Beyond the limitations of perturbation methods for real random eigenvalue problems using Exceptional Points and analytic continuation

In connection with the study of perturbation methods for differential eigenvalue problems, Aronszajn put forth a theory of systems (X, Y; A, B) consisting of a pair of linear transformations A, B:X → Y (see [1]; cf. also [2]). Here X and Y are complex vector spaces, possibly of infinite dimension. The algebraic aspects of this theory, where no restrictions of topological nature are imposed, where developed in [3] and [5]. We hasten to point out that the category of C2-systems (definition in § 1) in which this algebraic investigation takes place is equivalent to the category of all right modules over the ring of matrices of the form

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Vibration Characteristics Analysis of Multibody Systems With Random Parameters Based on MSTMM

Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2019-97244 ◽

2019 ◽

Author(s):

Guoping Wang ◽

Yunfei Miao ◽

Xue Rui ◽

Tianxiong Tu ◽

Xiaoting Rui

Keyword(s):

Multibody Systems ◽

Eigenvalue Problems ◽

Memory Storage ◽

Perturbation Approach ◽

Random Parameters ◽

Computational Stability ◽

Probabilistic Characterization ◽

Important Research Topic ◽

Characteristics Analysis ◽

Random Eigenvalue

Abstract Dynamics characteristics of linear multibidy systems are governed by the eigenfrequencies and the eigenvectors. The study of probabilistic characterization of the eigensolutions is now an important research topic in the field of multibody systems with random parameters. In this paper, by combining transfer matrix method for multibody system (MSTMM) and perturbation approach, a new method named as perturbation MSTMM is presented for random eigenvalue problems of multibody systems. This method has the advantages of, such as low memory storage requirement, high computational efficiency and high computational stability, etc., for dynamic design of multibody systems with random parameters. By using the proposed method, the rapid computation of random eigenvalue problems of general systems with random parameters can be realized, and the problem of repeated eigenvalues can be solved simply and conveniently. Formulations of the proposed method as well as some numerical examples are given to validate the proposed method. The simulation results of the eigenfrequencies are validated by experiment results. All the numerical applications show the merits and efficacy of the proposed method.

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