CALCULATING RESPONSE SPECTRAL MOMENTS BY COMPLEX MODAL ANALYSIS

Response spectral moments are useful for system reliability analysis.Usually,spectral mo- ments are calculated by the frequency domain method.Based on the time domain modal analysis of random vibrations,the authors present a new method for calculating response spectral moments through response correlation functions.The method can be applied to both classical and non-classical damping cases and to three kinds of random excitations,i.e.,white noise,band-limited white noise, and filtered white noise.

On the Spectral Moments of Wind Waves

In order to obtain high order spectral moments, the residual moment M(w(n))(i) = integral(0)(wn) w(i)S(w)dw, as proposed by Denis s, is presented for approximate estimation of spectral moment m(i) = integral(0)(infinity) w(i)S(w)dw. Glazman's partial averaging idea is discussed. It is pointed out that Glazman's method and definition of non-dimensional spectral moment can not be used to estimate spectral moments for engineering purposes and that method is not supported by theory and computation. The non-dimensional spectral moment of PM spectrum, which should be expressed as [GRAPHICS] is related to wind speed. The 0 - 8th moments of PM spectrum are estimated for wind speeds of 10, 20 and 30 m/s and some discussions are given.

Calculation of Random Response Spectral Moments of Elastic-viscoelastic Combined Systems

In random vibration analysis, the importance of spectral moments of the response stems from their relevance to system performance prediction. Usually,spectral moments are obtained by the frequency domain method. In present paper, the random response spectral moments of elastic-viscoelastic combined systems are calculated by complex modal analysis in the time domain. The analytical form results are obtained for random response spectral moments of an elastic-viscoelastic combined system to a stationary white noise excitation. The method presented is simple and easy to apply. It is hoped that this study would pave a way for the analysis of reliability of elastic-viscoelastic combined systems subjected to random excitations.

Ordering of Spectral Moments of Tricyclic Graphs with Given Bases

The spectral moments are the important algebraic invariants of graphs.In this paper,on the basis of definitions of tricyclic graphs,base and the sequence of spectral moments,respectively,we study tricyclic graphs with given bases on the lexicographical order of the spectral moments sequence,and find the last and the first graphs.The results is very helpful for studying all tricyclic graphs ordering by spectral moments.

On the Spectral Moment of Quasi-Unicyclic Graphs

A connected graph G=(V(G),E(G)) is called a quasi-unicyclic graph,if there exists u0∈V(G) such that G-u0 is a unicyclic graph.Denote Q(n,d0)={G:G is a quasi-unicyclic graph of order n with G-u0 being a unicyclic graph and dG(u0)=d0}.Let A(G) be the adjacency matrix of a graph G,and let λ1(G),λ2(G),…,λn(G) be the eigenvalues in non-increasing order of A(G).The number n∑i=1λi^k(k=0,1,…,n-1) is called the k-th spectral moment of G,denoted by Sk(G).Let S(G)=(S0(G),S1(G),…,Sn-1(G)) be the sequence of spectral moments of G.For two graphs G1,G2,we have■ if for some k(k=1,2,…,n-1), and we have Si(G1)=Si(G2)(i=0,1,…,k-1) and Sk(G1)<Sk(G2).In this paper,we determine the second to the fourth largest quasi-unicyclic graphs,in an S-order,in the set Q(n,d0),respectively.

带支撑广义Maxwell粘弹性阻尼耗能结构风振响应分析

工程中粘弹性阻尼器的安装通过支撑与结构进行连接,但在安装粘弹性阻尼器的耗能结构随机响应分析中,为了简化计算过程,将支撑的刚度看作无穷大或者忽略支撑刚度的影响。实际上,对支撑刚度的影响加以考虑更能符合工程实际。针对考虑支撑刚度影响的粘弹性阻尼耗能结构风振响应分析过程复杂的问题,提出了一种求解考虑支撑影响的广义Maxwell粘弹性阻尼耗能结构基于Davenport谱风振响应的简明解析解法。在广义Maxwell粘弹性阻尼器微分型本构模型基础上,给出了考虑支撑刚度的粘弹性阻尼器等效本构关系。将粘弹性阻尼器等效本构关系与结构运动方程联立,采用复模态法将其解耦,获得结构风振响应的统一表达式。将耗能结构在Davenport风速谱下的系列响应功率谱密度函数分解为频域响应函数与Davenport功率谱密度函数的乘积形式,基于随机振动理论中谱矩的定义,对响应功率谱密度函数积分后获得无积分项的系列响应谱矩表达式。在算例中通过与虚拟激励法计算结果对比,验证了所提解法的准确性,并分析了支撑刚度在耗能系统中的影响。

