单杠结构差分离散系统的振动反问题

计算物理 ›› 2016, Vol. 33 ›› Issue (4): 410-418.

单杠结构差分离散系统的振动反问题

何敏, 章礼华, 王其申

安庆师范大学物理与电气工程学院, 安徽安庆 246133

收稿日期:2015-06-19 修回日期:2015-11-27 出版日期:2016-07-25 发布日期:2016-07-25
作者简介:何敏(1975-),男,硕士,副教授,从事振动的定性性质和反问题研究,E-mail:hemm@aqtc.edu.cn
基金资助:
国家自然科学基金（10772001），2013年安徽高校省级自然科学研究重点项目（KJ2016A429）和安徽省高校优秀青年人才支持计划重点项目（gxyqZD2016206）资助

Inverse Problems in Vibration for Difference Discrete Systemsof a Horizontal Bar Structure

HE Min, ZHANG Lihua, WANG Qishen

School of Physics & Electrical Engineering, Anqing Normal University, Anqing 246133, China

Received:2015-06-19 Revised:2015-11-27 Online:2016-07-25 Published:2016-07-25

摘要/Abstract

摘要： 研究组合结构中的杆-梁-杆组合单支结构，或称单杠结构的模态反问题，从数学上证明单杠结构差分离散系统固有振动的刚度矩阵的符号振荡性，并导出其频率和振型的一些定性性质.在此基础上，探讨由两组位移或应变振型及相应频率构造物理参数的条件和方法，给出两个计算实例.讨论结构参数关于其几何对称轴具有对称性的条件下的模态反问题，并给出计算实例.计算结果表明，上述反问题提法合理，解法正确.

关键词: 模态反问题, 单杠结构, 定性性质, 对称结构

Abstract: Inverse mode problem of a horizontal bar structure, a single branch structure of a rod-beam-rod system, is investigated. Sign-oscillatory properties of inherent vibration stiffness matrix of discrete horizontal bar structure are shown mathematically. In addition, qualitative properties of frequencies and modes are introduced. Physical parameters of horizontal bar structure are constructed from two sets of displacement or strain modes and corresponding circular frequencies. Several numerical examples are given. A particular inverse mode problem is discussed, where structure parameters of horizontal bar are symmetrical for geometrical symmetry axis. It shows that formulation of inverse problems is reasonable and solution method is validated.

Key words: inverse mode problem, horizontal bar structure, qualitative property, symmetric structure

中图分类号:

何敏, 章礼华, 王其申. 单杠结构差分离散系统的振动反问题[J]. 计算物理, 2016, 33(4): 410-418.

HE Min, ZHANG Lihua, WANG Qishen. Inverse Problems in Vibration for Difference Discrete Systemsof a Horizontal Bar Structure[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(4): 410-418.

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