Difference Analysis of Site Dominant Frequencies Obtained from Response Spectra and Fourier Spectra of Earthquake Motion
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摘要: 强震动记录的HVSR法常用于评估场地卓越频率,计算强震动记录HVSR时常采用加速度反应谱或加速度傅里叶谱,但两者会给出不同的评估值。为揭示反应谱比和傅里叶谱比评估场地卓越频率的差异,本文选取日本KiK-net台网中场地条件可近似为一维场地模型的16个台站,以其获取的强震动记录开展场地卓越频率研究。首先提出了评估场地卓越频率的数据处理方法,主要包括S波截取、Taper预处理、基于高斯拟合的自动寻峰。探讨并给出了阻尼比、平滑的带宽系数取值对场地卓越频率评估的影响规律;对反应谱阻尼比取10%,对傅里叶谱平滑的带宽系数取20~40之间获取的场地卓越频率较为准确。然后对比分析了利用地震动加速度反应谱比和傅里叶谱比得到的场地卓越频率与场地土层模型计算得到的基于传递函数的自振频率。研究结果表明,对大多数台站而言,采用傅里叶谱比计算场地卓越频率具有明显的优势,对于Ⅱ、Ⅲ、Ⅳ类场地上的台站均有如此结论,只有对少数特定台站,采用反应谱比方法效果更好。Abstract: The Horizontal-to-Vertical Spectral Ratio (HVSR) method for strong motion records is commonly used to evaluate a site’s predominant frequency. Both the acceleration response spectrum and the acceleration Fourier spectrum are frequently employed to calculate the HVSR of strong motion records, but these two approaches often yield different results. To investigate the differences in predominant site frequency between the response spectrum ratio and the Fourier spectrum ratio, this study analyzes 16 stations from Japan’s KiK-net network, where site conditions can be approximated using a one-dimensional site model. First, data processing methods for evaluating site predominant frequency were developed. These include S-wave interception, taper preprocessing, and automatic peak identification based on Gaussian fitting. The effects of damping ratio and smoothed bandwidth ratio on site frequency evaluation were examined. It was found that using a 10% damping ratio for the response spectrum and a smoothing bandwidth ratio of 20~40 for the Fourier spectrum yielded more accurate results. Next, the predominant site frequencies obtained from the ground motion acceleration response spectrum and Fourier spectrum were compared with the natural frequency calculated from the site soil model using the transfer function. The results indicate that the Fourier spectrum ratio provides a more accurate estimate of the predominant site frequency compared to the response spectrum ratio for most stations, particularly those located on Class II, III, and IV sites. However, a few specific stations showed better results when using the response spectrum method.
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引言
关于场地地震反应的分析已有大量研究成果,研究表明土壤在地震作用下会表现出材料非线性效应ADDIN EN.CITE.DATA(Joyner等,1975;Huang等,2001;Arslan等,2006;Hosseini等,2012)。等效线性化方法ADDIN EN.CITE.DATA(Schnabel等,1972;Idriss等,1992;Bardet等,2000;王笃国等,2016)是一种频域方法,通过在不同土体应变条件下选择等效阻尼比和剪切模量,将非线性问题转化为线性问题。当采用材料非线性本构模型描述土体非线性时,需采用时间积分算法求解非线性动力有限元方程。时间积分算法可分为隐式方法和显式方法。隐式算法每时刻需求解线性代数方程组,计算效率相对较低,如Wilson-θ法和Newmark法等。显式算法无需求解线性代数方程组,适合于强非线性和自由度数目较大的问题。研究者已提出多种显式时间积分算法ADDIN EN.CITE.DATA(Chung等,1994;王进廷等,2002;Belytschko等,2014)。作者近期提出一种二阶精度的单步显式算法,该算法适合变时步问题,在线弹性范围内稳定性较好。本文将该算法推广至求解非线性动力有限元方程中,并将其应用于地震波垂直入射时非线性地震反应分析。
