地震研究

针对应用多次透射人工边界公式求解散射问题时可能出现的飘移失稳现象,对比分析了实时降阶法、修正算子法、附加黏弹器法和改进输入法的消飘效果和对计算精度的影响,结果表明:4种方法均可有效消除或抑制比较缓慢的飘移失稳现象; 飘移趋势强烈时,修正算子法和附加黏弹器法可能无法有效地抑制失稳; 当阻尼较小时,采用实时降阶法可能引入额外的低频误差; 在能够确定适当参数值的前提下,修正算子法和附加黏弹器法能够提高低频计算精度; 改进输入法则无需人为设置参数,能够在抑制飘移失稳的同时提高计算精度。

:For solving the wave scattering problems with Multi-Transmitting Formula,the effects of the real-time order reduction method,the modified operator method,the adding visco-elastic elements method and the improved wave input method on eliminating drift instability and on computation accuracy are compared and analyzed to provide useful reference for engineering application of this artificial boundary.The results show these four methods can effectively eliminate the relatively slow drift instability phenomenon; when the instability trend is strong,the modified operator method and the adding visco-elastic elements method cannot depress the instability effectively.The low-frequency errors may be introduced by the real-time order reduction method when the damping is small.Under the premise that the values of parameters can be determined appropriately,the modified operator method and the adding visco-elastic elements method can improve the calculation accuracy of low-frequency.The improved wave input method can depress drift instability and improve calculation accuracy without setting parameters artificially.

引言
1 飘移失稳机制
2 消飘措施
3 消除飘移措施分析
4 结论

图1 二维均匀水平地表场地计算模型示意图<br/>Fig.1 Two-dimensional uniform horizontal surface site calculation model

图1 二维均匀水平地表场地计算模型示意图
Fig.1 Two-dimensional uniform horizontal surface site calculation model

图2 SH入射波位移时程<br/>Fig.2 The displacement time history of the incidence SH wave

图2 SH入射波位移时程
Fig.2 The displacement time history of the incidence SH wave

图3 算例一中采用实时降阶法(a)、修正算子法(b)、附加黏弹器法(c)、改进输入法(d)后获得的观测点位移时程<br/>Fig.3 The displacement time histories at observation point in first example using the real-time order reduction method(a),the modified operator method(b),the adding visco-elastic elements method(c)and the improved wave input method(d)

图3 算例一中采用实时降阶法(a)、修正算子法(b)、附加黏弹器法(c)、改进输入法(d)后获得的观测点位移时程
Fig.3 The displacement time histories at observation point in first example using the real-time order reduction method(a),the modified operator method(b),the adding visco-elastic elements method(c)and the improved wave input method(d)

图4 二维不规则凹陷场地计算模型示意图<br/>Fig.4 Two-dimensional irregular canyon topography site calculation model

图4 二维不规则凹陷场地计算模型示意图
Fig.4 Two-dimensional irregular canyon topography site calculation model

图5 算例二中采用实时降阶法(a)、修正算子法(b)、附加黏弹器法(c)、改进输入法(d)后获得的观测点位移时程<br/>Fig.5 The displacement time histories at observation point in second example using the real-time order reduction method(a),the modified operator method(b),the adding visco-elastic elements method(c)and the improved wave input method(d)

图5 算例二中采用实时降阶法(a)、修正算子法(b)、附加黏弹器法(c)、改进输入法(d)后获得的观测点位移时程
Fig.5 The displacement time histories at observation point in second example using the real-time order reduction method(a),the modified operator method(b),the adding visco-elastic elements method(c)and the improved wave input method(d)

图6 SH入射波位移时程(a)和频谱曲线(b)<br/>Fig.6 The displacement time history(a)and frequency spectrum curve(b)of the incidence of the SH wave

图6 SH入射波位移时程(a)和频谱曲线(b)
Fig.6 The displacement time history(a)and frequency spectrum curve(b)of the incidence of the SH wave

图7 瑞利阻尼刚度系数β为0.000 02时的观测点位移时程(a)、频谱曲线(b)、以及频率分别为1(c),2(d),3(e),4(f)Hz时的波动成分地表放大系数误差<br/>Fig.7 The displacement time history(a),spectrum curve(b)of observation point and the frequencies are 1(c),2(d),3(e)and 4(f)Hz when Rayleigh damping stiffness coefficient β is 0.000 02

图7 瑞利阻尼刚度系数β为0.000 02时的观测点位移时程(a)、频谱曲线(b)、以及频率分别为1(c),2(d),3(e),4(f)Hz时的波动成分地表放大系数误差
Fig.7 The displacement time history(a),spectrum curve(b)of observation point and the frequencies are 1(c),2(d),3(e)and 4(f)Hz when Rayleigh damping stiffness coefficient β is 0.000 02

图8 瑞利阻尼刚度系数β为0.001时的观测点位移时程(a)、频谱曲线(b)、以及频率分别为1(c),2(d),3(e),4(f)Hz时的波动成分地表放大系数误差<br/>Fig.8 The displacement time history(a),spectrum curve(b)of observation point and the frequencies are 1(c),2(d),3(e)and 4(f)Hz when Rayleigh damping stiffness coefficient β is 0.001

图8 瑞利阻尼刚度系数β为0.001时的观测点位移时程(a)、频谱曲线(b)、以及频率分别为1(c),2(d),3(e),4(f)Hz时的波动成分地表放大系数误差
Fig.8 The displacement time history(a),spectrum curve(b)of observation point and the frequencies are 1(c),2(d),3(e)and 4(f)Hz when Rayleigh damping stiffness coefficient β is 0.001

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备注

引言

1 飘移失稳机制

2 消飘措施

3 消除飘移措施分析

4 结论

期刊信息