（12）： 1113-1123. |
| [19] | LI R， NI X Q， CHENG G D. Symplectic superposition method for benchmark flexure solutions for rectangular thick plates［J］. Journal of Engineering Mechanics， 2015， 141（2）： 04014119. |
| [20] | LI R， TIAN Y， WANG P C， et al. New analytic free vibration solutions of rectangular thin plates resting on multiple point supports［J］. International Journal of Mechanical Sciences， 2016， 110： 53-61. |
| [21] | LI R， WANG B， LV Y F， et al. New analytic solutions for static problems of rectangular thin plates point-supported at three corners［J］. Meccanica， 2017， 52（7）： 1593-1600. |
| [22] | 祝圣博， 仝真真， 倪一文， 等. 压电复合材料纳米圆柱壳自由振动问题的辛方法［J］. 辽宁工程技术大学学报（自然科学版）， 2023， 42（1）： 12-17. |
| ZHU S B， TONG Z Z， NI Y W， et al. A symplectic approach for free vibration of piezoelectric composite cylindrical nanoshells［J］. Journal of Liaoning Technical University （Natural Science）， 2023， 42（1）： 12-17 （in Chinese）. | |
| [23] | XU X S， MA Y， LIM C W， et al. Dynamic buckling of cylindrical shells subject to an axial impact in a symplectic system［J］. International Journal of Solids and Structures， 2006， 43（13）： 3905-3919. |
| [24] | XU X S， MA J Q， LIM C W， et al. Dynamic torsional buckling of cylindrical shells［J］. Computers and Structures， 2010， 88（5/6）： 322-330. |
| [25] | TONG Z Z， NI Y W， ZHOU Z H， et al. Exact solutions for free vibration of cylindrical shells by a symplectic approach［J］. Journal of Vibration Engineering & Technologies， 2018， 6（2）： 107-115. |
| [26] | GAO R X， SUN X B， LIAO H T， et al. Symplectic wave-based method for free and steady state forced vibration analysis of thin orthotropic circular cylindrical shells with arbitrary boundary conditions［J］. Journal of Sound and Vibration， 2021， 491： 115756. |
| [27] | GAO R X， ZHANG Y H， SUN X B， et al. Forced vibration analysis of thin cross-ply laminated circular cylindrical shells with arbitrary boundary conditions using the symplectic wave-based method［J］. Thin-Walled Structures， 2023， 190： 110992. |
| [28] | 曹志远. 板壳振动理论［M］. 北京： 中国铁道出版社， 1989. |
| CAO Z Y. Vibration theory of plate and shell［M］. Beijing： China Railway Publishing House， 1989 （in Chinese）. |
/
| 〈 |
|
〉 |
CJA