1. 非线性动力有限元方程的显式时间积分算法
设已知非线性体系第${t_i}$时步的受力状态,求解第${t_{i + 1}}$时步的非线性结构动力学方程:
$${\boldsymbol{M}}{{\boldsymbol{\ddot u}}_{i + 1}}{\boldsymbol{ + C}}{{\boldsymbol{\dot u}}_{i + 1}} + {\boldsymbol{f}}_{i + 1}^S{\boldsymbol{ = }}{{\boldsymbol{f}}_{i + 1}}$$ (1) 式中M、C、${{\boldsymbol{f}}^S}$和${\boldsymbol{f}}$分别表示非线性体系的质量矩阵、阻尼矩阵、内力向量和外荷载向量;u表示位移,点号对时间t求导,i+1表示第${t_{i + 1}}$时刻。第i+1时刻时间步长为:
$${\boldsymbol{\Delta }}{t_i} = {t_{i + 1}} - {t_i}$$ (2) 文献显式方法求解非线性方程(1)的过程如下,第i+1时刻位移${{\boldsymbol{u}}_{i + 1}}$为:
$${{\boldsymbol{u}}_{i + 1}} = {{\boldsymbol{u}}_i} + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}{{\boldsymbol{\dot u}}_i} + \frac{{\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}^2}}{2}{{\boldsymbol{\ddot u}}_i}$$ (3) 第i+1时刻位移增量$\mathit{\Delta }{{\boldsymbol{u}}_i}$、内力增量$\mathit{\Delta }{\boldsymbol{f}}_i^S$和内力全量${\boldsymbol{f}}_{i + 1}^S$分别为:
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{{\boldsymbol{u}}_i} = {{\boldsymbol{u}}_{i + 1}} - {{\boldsymbol{u}}_i}$$ (4) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{f}}_i^S = {\boldsymbol{f}}(\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{{\boldsymbol{u}}_i})$$ (5) $${\boldsymbol{f}}_{i + 1}^S = {\boldsymbol{f}}_i^S + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{f}}_i^S$$ (6) 第i+1时刻预估速度${{\boldsymbol{\dot {\tilde u}}}_{i + 1}}$、预估加速度${{\boldsymbol{\ddot {\tilde u}}}_{i + 1}}$、速度${{\boldsymbol{\dot u}}_{i + 1}}$和加速度${{\boldsymbol{\ddot u}}_{i + 1}}$分别为
$${{\boldsymbol{\dot {\tilde u}}}_{i + 1}} = {{\boldsymbol{\dot u}}_i} + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}{{\boldsymbol{\ddot u}}_i}$$ (7) $${{\boldsymbol{\ddot {\tilde u}}}_{i + 1}} = {{\boldsymbol{M}}^{ - 1}}({{\boldsymbol{f}}_{i + 1}} - {\boldsymbol{C\dot {\tilde u}}}_{i + 1}^{} - {\boldsymbol{f}}_{i + 1}^S)$$ (8) $${{\boldsymbol{\dot u}}_{i + 1}} = {{\boldsymbol{\dot u}}_i} + \frac{{\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{t_i}}}{2}({{\boldsymbol{\ddot u}}_i} + {{\boldsymbol{\ddot {\tilde u}}}_{i + 1}})$$ (9) $${{\boldsymbol{\ddot u}}_{i + 1}} = {{\boldsymbol{M}}^{ - 1}}({{\boldsymbol{f}}_{i + 1}} - {\boldsymbol{C\dot u}}_{i + 1}^{} - {\boldsymbol{f}}_{i + 1}^S)$$ (10) 式(3)—式(10)为求解式(1)的显式算法。算法中需由位移增量计算内力增量,目前常用的应力计算方法包括向前欧拉法、向后欧拉法和完全隐式计算法等ADDIN EN.CITE.DATA(Sloan等,1992;2001;Ahadi等,2003)。下面给出式(5)由位移增量计算内力增量的过程,即一种带误差控制的修正欧拉算法。
对于每个有限单元,由位移增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{u}}_i^e$计算应变增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e$的表达式为:
