Abstract

This article gives a review of three approaches to solving the problems of detecting local rod and pipeline defects and related problems. In the first approach, local defects are modeled by the matching conditions; in the second approach, by delta functions entering into the differential equation; and in the third approach, longitudinal cavities and cracks are modeled by continuous rod sections with modified stiffness, cross-sectional area, and density. This two-part review describes the works devoted to the detection of defects in distributed mechanical systems using natural frequencies, as well as using transmitted and reflected waves. The second part of the review is devoted to works that use the second and third approaches, i.e., defect modeling by delta functions and continuous rod sections with modified stiffness, cross-sectional area, and density.

中文翻译：

---

局部杆缺陷检测研究概述

摘要

本文概述了三种解决解决局部杆和管道缺陷及相关问题的方法。第一种方法是通过匹配条件对局部缺陷建模。在第二种方法中，通过将德尔塔函数输入到微分方程中；在第三种方法中，纵向空腔和裂缝是通过连续的杆截面模拟的，这些杆截面具有改进的刚度，横截面积和密度。这篇由两部分组成的综述介绍了致力于利用固有频率以及透射波和反射波检测分布式机械系统中的缺陷的工作。审查的第二部分专门介绍使用第二种方法和第三种方法的工作，即通过增量函数对连续的杆段进行缺陷建模，并修改刚度，横截面积，