On various eigenvalue problem formulations for viscously damped linear mechanical systems

M. Guergoeze

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On various eigenvalue problem formulations for viscously damped linear mechanical systems

机译：关于粘滞阻尼线性机械系统的各种特征值问题公式

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The state-space method is frequently used to obtain the eigenvalues of a viscously damped linear mechanical system. Differences in the definition of the state vector and auxiliary matrices found in the literature lead to differences in the formulation of the eigenvalue problems and this in turn can cause difficulties for students on mechanical vibration courses. In this study, various eigenvalue problem formulations in different textbooks have been examined, relationships between them have been established and results have been applied to a numerical example of a system with two degrees of freedom.

机译：状态空间法通常用于获得粘滞阻尼线性机械系统的特征值。文献中发现的状态向量和辅助矩阵的定义不同会导致特征值问题的表述方式不同，从而给机械振动课程的学生带来困难。在这项研究中，检查了不同教科书中的各种特征值问题公式，建立了它们之间的关系，并将结果应用于具有两个自由度的系统的数值示例。

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来源
《International Journal of Mechanical Engineering Education》 |2005年第3期|p.235-243|共9页
作者
M. Guergoeze;
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作者单位

Faculty of Mechanical Engineering, Istanbul Technical University, 34439 Guemuessuyu, Istanbul, Turkey;

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原文格式 PDF
正文语种 eng
中图分类机械、仪表工业;
关键词
mechanical systems; viscous damping; state-space method; eigenvalue problems;

机译：机械系统;粘滞阻尼;状态空间法;特征值问题;

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1. A NEW MATRIX PERTURBATION METHOD FOR ANALYTICAL SOLUTION OF THE COMPLEX MODAL EIGENVALUE PROBLEM OF VISCOUSLY DAMPED LINEAR VIBRATION SYSTEMS [J] . 吕振华, 冯振东, 方传流应用数学和力学：英文版 . 1991,第008期

机译：一种新的矩阵扰动方法，用于粘性线性振动系统复杂模态特征值问题的分析解
2. Nonlinear damping models for linear conservative mechanical systems with preserved eigenspaces: a port-Hamiltonian formulation [J] . Thomas Hélie, Denis Matignon IFAC PapersOnLine . 2015,第13期

机译：具有保留特征空间的线性保守机械系统的非线性阻尼模型：哈密尔顿港公式
3. Nonlinear damping models for linear conservative mechanical systems with preserved eigenspaces: a port-Hamiltonian formulation [J] . Thomas Hélie, Denis Matignon IFAC PapersOnLine . 2015,第13期

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4. Nonlinear damping models for linear conservative mechanical systems with preserved eigenspaces: a port-Hamiltonian formulation [C] . Thomas Helie, Denis Matignon IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control . 2016

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5. RESPONSE OF LINEAR, VISCOUS DAMPED SYSTEMS TO EXCITATIONS HAVING TIME-VARYING FREQUENCY. [D] . CRONIN, DONALD LESLIE. 1966

机译：线性，粘性阻尼系统对具有时变频率的激励的响应。
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7. Fractional Derivative Finite Deformation Theory and Nonlinear Finite Element Method in Viscoelasticity : Formulation of Damping Matrix and Equations of Motion(Mechanical Systems) [O] . Hiroshi NASUNO, Nobuyuki SHIMIZU, Masataka FUKUNAGA 2010

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On various eigenvalue problem formulations for viscously damped linear mechanical systems

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