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e = {{\boldsymbol{B}}^e}\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{u}}_i^e$$ (11) 式中Be为应变矩阵。将ti时刻单元应变增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e$赋值给子步应变增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$,ti时刻单元应力${\boldsymbol{ \pmb{\mathit{ σ}} }}_i^e$赋值给${\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e$,初始化子步应变增量和应力状态分别为:
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e \leftarrow \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e$$ (12) $${\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e \leftarrow {\boldsymbol{ \pmb{\mathit{ σ}} }}_i^e$$ (13) 每个子步中应力增量计算思路见图 1,具体计算公式如下:
$${\boldsymbol{D}}_1^e = {\boldsymbol{D}}({\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e)$$ (14) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e = {\boldsymbol{D}}_1^e\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (15) $${\boldsymbol{D}}_2^e = {\boldsymbol{D}}({\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e)$$ (16) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_2^e = {\boldsymbol{D}}_2^e\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (17) $$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_s^e = \frac{{\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_2^e}}{2}$$ (18) 式中${{\boldsymbol{D}}^e}$为单元应力-应变关系矩阵。判断每个子步中应力增量$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{{\boldsymbol{ \pmb{\mathit{ σ}} }}_s}$是否符合精度要求的误差判断式为:
$${e_r} = \frac{{\left\| {\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_1^e - \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_2^e} \right\|}}{{\left\| {{\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_s^e} \right\|}}$$ (19) 判断误差er是否小于预先给定的判断值st,条件不满足时,缩小子步应变增量为:
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e \leftarrow A\sqrt {{{{s_t}} \mathord{\left/ {\vphantom {{{s_t}} {{e_r}}}} \right. } {{e_r}}}} \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (20) 式中A为误差峰值系数。采用缩小的子步应变增量重新进行式(14)—式(19)的计算与判断,循环直至满足精度要求,更新剩余应变增量和应力状态分别为:
$$\mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e \leftarrow \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_i^e - \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ ε}} }}_s^e$$ (21) $${\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e \leftarrow {\boldsymbol{ \pmb{\mathit{ σ}} }}_{i + 1}^e + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}{\boldsymbol{ \pmb{\mathit{ σ}} }}_s^e$$ (22) 利用更新剩余应变增量和应力状态循环执行式(14)—式(20),直至剩余应变增量小于等于零结束。
利用求得的第i+1时刻单元应力可得到单元应力增量和内力增量分别为:
$$ \Delta \boldsymbol{\sigma }_i^e = \boldsymbol{\sigma }_{i + 1}^e - \boldsymbol{\sigma }_i^e $$ (23) $$ \Delta {\boldsymbol{f}}_i^S{\rm{ = }}\sum\limits_e {\int {{{\boldsymbol{B}}^{e{\rm{T}}}}\boldsymbol{\Delta }{\boldsymbol{\sigma }}_i^e{\bf{d}}A} } $$ (24) 2. 地震波垂直入射时场地非线性地震反应分析
