基于Kirchhoff平板理论，利用特定阶模态的正交性推导含复杂应力的结构功率流解析式，用于计算含任意分布应力的结构功率流，并通过数值算例验证了所推导的结构功率流解析式的正确性.同时，利用结构功率流解析式分析某焊接平板的复杂应力对结构速度场和内力场以及功率流的影响.结果表明，复杂应力对焊接平板功率流的影响比对其速度场和内力场的影响更大.在实际工程的振动预测及控制中，应考虑应力因素的影响.
Based on the Kirchhoff plate theory, the orthogonality of specific order modes is used to derive the power flow equation of complex stressed structure, which can help to calculate the power flow of the structure with arbitrary stress distribution. The equation is validated by the numerical examples. Meanwhile, the influences of welding stress on a vibrating plate’s velocity, structural internal force and power flow are obtained. The results show that the influence of stress on power flow is more significant than velocity and internal force field. It should be taken it into account in actual engineering vibration prediction and reduction.
［1］杨念, 陈炉云, 张裕芳. 基于波函数法的结构振动功率流研究［J］. 振动与冲击, 2014, 33(2): 173177.
YANG Nian, CHEN Luyun, ZHANG Yufang. Wave based method for steadystate power flow analysis［J］. Journal of Vibration and Shock, 2014, 33(2): 173177.
［2］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分析［J］. 上海交通大学学报, 2014, 48(8): 772777.
CHEN Luyun, LI Leixin, ZHANG Yufang. Characteristics analysis of structuralacoustic of cylindrical shell with prestress in local areas［J］. Journal of Shanghai Jiao Tong University, 2014, 48(8): 772777.
［3］CHEN C S, CHENG W S, TAN A H. Nonlinear vibration of initially stressed plates with initial imperfections［J］. ThinWalled Structures, 2005, 43 (1): 3345.
［4］ZHANG Y L, GORMAN D G, REESE J M. Vibration of prestressed thin cylindrical shells conveying fluid［J］. ThinWalled Structures, 2003, 41 (12): 11031127.
［5］高永毅, 刘德顺. 利用试验模态分析进行残余应力评估的研究［J］. 振动与冲击, 2005, 24(5): 111114.
GAO Yongyi, LIU Deshun. Studies on estimation of residual stress using modal analysis［J］. Journal of Vibration and Shock, 2005, 24(5): 111114.
［6］ZEINODDINI M, HARDING J E, PARKE G A R. Dynamic behavior of axially preloaded tubular steel members of offshore structures subjected to impact damage［J］. Ocean Engineering, 1999, 26(10): 963978.
［7］MATSUNAGA H. Free vibration of thick circular cylindrical shells subjected to axial stresses［J］. Journal of Sound and Vibration, 1998, 221(1): l17.
［8］LIU Z Z, LI T Y, ZHU X, et al. Effect of hydrostatic pressure on input power flow in submerged ringstiffened cylindrical shells［J］. Journal of Ship Mechanics, 2011, 15(3): 301312.
［9］ZHANG X M, LIU G R, LAM K Y. Vibration analysis of thin cylindrical shells using wave propagation approach［J］. Journal of Sound and Vibration, 2001, 239(3): 397403.
［10］ZHANG X M, LIU G R, LAM K Y. Frequency analysis of cylindrical panels using a wave propagation approach［J］. Applied Acoustics, 2001, 62(5): 527543.
［11］熊健民, 周俊荣, 周金枝. 基于ANSYS预应力简支梁固有频率的研究［J］. 固体力学学报, 2008, 29(S1): 158161.
XIONG Jianmin, ZHOU Junrong, ZHOU Jinzhi. Research of prestress simplesupported beam’s natural frequency based on ANSYS［J］. Chinese Journal of Solid Mechanics, 2008, 29(S1): 158161.
［12］GRADIN M, RIXEN D. Mechanical vibrations: Theory and application to structural dynamics［M］. Hoboken, USA: Wiley Press, 2014: 213215.
［13］VERGOTE K, VANDEPITTE D, DESMET W. Application of the wave based method for the calculation of structural intensity and power flow in plates［C］∥Proceedings of ISMA. Leuven, Belgium: ISMA, 2008: 16531666.
［14］刘勇.复杂应力对圆柱壳结构的动力特性影响研究［D］.上海：上海交通大学船船舶与海洋工程学院, 2014.
