The effect on bending waves by defects in pinned elastic plates
The effect on bending waves by defects in pinned elastic plates
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DOI：
10.1016/j.jsv.2012.06.013
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发表时间：
2012-11
影响因子：
4.7
通讯作者：
Ph. D Mr. Michael Smith;student;Ph. D Michael Smith;R. Porter;T. Williams;Michael J. A. Smith
中科院分区：
文献类型：
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作者：
Ph. D Mr. Michael Smith;student;Ph. D Michael Smith;R. Porter;T. Williams;Michael J. A. Smith
本文给出了具有有限缺陷的周期性刚性固定无限薄弹性板的面外位移问题的若干解。我们首先考虑一个单一的一维周期引脚阵列。我们导出了阵列中中心引脚被迫振荡所产生位移的解析解，并证明该解与有限数量引脚被移除时阵列对平面波的散射问题密切相关。然后将注意力集中在具有缺陷的钉住点的双周期矩形阵列上。解决这类问题的核心是理解没有缺陷的周期阵列中的Bloch-Floquet波，并描述了计算相关色散面的简单方法。然后寻求三个问题的解决方案：通过有限数量的缺失引脚捕获局部波；由一整排缺失的大头针捕获波浪；以及由于单个针的作用力而产生的波辐射模式。所有的问题都用有界格林函数对弹性薄板进行解析处理，使用离散傅里叶变换解法和对出现的一维和二维格和进行简单、明确和快速收敛的评估。
This paper presents solutions to a number of problems posed for the out-of-plane displacement of infinite thin elastic plates that are rigidly pinned in periodic configurations, but that possess a finite number of ‘defects’. We begin by considering a single one-dimensional periodic array of pins. We derive an analytic solution for the displacement produced by the forced oscillation of the central pin in the array, and this solution is shown to be closely connected to the problem of scattering of plane waves by an array when a finite number of pins are removed. Attention then focuses on doubly periodic rectangular arrays of pinned points possessing defects. Central to approaching such problems is an understanding of Bloch–Floquet waves in periodic arrays in the absence of defects and a simple method is described for computing the associated dispersion surfaces. The solutions to three problems are then sought: the trapping of localised waves by a finite number of missing pins; trapping of waves by entire rows of missing pins; and the wave radiation pattern due to the forcing of a single pin. All problems are treated analytically using bounded Green's functions for thin elastic plates, a discrete Fourier transform solution method and simple, explicit and rapidly convergent evaluations of the one- and two-dimensional lattice sums that arise.