CAJ | 학술논문

发展了广义谐和小波在确定非线性系统随机动力响应中的应用。首先，利用周期广义谐和小波展开非线性动力微分方程，并考虑小波的联系系数后，可将动力微分方程转化为一组非线性代数方程。其次，利用 Newton 迭代法数值解答了非线性代数方程，得到了非线性动力响应的小波变换。最后，根据响应时变功率谱与各阶小波变换之间的关系，计算求得了非线性动力响应的功率谱密度。数值模拟显示了本文建议方法与 Monte Carlo 模拟之间的吻合程度。
발전료엄의해화소파재학정비선성계통수궤동력향응중적응용。수선，이용주기엄의해화소파전개비선성동력미분방정，병고필소파적련계계수후，가장동력미분방정전화위일조비선성대수방정。기차，이용 Newton 질대법수치해답료비선성대수방정，득도료비선성동력향응적소파변환。최후，근거향응시변공솔보여각계소파변환지간적관계，계산구득료비선성동력향응적공솔보밀도。수치모의현시료본문건의방법여 Monte Carlo 모의지간적문합정도。
An application of generalized harmonic wavelet in the response determination of nonlinear stochastic dynamic system was developed.Based on the wavelet expansion of the nonlinear differential equation and the newly developed wavelet connection coefficients,the dynamic differential equation was converted into a set of nonlinear algebra equations.Then,the Newton’s method was utilized to solve the algebra equations.According to the relationship between the time-varying power spectrum density (PSD)and the wavelet coefficients,the PSD of the response was thus obtained. Pertinent numerical simulations demonstrate the reliability of the proposed technique.