【摘要】：波動彌散方程的求解是分析彈性波或聲波問題時的一種比較常見的過程,求解所得的曲線即為彌散曲線。其方程形式一般是關(guān)于波數(shù)與頻率的一個二元超越方程,當(dāng)波數(shù)為復(fù)數(shù)時,方程實際為三元超越方程。這類方程沒有解析解,由于方程的變量和參數(shù)涉及復(fù)數(shù)域,一般的數(shù)值求解方法也難以處理。本文提出了一種基于模值收斂性的數(shù)值方法,求解一般波動彌散方程復(fù)波數(shù)域內(nèi)的解。首先論述了本方法的理論依據(jù),然后介紹了其求解步驟,最后將本方法應(yīng)用于求解復(fù)波數(shù)域波動彌散方程的具體算例。通過對比可以發(fā)現(xiàn):本方法廣泛有效地解決了復(fù)波數(shù)域內(nèi)波動彌散曲線的求解問題,適用于不同形式波動彌散方程的求解。
[Abstract]:The solution of wave dispersion equation is a common process in the analysis of elastic wave or acoustic wave problem. The obtained curve is called dispersion curve. The equation is generally a binary transcendental equation about wavenumber and frequency. When the wavenumber is complex, the equation is actually a ternary transcendental equation. Because the variables and parameters of the equation are related to the complex field, the general numerical method is difficult to deal with. In this paper, a numerical method based on modular convergence is proposed to solve the solutions in complex wavenumber domain of general wave dispersion equations. First, the theoretical basis of this method is discussed, then the steps of its solution are introduced. Finally, the method is applied to the solution of wave dispersion equation in complex wavenumber domain. By comparison, it is found that this method can solve the problem of wave dispersion curve in complex wavenumber domain widely and effectively, and can be applied to the solution of wave dispersion equation in different forms.
【作者單位】： 南京航空航天大學(xué)航空宇航學(xué)院機(jī)械結(jié)構(gòu)力學(xué)及控制國家重點實驗室;
【基金】：國家自然科學(xué)基金(11502108;11232007;51405225) 中央高校基本科研業(yè)務(wù)費——南京航空航天大學(xué)杰出人才培育基金(NE2013101) 江蘇省自然科學(xué)基金(SBK20140037;BK20140808)
【分類號】：O241.8

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