Eigenvalue sensitivity analysis based on the transfer matrix method

被引:12
作者
Bestle, Dieter [1 ]
机构
[1] Brandenburg Univ Technol Cottbus Senftenberg, Engn Mech & Vehicle Dynam, Cottbus, Germany
来源
INTERNATIONAL JOURNAL OF MECHANICAL SYSTEM DYNAMICS | 2021年 / 1卷 / 01期
关键词
adjoint variable method; direct differentiation; sensitivity analysis; transfer matrix method;
D O I
10.1002/msd2.12016
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
For linear mechanical systems, the transfer matrix method is one of the most efficient modeling and analysis methods. However, in contrast to classical modeling strategies, the final eigenvalue problem is based on a matrix which is a highly nonlinear function of the eigenvalues. Therefore, classical strategies for sensitivity analysis of eigenvalues w.r.t. system parameters cannot be applied. The paper develops two specific strategies for this situation, a direct differentiation strategy and an adjoint variable method, where especially the latter is easy to use and applicable to arbitrarily complex chain or branched multibody systems. Like the system analysis itself, it is able to break down the sensitivity analysis of the overall system to analytically determinable derivatives of element transfer matrices and recursive formula which can be applied along the transfer path of the topology figure. Several examples of different complexity validate the proposed approach by comparing results to analytical calculations and numerical differentiation. The obtained procedure may support gradient-based optimization and robust design by delivering exact sensitivities.
引用
收藏
页码:96 / 107
页数:12
相关论文
共 13 条
  • [1] A unified approach for treating linear multibody systems involving flexible beams
    Abbas, Laith K.
    Zhou, Qinbo
    Bestle, Dieter
    Rui, Xiaoting
    [J]. MECHANISM AND MACHINE THEORY, 2017, 107 : 197 - 209
  • [2] Transfer matrix method for the determination of the free vibration of two elastically coupled beams
    Abbas, Laith K.
    Bestle, Dieter
    Rui, Xiaoting
    [J]. ADVANCED MATERIALS DESIGN AND MECHANICS II, 2013, 372 : 301 - +
  • [3] Bestle D., 1994, Analyse und Optimierung von Mehrkorpersystemen
  • [4] Recursive eigenvalue search algorithm for transfer matrix method of linear flexible multibody systems
    Bestle, Dieter
    Abbas, Laith
    Rui, Xiaoting
    [J]. MULTIBODY SYSTEM DYNAMICS, 2014, 32 (04) : 429 - 444
  • [5] Choi K.K., 2005, STRUCTURAL SENSITIVI
  • [6] RATES OF CHANGE EIGENVALUES AND EIGENVECTORS
    FOX, RL
    KAPOOR, MP
    [J]. AIAA JOURNAL, 1968, 6 (12) : 2426 - &
  • [7] DERIVATIVES OF EIGENSOLUTIONS FOR A GENERAL MATRIX
    GARG, S
    [J]. AIAA JOURNAL, 1973, 11 (08) : 1191 - 1194
  • [8] Golub Gene H., 2007, Johns Hopkins Series in the Mathematical Sciences, V3
  • [9] Lancaster P., 1964, Numer. Math., V6, P377, DOI [DOI 10.1007/BF01386087, /10.1007/BF01386087]
  • [10] Murthy DV, 1987, SENSITIVITY ANAL ENG, P177