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湍流边界层作用下薄板随机振动声辐射的辛方法 被引量:3
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作者 潘晨鸽 李榆银 张亚辉 《应用数学和力学》 CSCD 北大核心 2018年第1期50-63,共14页
基于辛对偶体系,研究了湍流边界层作用下薄板随机振动的声辐射问题.首先对湍流边界层的互功率谱密度函数进行Fourier级数展开,从而可将随机场激励下结构随机声辐射问题转化为在空间和时间简谐压力作用下结构确定性响应的求解;然后将薄... 基于辛对偶体系,研究了湍流边界层作用下薄板随机振动的声辐射问题.首先对湍流边界层的互功率谱密度函数进行Fourier级数展开,从而可将随机场激励下结构随机声辐射问题转化为在空间和时间简谐压力作用下结构确定性响应的求解;然后将薄板的运动方程导入辛对偶体系,并采用分离变量法得到辛本征问题;最后采用辛本征向量对待求的响应向量和作用力向量进行展开,即可得到解耦后的方程,由此降低了方程的求解难度,并可得到问题的辛解析解.由于该文方法在辛对偶体系下进行求解,相比模态叠加法,避免了模态截断问题,在精度上具有较大优势.算例部分首先考虑空间和时间简谐压力作用的情况,通过与模态叠加法结果的对比,验证了该文方法的有效性.随后采用该文方法求解了湍流边界层作用下随机声场的声压功率谱密度函数的声压级,讨论了因Fourier级数截断而产生的收敛性问题,并研究了薄板随机振动辐射声场的指向性. 展开更多
关键词 辛对偶体系 湍流边界层 随机振动 随机声辐射
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Stochastic dynamic simulation of the 100-kyr cycles in climate system
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作者 DUAN MingKeng ZHOU XiuJi 《Science China Earth Sciences》 SCIE EI CAS CSCD 2015年第3期420-428,共9页
Based upon the stochastic resonance theory,the formation mechanism of 100-kyr cycles in climate system is numerically studied in the perspective of stochastic dynamics.In this study,firstly we combine the idealized al... Based upon the stochastic resonance theory,the formation mechanism of 100-kyr cycles in climate system is numerically studied in the perspective of stochastic dynamics.In this study,firstly we combine the idealized albedo model with the geological evidence and observation in climate system to construct a new albedo model.Secondly,a bistable nonlinear system is constructed by introducing the albedo model into zero-dimensional energy balance model.Finally,based on this new system,with the solar radiation cycles and stochastic perturbation simultaneously taken into account,the variation of 100-kyr cycles is analyzed by numerical simulations.The results show that,when the noise intensity reaches a certain value,the stochastic resonance can be triggered.However,the noise intensity in this level does not exist in the actual climate system.In order to explain the formation mechanism of 100-kyr glacial-interglacial cycles forced by the weak solar radiation cycles,besides the solar radiation stochastic perturbation,the stochastic dynamic effects of the other "non-solar" radiation stochastic perturbation in the climate change processes should also be considered.The stochastic dynamic simulations taking the two types of stochastic perturbation into consideration show that,when the two types of appropriately observable stochastic perturbation are introduced,the stochastic resonance also can be generated.In this situation,the contribution rate of solar radiation stochastic perturbation is about 38%,which proves the importance of solar radiation stochastic perturbation in the formation of 100-kyr climate cycles. 展开更多
关键词 solar radiation climate change stochastic dynamics stochastic resonance energy balance model
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