本节将上述非线性有限元方程的显式时间积分算法应用于地震波垂直入射时场地非线性地震反应分析中。假定基岩为线弹性半空间,考虑基岩上覆土层的材料非线性,不考虑土体阻尼。在土层下部设置黏性边界条件模拟半空间基岩的辐射阻尼,并在该处以等效结点力的方式实现地震动输入。
计算模型见图 2,选取A点作为观测点。土体非线性材料本构模型选取邓肯-张模型,土体线弹性参数见表 1,未给出配套的非线性参数,故算例中的非线性参数参考实际情况选取,后续研究中将使用更真实表现土体非线性行为的本构模型及真实工程场地参数。算例中的大气压参数取100kPa,内摩擦角增量取0°。入射地震动分别选取狄拉克脉冲和实测地震动(Gilroy Array #3,Coyote Lake, 1979)。入射狄拉克脉冲见图 3,观测点结果见图 4,实测地震动见图 5,观测点结果见图 6。图 4、图 6中给出采用中心差分法的计算结果作为参考解,由图 4、图 6可知,本文算法与中心差分法计算结果吻合较好,说明本文算法的有效性。
表 1 土层参数Table 1. Parameters of soils土质 深度/
m$\rho $/
(g/cm3)cs /
(m/s)v
-EN
-Rf
-c/
(MPa)θ/(°) D
-F
-人工填土 0—1.0 1.9 140 0.33 0.33 0.758 0.084 26.9 1.06 0.021 全新世砂土 1.0—5.1 1.9 140 0.32 0.33 0.758 0.084 26.9 1.06 0.021 全新世砂土 5.1—8.3 1.9 170 0.32 0.36 0.768 0.120 31.0 1.11 0.015 更新世粘土 8.3—11.4 1.9 190 0.40 0.44 0.822 0.188 28.4 1.01 0.012 更新世粘土 11.4—17.2 1.9 240 0.30 0.44 0.822 0.188 28.4 1.01 0.012 更新世砂土 17.2—22.2 2.0 330 0.26 0.51 0.840 0.300 30.0 1.02 0.011 基岩 >22.2 2.0 330 0.26 - - - - - - 表 1中ρ、cs、v、EN、Rf、c、θ为模型参数,分别表示密度、剪切波速、泊松比、无量纲幂次、破坏比、土的内聚力、土的摩擦角。D、F为试验常数。
3. 结论
本文发展一种求解材料非线性结构动力学方程的显式时间积分算法,并应用于地震波竖直入射时非线性地震反应分析中,通过算例验证了该方法的有效性。该显式算法具有无需对角阻尼矩阵、单步、稳定性良好等优点。本文考虑了邓肯-张非线性弹性本构模型,下步研究可考虑将该显式算法扩展到弹塑性本构模型及更能反映土层真实变形的本构模型中。
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表 1 16个选定台站详细信息
Table 1. Details of the 16 selected stations
台站名称 台站编号 纬度 经度 覆盖土层厚度/m 钻孔深度/m 场地分类 中国场地
分类类别选取强震动
记录数量/个VS30/(m·s−1) 类别 TAKAHAGI IBRH13 66°33'N 140°57'E 24 100 144 E Ⅱ 61 KASUMIGAURA IBRH17 36°08'N 140°31'E 235 510 335 D Ⅱ 38 TAMAYAMA IWTH02 39°82'N 141°38'E 19 102 168 E Ⅱ 55 KUJI-N IWTH08 40°26'N 141°78'E 20 100 301 D Ⅱ 27 KANEGASAKI IWTH24 39°19'N 141°01'E 56 150 390 C Ⅱ 12 RIKUZENTAKATA IWTH27 39°03'N 141°53'E 4 100 375 C Ⅱ 50 TSURUI-E KSRH06 43°22'N 144°42'E 70 237 240 D Ⅱ 21 HAMANAKA KSRH10 43°20'N 145°11'E 36 255 486 C Ⅱ 9 KAWANISHI NIGH11 37°17'N 138°74'E 56 205 237 D Ⅱ 4 UJIIE TCGH12 36°69'N 139°98'E 50 120 670 C Ⅱ 39 TAIKI TKCH08 42°48'N 143°15'E 36 100 326 D Ⅱ 21 YABUKI FKSH11 37°20'N 140°33'E 86 115 204 D Ⅲ 41 TSURUI-S KSRH07 43°13'N 144°32'E 82 222 305 D Ⅲ 22 IWAKI-E FKSH14 37°02'N 140°97'E 52 147 213 D Ⅲ 24 BEKKAI-E NMRH04 43°39'N 145°12'E 186 216 353 D Ⅳ 16 ISHIGE IBRH10 36°11'N 139°98'E 190 900 344 D Ⅳ 19 表 2 典型台站不同阻尼比取值峰值频率变化
Table 2. Peak frequency variation of typical stations with different damping ratio values
台站名 阻尼比 峰值频率/Hz 传递函数峰值频率/Hz IWTH02 0.01 5.3413 4.91 0.05 5.1903 0.1 5.0582 KSRH07 0.01 2.4020 2.51 0.05 2.4066 0.1 2.4128 IWTH08 0.01 2.4883 3.37 0.05 2.4916 0.1 2.5366 表 3 典型台站不同平滑的带宽系数取值峰值频率变化
Table 3. Peak frequency variation of typical stations with different values of smooth bandwidth factor