支撑刚度对黏弹性阻尼耗能结构的随机风振响应特性研究

针对随机风振激励下实用黏弹性阻尼耗能系统的响应分析复杂且支撑刚度影响研究不足的问题,提出了考虑安装支撑的黏弹性阻尼耗能结构的随机风振响应谱矩及方差的计算方法,并分析了支撑刚度对结构的动力响应特性。首先,依据黏弹性阻尼器与安装支撑的串联关系,建立六参数实用黏弹性阻尼器等效微分型本构方程。其次,综合运用复模态法、虚拟激励法和功率谱二次分解法,推导出耗能结构响应量(位移、层间位移、阻尼力、支撑位移)0~2阶谱矩的解析解。最后,通过算例验证了所提方法的精确性,并研究了支撑刚度对黏弹性阻尼器减震性能与结构可靠度的影响。研究表明,阻尼器支撑刚度越大,阻尼器减震性能越能得到发挥,工程应用时有必要考虑支撑刚度的不利影响。

带支撑六参阻尼器隔震结构基于李鸿晶谱的简明解法研究

考虑带支撑六参数黏弹性阻尼器耗能隔震结构在李鸿晶谱激励下求解地震响应较为复杂,提出了一种能够获得随机地震响应的简明解法。采用带支撑六参数黏弹性阻尼器分析模型,以微分本构方程实现黏弹性阻尼器隔震结构的数学建模,结合复模态法与虚拟激励法,获得了隔减震体系系列响应(位移、速度以及阻尼器受力)频域解的统一表达式;以李鸿晶谱作为激励功率谱,将激励功率谱与结构频率响应特征值函数进行简化,获得了该随机激励下系统响应功率谱、响应谱矩及响应方差的简明解;给出算例,与此类问题传统的常用分析方法进行对比,验证所提方法在该系统下分析动力响应的合理性和高效性,并讨论了不同支撑刚度对阻尼器减震效果的影响。

组合体结构随机地震动响应的简明解法

在两相邻结构间设置耗能阻尼器能有效降低结构在地震作用下的响应,文中对相邻建筑结构设置Maxwell型阻尼器而形成组合体的结构地震动响应进行了研究。频域法中,结构响应功率谱表示为频率响应特征函数模值平方项(称之为频率响应特征值函数)与随机激励功率谱的乘积,文中提出了响应功率谱二次正交化法并获得了结构系列响应(绝对位移与层间位移)0~2阶谱矩及方差的简明封闭解。首先,综合复模态法与虚拟激励法提出了组合体结构频率响应特征值函数的二次正交式;其次,运用留数定律给出胡聿贤地震谱的二次正交式,由此求解出组合体结构响应功率谱密度函数的二次正交式;最后,得到了组合体结构系列响应0~2阶谱矩及方差的简明封闭解。通过算例验证了所提方法的正确性,并验证了相邻结构间设置连接阻尼器具有良好的减震性能。

Estimating seismic moments and Lg Q using Lg spectra

A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic moments (M0) and source corner frequencies (fc) of several Jiashi (Xinjiang, China) earthquakes, as well as the apparent Lg Q models for the paths from Jiashi to eight seismic stations (WMQ, AAK, TLG, MAKZ, KUR, VOS, ZRN and CHK) in Central Asia. The resultant seismic moments correlate well with the M0 values obtained by Harvard University using the centroid moment tensor (CMT) inversion and the surface-wave magnitudes as well. After the correction by a typical value of average radiation coefficient for regional SV waves, the M0 values from Lg spectral inversion are still close to the corresponding values obtained from CMT inversion. The obtained ap- parent Q0Lg values (Lg Q at 1 Hz) are consistent with the tectonic features of corresponding propagation paths. The Q0Lg values are 351±87, 349±86 and 300±27 for the paths from Jiashi to AAK, TLG and MAKZ, respectively. They are smaller than Q0Lg values for the paths to KUR, VOS, ZRN and CHK, which are 553±72, 569±58, 550±57 and 603±65, respectively. These results agree with the condition that the paths to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area where relatively strong seismic activities and large variations of topography are exhibited, while the paths to KUR, VOS, ZRN and CHK mainly propagate through the stable area of Kazak platform. The Q0Lg value for the path to WMQ is 462±56. This is also in agreement with the condition that the path to WMQ is basically along the border area between Tianshan Mountain and Tarim Basin, and along this path the variations of topography and crustal thickness are moderate in comparison with that along the path to MAKZ.

