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Non-Model Based Expansion from Limited Points to an Augmented Set of Points Using Chebyshev Polynomials

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Abstract

Expansion of measured dynamic response at a limited set of points is of great interest in the study of structural dynamic systems. Measurements at limited points on a structure can be expanded to unmeasured points by using System Equivalent Reduction Expansion Process (SEREP). However, a finite element model is required to obtain the mode shapes of the system. In this work, a non-model based expansion technique is proposed to expand the vibration characteristics at a sparse set of points to a much larger set of points without the use of a finite element model. Shape functions based on orthogonal polynomials can be used to decompose the deformation of vibrating structures into the summation of a set of shape functions with corresponding weighting coefficients. To obtain the vibration characteristics at an augmented set of points, measurements at a sparse set of points can be related to a set of shape functions which have the same mesh resolution as the sparse configuration. The vibration characteristics at an augmented set of points can then be reconstructed from the shape functions of the high resolution and scaled shape function weighting coefficients of the sparse configuration. Only a sparse set of measurements, geometry and coordinates of measured points are needed. In the work studied here, an analytical plate and a Base-Upright (BU) structure are used as samples to study the application of the proposed method. Both analysis and experiment are used to prove the concept.

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Acknowledgements

Some of the work presented herein was partially funded by Air Force Research Laboratory Award FA8651-16-2-0006 “Nonstationary System State Identification Using Complex Polynomial Representations”. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the particular funding agency. The authors are grateful for the support obtained. Distribution A. Approved for public release; distribution unlimited. (96TW-2018-0237).

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Authors and Affiliations

  1. Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, One University Avenue, Lowell, MA, 01854, USA

    Y. Chen, P. Logan & P. Avitabile

  2. Air Force Research Laboratory, Munitions Directorate, Fuzes Branch, Eglin Air Force Base, 306 W. Eglin Blvd., Bldg 432, Eglin AFB, FL, 32542-5430, USA

    J. Dodson

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  1. Y. Chen
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  2. P. Logan
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  3. P. Avitabile
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  4. J. Dodson
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Correspondence to Y. Chen.

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Appendix

Appendix

Fig. 21
figure 21

The deformation format of the first 10 terms of 2D Chebyshev polynomial shape functions

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Chen, Y., Logan, P., Avitabile, P. et al. Non-Model Based Expansion from Limited Points to an Augmented Set of Points Using Chebyshev Polynomials. Exp Tech 43, 521–543 (2019). https://doi.org/10.1007/s40799-018-00300-0

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