台站名 平滑的带宽系数 峰值频率/Hz 传递函数峰值频率/Hz IWTH02 20 5.9310 4.91 30 6.0793 40 6.0942 50 6.1148 60 6.1354 70 6.1580 KSRH07 20 2.5778 2.51 30 2.5740 40 2.5759 50 2.5791 60 2.5745 70 2.5781 IWTH08 20 2.7308 3.37 30 2.7280 40 2.7157 50 2.7268 60 2.6971 70 2.7232 表 4 台站峰值数量统计
Table 4. Peak number statistics of 16 one-dimensional stations
台站名(场地类别) 显著峰数量/个 峰的数量变化 阻尼比 平滑的带宽系数 0.01 0.05 0.1 20 30 40 50 60 70 IWTH02(Ⅱ) 1 1 1 1 1 1 1 1 2 2 IBRH13(Ⅱ) 1 2 1 1 1 1 2 3 3 3 IWTH27(Ⅱ) 1 1 1 1 1 1 1 1 1 1 KSRH06(Ⅱ) 1 1 1 1 1 2 2 2 3 3 KSRH10(Ⅱ) 2 4 3 2 2 2 3 3 4 4 TCGH12(Ⅱ) 2 2 1 1 2 3 3 4 4 4 IWTH08(Ⅱ) 3 3 3 3 3 3 4 4 4 5 TKCH08(Ⅱ) 3 5 5 3 3 4 4 6 6 7 KSRH07(Ⅲ) 2 2 2 2 2 2 2 2 2 2 FKSH11 (Ⅲ) 3 4 3 2 3 3 5 5 5 5 FKSH14(Ⅲ) 5 5 4 4 4 5 6 6 7 8 IBRH10(Ⅳ) 4 4 3 2 4 4 5 5 5 5 FKSH14(Ⅲ) 5 5 4 4 4 5 6 6 7 8 NMRH04(Ⅳ) 5 7 4 2 5 5 6 7 7 8 IBRH17(Ⅱ) 6 9 2 2 6 8 9 9 9 9 NIGH11(Ⅱ) 6 4 4 3 5 6 6 7 8 11 表 5 16个一维观测台站峰值数据统计
Table 5. Peak number statistics of 16 one-dimensional stations
场地类别 显著峰数量/个 反应谱最优参数对应的峰值频率 傅里叶谱最优参数对应的峰值频率 理论传递函数对应的
峰值频率/Hz阻尼比 峰值频率/Hz 带宽系数 峰值频率/Hz IBRH13(Ⅱ) 1 0.1 2.5910 20 3.0665 3.11 IWTH02(Ⅱ) 1 0.1 5.0582 20 5.9310 4.91 IWTH08(Ⅱ) 1 0.01 2.5883 20 2.7308 3.37 2 0.1 6.4100 40 8.0736 9.23 3 0.1 10.9237 40 15.3087 15.01 IWTH27(Ⅱ) 1 0.01 6.1773 20 7.7455 9.4 KSRH10(Ⅱ) 1 0.1 1.8353 20 1.9810 1.99 IBRH17(Ⅱ) 1 0.01 0.3534 20 0.3504 0.39 2 0.01 0.9096 20 0.9047 1.06 3 0.01 1.3833 20 1.4935 1.5 IWTH24(Ⅱ) 1 0.1 2.5140 20 2.7376 3.37 2 0.1 6.3388 40 8.1129 9.23 3 0.1 10.8505 20 15.3724 15.01 KSEH06(Ⅱ) 1 0.1 5.7812 20 6.3617 6.65 NIGH11(Ⅱ) 2 0.1 4.5118 20 4.6040 3.9 3 0.1 6.8949 20 8.4756 6.09 4 0.1 10.01 20 14.5878 9.36 TCGH12(Ⅱ) 1 0.1 5.2806 20 6.6765 7.22 2 0.05 7.2384 20 9.3454 9.25 TKCH08(Ⅱ) 3 0.1 6.7590 20 8.1318 8.35 FKSH11 (Ⅲ) 1 0.1 1.5472 60 1.6730 2.12 2 0.1 4.5552 70 5.2341 5.86 3 0.01 6.8218 50 8.0801 9.61 KSRH07(Ⅲ) 1 0.01 2.4128 60 2.5635 2.51 2 0.01 6.9196 20 8.8538 7.02 FKSH14(Ⅲ) 1 0.1 1.1760 40 1.1875 1.35 2 0.1 3.6658 20 3.9909 4.01 3 0.1 5.2186 40 5.9271 6.4 4 0.1 6.3233 40 7.7832 8.83 NMRH04(Ⅳ) 3 0.1 0.4053 20 0.4089 0.61 4 0.1 1.7428 30 1.9726 1.61 5 0.1 2.3917 20 4.3434 2.04 IBRH10(Ⅳ) 1 0.01 0.7869 40 0.7931 0.78 2 0.01 1.1389 20 1.1897 1.27 表 6 场地卓越频率或其范围统计
Table 6. Frequency of excellence or its range statistics
场地类别 显著峰数量/个 卓越频率值/Hz 卓越频率值范围/Hz 选取方法 IWTH02(Ⅱ) 1 5.05 — SA KSRH10(Ⅱ) 1 1.98 — FAS IWTH27(Ⅱ) 1 7.74 — FAS IBRH13(Ⅱ) 1 3.06 — FAS KSRH06(Ⅱ) 1 6.36 — FAS KSRH07(Ⅲ) 2 — 2.560~8.850 FAS FKSH14(Ⅲ) 2 — 1.180~7.780 FAS IBRH10(Ⅳ) 2 — 0.790~1.180 FAS TCGH12(Ⅱ) 2 — 0.107~0.381 FAS IWTH08(Ⅱ) 3 — 2.730~8.070 FAS TKCH08(Ⅱ) 3 — 0.123~0.551 FAS IWTH24(Ⅱ) 3 — 0.084~0.593 FAS FKSH11 (Ⅲ) 3 — 1.670~8.00 FAS NMRH04(Ⅳ) 5 — 0.263~2.467 SA NIGH11(Ⅱ) 6 — 0.097~0.355 SA IBRH17(Ⅱ) 6 — 0.163~0.297 FAS -
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