Higher order interaction of elastic waves in weakly nonlinear hollow circular cylinders. I. Analytical foundation
Higher order interaction of elastic waves in weakly nonlinear hollow circular cylinders. I. Analytical foundation
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DOI：
10.1063/1.4879459
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发表时间：
2014-06
影响因子：
3.2
通讯作者：
Yang Liu;C. Lissenden;J. Rose
中科院分区：
文献类型：
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作者：
Yang Liu;C. Lissenden;J. Rose
本文建立了一个分析弱非线性空心圆柱体中两个平行波相互作用产生的高次谐波累积行为的数学框架。在具有K阶非线性（N ≤ K）的圆柱体中，由于N阶模态相互作用，得到了总数为（N + 1）（N + 2）/2 − 3的非线性边值问题.基于曲线坐标系中的非线性强迫项，研究了两波二次相互作用的二次谐波（二次谐波、和差谐波）的累积准则。这些准则由同步条件、主模态的周向阶数以及主波场和次波场的性质（即，扭转或纵向。广义分析，提供洞察的累积性质的N阶谐波的两个准直波的N阶相互作用进行考虑圆柱体与…
A mathematical framework to analyze the cumulative behavior of higher order harmonic generation due to the interaction of two collimated waves in a weakly nonlinear hollow circular cylinder is formulated in this article. A total number of (N + 1)(N + 2)/2 − 3 nonlinear boundary problems are formulated due to the Nth order mode interactions in a cylinder with Kth order nonlinearity (N ≤ K). The cumulative criteria for the second order harmonics (second harmonics, sum and difference harmonics) due to the quadratic interactions of two waves are examined based on the nonlinear forcing terms in curvilinear coordinates. These criteria are formulated by a synchronism condition, the circumferential orders of the primary modes, as well as the nature of the primary and the secondary wave fields, i.e., torsional or longitudinal. A generalized analysis that provides insight into the cumulative nature of the Nth order harmonics by Nth order interaction of two collimated waves is conducted by considering a cylinder wit...