THE RESPONSE OF TWO-DIMENSIONAL PERIODIC STRUCTURES TO POINT HARMONIC FORCING
THE RESPONSE OF TWO-DIMENSIONAL PERIODIC STRUCTURES TO POINT HARMONIC FORCING
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DOI：
10.1006/jsvi.1996.0542
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发表时间：
1996-10
影响因子：
4.7
通讯作者：
R. Langley
中科院分区：
文献类型：
--
作者：
R. Langley
摘要：本文研究了一个无限二维周期结构在点谐波荷载作用下的响应。首先考虑一个阻尼有限系统，然后允许系统大小趋于无穷大。结果表明，远场响应可以用分析系统平面波运动时出现的“相常数面”的性质来表示。在一个通带内，发现响应的物理性质受到腐蚀性或其他腐蚀性的强烈影响。在没有焦散的情况下，响应幅度具有相对平滑的空间分布；如果存在焦散，则响应幅度具有复杂的空间格局，并出现极低响应的“死区”。将该理论应用于一个二维质量/弹簧周期系统，并与一个大型有限系统的精确响应计算进行了比较——两组结果非常吻合。这项工作适用于所有类型的二维周期结构，包括正交加筋板和壳，它提出了设计周期结构作为空间滤波器将敏感设备与局部激励源隔离的可能性。
Abstract This analysis is concerned with the response of an infinite two-dimensional periodic structure to point harmonic loading; initially a damped finite system is considered and the system size is then allowed to tend to infinity. It is shown that the response in the far field can be expressed in terms of the properties of the “phase constant surfaces” which arise in the analysis of plane wave motion through the system. Within a pass band it is found that the physical nature of the response is strongly affected by the presence or otherwise of a caustic. In the absence of a caustic the response amplitude has a relatively smooth spatial distribution; if a caustic is present then the response amplitude has a complex spatial pattern and a “dead region” of very low response occurs. The theory is applied to a two-dimensional mass/spring periodic system and a comparison is made with an exact calculation for the response of a large finite system—excellent agreement is obtained between the two sets of results. The work has application to all types of two-dimensional periodic structures, including orthogonally stiffened plates and shells, and it raises the possibility of designing a periodic structure to act as a spatial filter to isolate sensitive equipment from a localized excitation source.