单自由度混联Ⅱ型惯容系统随机地震动响应分析

提出了基于Clough-Penzien谱的混联Ⅱ型惯容结构地震动响应封闭解的计算方法,并基于所提方法研究了单自由度混联Ⅱ型惯容结构的减震性能及影响因素.首先,建立混联Ⅱ型惯容结构的运动方程,获得了结构位移与惯容出力等结构响应频域解的统一表达式.其次,基于有理式分解与留数定理分别获得了频率响应特征值函数与Clough-Penzien谱的二次正交式,进而获得了结构响应功率谱的二次正交式.最后,得到了结构与惯容随机地震动响应0~2阶谱矩的简明封闭解.利用所提方法和虚拟激励法分别对一算例进行分析,验证了所提方法的正确性;同时,利用所提方法分析了惯容各参数对结构抗震性能的影响.研究表明:该文方法获得的响应解为封闭解,在计算效率与计算准确性上都优于虚拟激励法.当μ_(ω)不变时,随着μ_(m)与μ_(ξ)增大,减震性能增强;当μ_(ω)=1时,对减震性能的影响最大.

A method of moments for calculating dynamic responses beyond linear response theory

A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confined within linear response theory. The calculating experience suggests that the proposed technique is simple and efficient in implementation, and the comparison with stochastic simulation shows that the first three orders of susceptibilities calculated by the proposed technique have high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and another observed phenomenon of stochastic resonance in the systems induced by the location of a single periodic orbit is disclosed and explained.

多自由度混联Ⅰ型惯容减震系统地震响应分析

针对惯容系统在多自由度结构中的应用和布置方案研究不足的问题,提出多自由度惯容系统响应频域解及谱矩的计算方法,并基于响应频域解及谱矩表达式确定了惯容系统的布置方案。通过引入状态变量将结构运动方程和混联Ⅰ型惯容系统的微分型本构关系转化为用矩阵形式表示的状态方程,进而推导了结构位移、速度、层间位移角等系列响应的频域统一解。然后,将响应功率谱转化为二次分解式(圆频率与复特征值平方和倒数的线性组合形式),并将其代入谱矩的定义式,获得了位移、速度等系列响应的0~2阶谱矩。最后,以一栋18层的结构为例,验证了所提封闭解的正确性;分析了复振型个数对结构响应精度的影响;确定并探究了惯容系统在多层结构中布置方案的可行性。结果表明:所提谱矩的封闭解正确适用;高阶振型对结构响应的影响较弱,考虑前若干振型可达到较高的计算精度;所提惯容系统布置方案具有简单易行且效果良好的特点。

混联Ⅰ型惯容系统基于李鸿晶谱的地震响应分析

针对设有混联Ⅰ型惯容系统的耗能结构基于李鸿晶谱的响应分析较为繁琐的问题,提出求解地震响应的简明封闭解法,并研究了惯容系统基本参数对减震性能的影响。首先,建立惯容系统和结构之间的微分型本构关系,并运用复模态法和虚拟激励法获得结构系列响应的统一解。其次,将结构系列响应的功率谱密度函数精确转化为复特征值及结构自振频率平方和表示的二次分解式,进而获得响应0阶~2阶谱矩的简明封闭解。最后,通过数值算例验证了所提方法的正确性及计算的高效性,对惯容系统参数的研究表明,当惯容系数和阻尼系数越大,结构减震效果越好,而刚度系数对结构的减震效果取决于惯容系统名义圆频率与结构自振圆频率的比值,当两者比值为0.9时减震效果最好。

二维图像谱空间矩特征的轮胎老化视觉测量

在轮胎磨损及老化的工业非接触式的无损检测中,为定量衡量轮胎老化程度,提出一种图像谱空间距定量测量轮胎老化的算法。该算法采用高斯尺度滤波对轮胎胎面及轮轱侧面采集图像进行滤波,以去掉高频分量与噪声;然后采用Canny算法得到轮胎裂纹与自身的纹理轮廓图,由二维离散傅里叶变换得到反映裂纹密度数量的频谱图;最后提取该频谱图各谱线辅助频率u、v的一阶矩相对原点距离,来定量衡量轮胎裂纹数量与密度分布特征,从而完成对轮胎老化程度的定量测量。在轮胎经营部的现场实验表明,经过小批量样本的模型识别参数训练,该方法具有90%的老化程度识别准确率,具有一定的工业应用价值。

