一维分布的随机动载荷激励下结构频域响应的快速算法
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摘要
对于在复杂分布随机动载荷激励下,结构的动响应计算问题,目前现有的计算方法效率低下,给工程计算带来诸多不便。提出一种新的快速算法,首先将分布随机动载荷互功率谱函数利用二维勒让德正交多项式在正交域内进行分解,用有限的参数信息表示无穷的分布信息,把分布随机动载荷的动响应计算转化为确定性分布动载荷的动响应计算,对每一个频率点通过向量乘法计算得到响应的功率谱。将该快速算法与常规算法进行仿真比较,得出该快速算法是求分布随机动载荷的精确算法,计算效率大大高于常规算法,而且很方便的计入分布随机动载荷部分相干的效应。最后将该种算法编制成计算软件,结合有限元软件用于分布随机动载荷的计算。
Low-efficiency of current algorithm for calculating frequency domain response of structure,subjected to complex distributed random load,leads to inconvenience of engineering application.A new fast algorithm was introduced to solve the above problem.The cross power spectrum function of distributed random load was expanded by two-dimensional Legendre polynomials,and the infinite distributed information was expressed by finite parameters.Then the dynamic response computation under distributed random load was transformed into that under distributed harmonic load.The response power spectrum at each frequency point was obtained by vector multiplication.Compared with the regular algorithm,it can be concluded that the fast algorithm is accurate,and its efficiency is much higher than that of the regular algorithm.Moreover,it is convenient to consider the coherences of distributed random load.Combined with the software of finite element analysis,a computation software including the fast algorithm was compiled for computation of distributed random load.
Low-efficiency of current algorithm for calculating frequency domain response of structure,subjected to complex distributed random load,leads to inconvenience of engineering application.A new fast algorithm was introduced to solve the above problem.The cross power spectrum function of distributed random load was expanded by two-dimensional Legendre polynomials,and the infinite distributed information was expressed by finite parameters.Then the dynamic response computation under distributed random load was transformed into that under distributed harmonic load.The response power spectrum at each frequency point was obtained by vector multiplication.Compared with the regular algorithm,it can be concluded that the fast algorithm is accurate,and its efficiency is much higher than that of the regular algorithm.Moreover,it is convenient to consider the coherences of distributed random load.Combined with the software of finite element analysis,a computation software including the fast algorithm was compiled for computation of distributed random load.
引文
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[2]林家浩.随机地震响应功率谱的快速算法[J].地震工程与工程振动,1990,10(4):38-45.
[3]林家浩,张亚辉,随机振动的虚拟激励法[M].北京,科学出版社,2004.
[4]Lin J H,Guo X L,Zhi H,et al.Computer simulation of struc-tural random loading identification[J].Computer and Struc-ture.2001,79:375-387.
[5]Lin J H,Williams F W.Computation and analysis of multi-excitation random seismic responses[J].Engineering Compu-tations,1992,9(5):561-574.
[6]Xue S D,Li MH,Cao Z,et al.Random vibration analysis of Lattice Shell subjected to multi-dimensional earthquake inputs[C].Proc.Int.Conf.On advances in structural dynamic(ASD2000),Elsevier,2000:777-784.
[7]姜金辉,张方,付春涛.盒状件分布动载荷频域识别方法[J].力学季刊,2008,29(2):272-277.
[8]张方,秦远田,邓吉宏.复杂分布动载荷识别技术研究[J].振动工程学报,2006,19(1):81-85.
[9]秦远田.动载荷识别应用技术研究[D].南京:南京航空航天大学,2008.
[9]秦远田,张方.具有连续分布梁模型动载荷的识别技术研究[J].振动与冲击,2005,24(2):126-133.
[10]Sansone G,Orthogonal Function[M].rew.English ed.New York:Dover,1991:169-294.
[11]Charles C Dyer,Peter S.S.Ip.An Elementary Introduction to Scientific Computing[M].Division of Physical Sciences,Uni-versity of Toronto at Scarborough,January2000.
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