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首页> 外文期刊>Applied Mathematical Modelling >Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations
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Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations

机译：悬链管道双色激励下的二阶非线性动力学

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摘要

The purpose of this study is to investigate the 2D nonlinear dynamics of catenary pipelines for marine applications approaching the solution in the frequency domain. The proposed methodology is seeking the transfer functions and in particular the quadratic magnification factors of the involved dynamic components assuming a bi-chromatic excitation, namely, a signal which arises from the superposition of two different sinusoidal harmonics. The sought solution is achieved by employing a perturbation technique that expands all dynamic components into series of perturbations relatively to a scaling factor, whilst the mathematical processing is performed into the complex space. The adopted procedure results in a series of problems which are solved separately and successively. Also, separate mathematical systems are derived for the sum- and the difference-frequency problems. The numerical results are obtained using a centered-differences approximation of the final set of ordinary differential equations. The correlation of the structural model with marine applications required the employment of a proper procedure for linearizing the nonlinear drag force at second-order. Finally, it is remarked that the outlined methodology can be effectively extended to polychromatic excitations and to the 3D space as well.
机译：这项研究的目的是研究在频域中接近解决方案的海上应用的悬链管道的二维非线性动力学。所提出的方法正在寻找传递函数，尤其是假设双色激励（即，由两个不同的正弦谐波叠加而产生的信号）的所涉及的动态分量的二次放大系数。所寻求的解决方案是通过采用扰动技术来实现的，该技术将所有动态分量相对于比例因子扩展为一系列扰动，同时在复杂的空间中执行数学处理。所采用的过程会导致一系列问题，这些问题将被分别依次解决。同样，针对和频和差频问题导出了单独的数学系统。数值结果是使用最后一组常微分方程的中心差近似得到的。结构模型与海洋应用的相关性要求采用适当的程序来线性化二阶非线性阻力。最后，要指出的是，概述的方法可以有效地扩展到多色激发以及3D空间。

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