微凸体分布计算方法对曲面接触预测的影响

为借助Greenwood-Williamson(GW)接触模型开展粗糙表面接触分析,基于微凸体识别的参数定义法和基于随机过程理论的谱矩法都被广泛用于微凸体分布参数计算。为厘清应用不同计算方法产生的接触求解差异,针对粗糙曲面接触,利用快速傅里叶变换重构获得不同统计分布下的粗糙表面随机样本,由三点定义法和谱矩法分别计算仿真样本的微凸体峰点分布参数,对样本开展GW接触分析,得到两种计算方法下接触预测结果,对结果进行了对比讨论,分析了样本表面统计分布参数、高通滤波常数、曲率半径和载荷的影响。最后,通过试验数据对谱矩法的计算偏差进行了检验,对微凸体分布参数计算给出了建议。

基于不同海域海况特点的通用型FPSO疲劳损伤分析

由于西非海域、墨西哥湾海域和巴西海域的海况特点存在明显差异,通用型FPSO在三个海域海况下的疲劳损伤呈现出较大差别,对通用型FPSO进行基于不同海域海况特点的疲劳损伤分析,结果表明,对于通用型FPSO,垂向弯矩对于船体结构疲劳强度的影响要比转矩的影响大得多,设计时应充分考虑垂向弯矩的影响;对于主船体关键热点,各海域不同系泊方式下的热点损伤均具有明显差异,其中多点系泊西非海域的疲劳损伤较大,巴西海域次之,墨西哥湾海域最小,内转塔系泊对应的疲劳损伤大于外转塔系泊,设计时应根据通用型FPSO的实际运行海域与系泊方式重点考虑损伤较大的海域与系泊方式。

NMI特征优化边界敏感的LSC遥感影像分割算法

针对线性谱聚类方法处理复杂场景的高分辨率遥感影像时存在地物边界丢失、过分割问题,提出基于归一化转动惯量特征优化边界敏感的线性谱聚类方法。首先,利用LOG算法提取影像边缘信息,将边缘信息与LSC算法融合,并将存在边缘信息的超像素块的区域质心替代原始聚类中心,改善地物边界信息丢失问题;然后,通过边缘敏感的LSC分割方法,对高分辨率影像进行分割,获取地物完整的初始超像素,并确定微小的超像素;最后,计算微小超像素与相邻超像素相似性度量值,并将其合并到相似性度量值最小的超像素,优化过分割结果。实验结果表明,该方法可以有效地解决地物边界丢失、过分割问题,获取较好的分割结果。

谱比法反演震源谱拐角频率的改进研究

由于地震波的信噪比,传播路径效应,震源机制差异和震源过程等因素的影响,传统的谱比法反演的拐角频率结果不精确,离散性大。以谱比法为基础,引入Bootstrap重采样法,KolmogorovSmirnov检验以及谱比趋势检验的筛选方法,对谱比法的反演结果进行精度评定和筛选,提高谱比法反演的拐角频率精度。将此方法应用于汶川地震余震的拐角频率、地震辐射能量、辐射效率以及能矩比等震源参数反演,建立拐角频率与地震矩之间的对应关系,验证谱比法以及三种筛选方法的可靠性。汶川地震余震震源参数反演结果表明,汶川地震余震的拐角频率与地震矩对应关系M0∝fc-3.295±0.25存在与自相似关系M0∝fc-3偏离现象。在地震释放能量方面,存在能矩比随地震矩增大而增大,以及大地震的辐射效率大于小地震的现象。

导弹支撑座连接螺栓松动故障诊断的实验研究

针对某导弹支撑座在环境激励下易引发连接螺栓松动这一具体问题,在支撑座模型结构的宽带随机振动实验的基础上,探讨了实验中的问题,根据支撑座连接螺栓在不同预紧力情况下的结构稳态响应信号,分析了信号功率谱特征的差异,提出了相应的谱矩松动故障特征的提取方法。分析结果表明,谱矩因子的降低作为该结构连接螺栓松动的诊断特征是可行的。