Boundary estimates for elliptic systems with L1–data
Boundary estimates for elliptic systems with L1–data
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DOI：
10.1007/s00526-007-0094-9
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发表时间：
2000
影响因子：
2.1
通讯作者：
H. Brezis;Jean Van Schaftingen
中科院分区：
文献类型：
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作者：
H. Brezis;Jean Van Schaftingen
绳索和电缆等结构元件是人类在寻求技术进步时使用的最古老的工具之一。例如，在巴比伦附近的内梅韦废墟中发现了一种铜线绳，它起源于公元前700年左右，1而在庞贝，估计有2400年历史的青铜绳已经被挖掘出来。2已知这些元件能够承受与弯曲和扭转载荷相比相对较大的轴向载荷，并且在拖曳操作、支撑结构、传导信号以及在设计用于在垂直和倾斜运输装置中承载有效载荷的系统中发挥了不可或缺的作用。在后一种应用中，电缆具有随时间变化的长度。然而，变化率很小，可以假设长度变化缓慢。因此，系统的动态特性在其操作期间缓慢地变化，使得系统不稳定。具有非平稳参数和激励的系统的响应与平稳系统的响应在性质上是不同的，特别是在参数的某些临界值附近，当发生通过共振区域的过渡时。非平稳共振现象通常是延迟的，并且经常伴随着拍频现象。因此，需要专门的治疗，以分析这些系统的反应。在这一领域进行了一些研究。Kevorkian 3考虑了具有缓慢变化的自然频率的谐波激励单自由度系统中的共振通道。在这项研究中，解决方案是通过匹配两个渐近展开：远离共振的外部扩展，和共振附近的内部扩展。Agrawal和Evan-Iwanowski，4和Evan-Iwanowski 5扩展了Mitropolskiii 6开发的渐近方法，用于确定非平稳、非线性多自由度系统的共振响应。描述通过内部共振缓慢演化的系统的行为的理论和方法已经由Ablowitz、Funk和纽韦尔提出，7并且还由
Structural elements such as ropes and cables are among the oldest tools used by humanity in its quest for technological advancement. For example, a copper wire rope was found in the ruins of Nemeveh near Babylon which originate from about 700 BC, 1 and in Pompeii bronze ropes estimated to be 2400 years old have been excavated. 2 These elements are known to have the ability to withstand relatively large axial loads in comparison to bending and torsional loads, and have played an indispensable role in towing operations, in supporting structures, in conducting signals and in systems designed to carry payloads in vertical and inclined transport installations. In this latter application cables are of timevarying length. However, the rate of change is small and the length may be assumed to vary slowly. Consequently, the dynamic characteristics of the system vary slowly during its operation, rendering the system non-stationary. The responses of systems with non-stationary parameters and excitations are qualitatively different from the responses of stationary systems, especially in the neighbourhood of some critical values of the parameters, when transitions through resonance regions occur. The non-stationary resonance phenomena are often delayed, and frequently accompanied by beat phenomena. Hence, specialised treatment is required in order to analyse the responses of these systems. A number of studies have been carried out in this area. Kevorkian3 has considered the passage through resonance in a harmonically excited single-degree-of-freedom system with a slowly varying natural frequency. In this study the solution was constructed by matching two asymptotic expansions: the outer expansion away from resonance, and the inner expansion near resonance. Agrawal and Evan-Iwanowski, 4 and Evan-Iwanowski5 have extended the asymptotic method developed by Mitropolskii6 for determining resonant responses of non-stationary, non-linear multi-degree-of-freedom systems. The theory and methodology to describe the behaviour of a system evolving slowly through internal resonance has been presented by Ablowitz, Funk and Newell, 7 and also by