Wave propagation in continuous periodic structures: Research contributions from Southampton, 1964-1995
Wave propagation in continuous periodic structures: Research contributions from Southampton, 1964-1995
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DOI：
10.1006/jsvi.1996.0076
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发表时间：
1996-02-29
影响因子：
4.7
通讯作者：
Mead, DJ
中科院分区：
文献类型：
--
作者：
Mead, DJ
在简要参考了其他研究者的一些早期研究之后，本文主要集中于南安普顿大学自1964年以来发展的分析和预测连续周期性工程结构中自由波和强迫波运动的方法。从已应用于周期梁和肋-皮结构的导纳方法开始，继续用波动方程的直接解的方法。这使用Floquet的原则，并已被应用到梁和准一维周期板和圆柱壳。给出了这些结构的传播和衰减常数的样本曲线。有限的讨论的传递矩阵，然后，在此之后，空间谐波的方法被引入作为最适合的方法来预测从振动的周期性结构辐射的声音。接下来回顾南安普顿提出的有关周期性结构的一些定理和变分原理，它们构成了用能量法求有限结构的固有频率或计算自由和强迫波动的基础。这导致了有限元法（在其标准和层次形式）被用来研究真正的二维和三维结构中的波动。这项工作的例子显示。相控阵接收函数的方法，然后介绍可能是最简单的方法建立精确的方程的均匀准一维周期性结构的传播常数。一个总结，最后介绍了有限的和早期的工作，在南安普顿简单的无序周期结构。(C)1996年学术出版社
After brief reference to some early studies by other investigators, this paper focuses mainly on methods developed at the University of Southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures. Beginning with receptance methods which have been applied to periodic beams and rib-skin structures, it continues with a method of direct solution of the wave equation. This uses Floquet's principle and has been applied to beams and quasi-one-dimensional periodic plates and cylindrical shells. Sample curves of the propagation and attenuation constants pertaining to these structures are presented. A limited discussion of the transfer matrix then follows, after which the method of space-harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure. Reviewed next are some theorems and variational principles relating to periodic structures which have been developed at Southampton, and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave motion by energy methods. This has led to the finite element method (in its standard and hierarchical forms) being used to study wave motion in genuine two-dimensional and three-dimensional structures. Examples of this work are shown. The method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi-one-dimensional periodic structures. A summary is finally presented of the limited and early work performed at Southampton on simple disordered periodic structures. (C) 1996 Academic Press Limited