现在做一个空间结构，地震分析采用振型分解反应谱法。由于该结构频谱密集，振型数取到80~100个，其振型质量参与系数都达不到90%，只是略超过80%。

1，请问各位大侠有遇到类似情况，是如何解决的？

2，90%的概念是来源于Wilson的书嘛？

3，90%的概念在中国规范中有何体现？

4，空间结构降低到80%有无依据？

一个04年老帖子，讨论内容对本帖有一定意义：

大跨空间结构动力分析时，取多少振型比较准确？
http://okok.org/forum/viewthread ... arch=true#pid308834

建筑结构地震动力学权威Wilson教授结构观点，在国内有ＳＡＰ２０００，Wilson的ＳＡＰ通过阿波罗登月计划和民兵导弹结构设计检验，很权威，９０％质量参与系数在业内均接受！不过Wilson的老师是华人结构大师林同炎教授！

林同炎又是茅以升学生

请不要满口“大师”，留意看我的帖子。

要是能达到90%，我也也想按90%取啊。但是空间结构的频谱密集，且以竖向震动为主，我的平动取不到90%啊。

问题已经解决：算400阶振型，累计质量参与系数能达到90%。

呵呵。

楼主可能使用的是特征根向量分析法
建议使用Ritz分析法，采用较少的振型可以达到90%的要求。

wilson强调质量参与系数是针对基底激励是加速度的情况,并且主要衡量基底剪力的精度.

"If all modes are used, these ratios will all be equal to 1.0. It is clear that the 90 percent
participation rule is intended to estimate the accuracy of a solution for base motion
only. It cannot be used as an error estimator for other types of loading, such as
point loads or base displacements acting on the structure"

同意楼上的观念,可考虑选用荷载相关的RITZ向量,参见wilson的话

"The numerical effort required to calculate the exact eigen solution can be
enormous for a structural system if a large number of modes are required.
However, many engineers believe that this computational effort is justifiable if
accurate results are to be obtained. One of the purposes of this section is to
clearly illustrate that this assumption is not true for the dynamic response
analyses of all structural systems.
It is possible to use the exact free-vibration mode shapes to reduce the size of
both linear and nonlinear problems. However, this is not the best approach for
the following reasons:
1. For large structural systems, the solution of the eigenvalue problem for the
free-vibration mode shapes and frequencies can require a significant amount
of computational effort.
2. In the calculation of the free-vibration mode shapes, the spatial distribution
of the loading is completely disregarded. Therefore, many of the mode
shapes that are calculated are orthogonal to the loading and do not
participate in the dynamic response.
14-8 DYNAMIC ANALYSIS OF STRUCTURES
3. If dynamic loads are applied at massless degrees-of-freedom, the use of all
the exact mode shapes in a mode superposition analysis will not converge to
the exact solution. In addition, displacements and stresses near the
application of the loads can be in significant error. Therefore, there is no
need to apply the “static correction method” as would be required if exact
eigenvectors are used for such problems.
4. It is possible to calculate a set of stiffness and mass orthogonal Ritz vectors,
with a minimum of computational effort, which will converge to the exact
solution for any spatial distribution of loading [2]".

请问定义Ritz法时，施加的荷载如何取舍和定义？

按Ritz法时计算验证，效果有一定改善，但是仍难以达到90%以上……

若是仅考虑单向地震，RITZ法施加的荷载为该方向的加速度，较少的振型很容易达到90%；
若是考虑三维地震，RITZ法施加的荷载为三个方向的加速度，可能会较多的振型；
另外质量参与系数只是来衡量基底剪力的精度，而基底剪力对于多高层来说是个主要指标，但质量参与系数在空间结构上的适用性有待探讨。

楼上的讨论,似乎对RITZ向量也按质量参与系数进行衡量,

但按wilson的说法,如果使用荷载相关的RITZ向量,则百分之九十的质量参与系数的要求将失去意义,该要求主要是针对自由振动特征向量而言的.

具体参见wilson的书<三维建筑静动力分析>的14章第11节 "CORRECTION FOR HIGHER MODE TRUNCATION"

现将该节最后一段摘录如下:

"Also, it is apparent that the mass participation factors associated with the LDR
solutions are not an accurate estimate the error in the foundation force. In this
case, 90 percent mass participation is not a requirement if LDR vectors are used.
If only five LDR vectors are used, the total mass participation factor is only 16.2
percent; however, the foundation force is over-estimated by 2.2 percent"

wilson特别指出,如果RITZ向量的个数不够,其得到的基底剪力的结果是偏保守的.

学习，比较深入的了解结构力学

不同意！

质量参与系数决定了地整力的合理性，决定了其与等效静力法的差异，如果质量参与系数国小，国外建议放大反应谱分析得到的地震力……

那若用ritz向量，如何知道多少振型足够精确？

回楼上leoson兄弟，这个问题也一直很困扰我。

最近偶然发现CLOUGH的书中有所论述（dynamic of structures,3ed,本论坛有 下载），似乎符合您的问题。

在其书323页，有一节叫"required number of vectors",其中提出了所谓的RITZ参与系数的概念 （ritz participation factor),简称为RPF. 详细论述见该书。这里贴出图片。