Abstract

In the current paper, a modified algebraic method (MAGM) is proposed as an effective semi-analytical technique for solving nonlinear damped oscillatory systems. A polynomial is supposed as the trial solution, and its unknown coefficients are easily determined through the algebraic method (AGM). In order to improve the solution, the Laplace transformation is applied to the series solution, and then the Padé approximants of the resultant equation are constructed. Finally, the inverse Laplace transformation is adopted to obtain a periodic solution for the nonlinear problem under consideration. The proposed method is then applied for obtaining approximate analytical solutions of a damped rotatory oscillator as well as nonlinear vibrations of a flexible beam excited by an axial force. The results are compared with those obtained by the fourth-order Runge–Kutta method, and good agreement is observed.

中文翻译：

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修正的代数方法求解非线性阻尼振动系统的近似解析解

摘要

在当前的论文中，提出了一种改进的代数方法（MAGM）作为解决非线性阻尼振动系统的有效半解析技术。多项式被认为是试验解，其未知系数很容易通过代数方法（AGM）确定。为了改善解，将Laplace变换应用于级数解，然后构造所得方程的Padé近似值。最后，采用拉普拉斯逆变换来获得所考虑非线性问题的周期解。然后将所提出的方法应用于获得阻尼旋转振荡器的近似解析解以及由轴向力激发的柔性梁的非线性振动。