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Parameter Reconstruction of Vibration Systems from Partial Eigeninformation.

Bo Dong¹, Matthew M Lin, Moody T Chu

¹Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024.

Journal of Sound and Vibration

|August 23, 2013

Summary

This summary is machine-generated.

This study presents a general method for solving structured inverse eigenvalue problems in vibration analysis. It enables the reconstruction of complex mass-spring systems, regardless of their configuration.

Keywords:

connectivity inverse eigenvalue problem linear inequality system low rank approximation maximin problem nonnegativity quadratic matrix polynomial quadratic programming

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Area of Science:

Mechanical Engineering
Applied Mathematics
Vibration Analysis

Background:

Quadratic matrix polynomials are essential for modeling vibration systems.
Physical constraints necessitate specific structures in these polynomials.
Reconstructing systems from observed behavior (inverse problem) is challenging due to these structures.

Purpose of the Study:

To generalize methods for solving structured inverse eigenvalue problems beyond serially linked systems.
To develop a systematic mechanism for generating inequality systems for arbitrary mass-spring configurations.
To provide a robust numerical approach for determining solvability and computing system parameters.

Main Methods:

Generalization of previous inequality system formulations.
Development of a systematic mechanism for generating inequality systems based on system interconnectivity.
Proposal of a numerical approach to solve the inverse problem and estimate errors.

Main Results:

A problem-independent and robust numerical approach for structured inverse eigenvalue problems.
Successful implementation into a software package.
Demonstration of the approach's general applicability through numerical experiments.

Conclusions:

The developed method effectively addresses structured inverse eigenvalue problems for general mass-spring systems.
The approach is systematic, automatic, and robust for diverse physical configurations.
This work provides a valuable tool for reconstructing complex vibration systems.