Nonlinear Oscillation Analysis by an Orthogonal Function Method

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Nonlinear oscillation analysis by an orthogonal function method

In this paper, an orthogonal function method is presented based on the idea to suppose periodic solution with the method of harmonic balance. The displacement is expressed in the form of trigonometric functions, a group of simplified eigenequations are obtained by the use of orthogonarity of trigonumetric functions and linear modes. The method overcomes the difficulty of a drift term existing ht systems with quadratic nonlinearities. The calculation examples show that the method has the advantages of high calculation precision, high convergence speed and little calculation work.     

螺钉预紧扭矩与其预应变转换方法

给出了累钉预紧扭矩与其预应变间的转换算法,算例表明庐方法具有工程上的现实意义。     

Duffing方程的分段求解方法

因为Duffing方程带有占εx^3项，难以用分析法求解，为了解决这一问题。研究人员已经做了很多努力，目前，比较有效的求解方法主要有：摄动法、三级数法、谐波平衡法、多尺度法等。本文尝试了在时域上分段求解的方法，即在一定的初始条件下将非线性项展开为多项式。把原方程近似地用线性非齐次常微分方程代替，运用解析法分段求解．本文还探讨了计算稳定性的判定方法。