Inverse eigenvalue problems for discrete gyroscopic systems

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-02-08 DOI:10.1080/17415977.2021.1879804

Hairui Zhang, Yongxin Yuan

引用次数: 1

Abstract

A discrete gyroscopic system is characterized by first-order ordinary differential equations defined by one symmetric and one skew-symmetric, which system describes the motion of a spinning body containing elastic parts. In this paper, we consider the inverse problems of such system: Given partial spectral data, find a system such that it is of the desired spectral data. The general solution of the problem is given and the best approximation solution to a pair of matrices is provided by QR-decomposition and matrix derivation. In addition, we also consider a special case in which the system operates below the lowest critical speed. The numerical examples show that the proposed method is effective.

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离散陀螺系统的特征值反问题

离散陀螺系统的特征是由一个对称和一个斜对称定义的一阶常微分方程，该系统描述了包含弹性部件的旋转体的运动。在本文中，我们考虑了这种系统的逆问题：给定部分光谱数据，找到一个系统，使其具有所需的光谱数据。给出了该问题的一般解，并通过QR分解和矩阵推导给出了一对矩阵的最佳逼近解。此外，我们还考虑了一种特殊情况，即系统在最低临界速度以下运行。算例表明，该方法是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.