Quantification of Vibration Localization in Periodic Structures

A Chandrashaker, S Adhikari & MI Friswell (Swansea University)

Journal of Vibration and Acoustics, Vol. 138, No. 2, April 2016, 021002, Paper No: VIB-15-1115


The phenomenon of vibration mode localization in periodic and near periodic structures has been well documented over the past four decades. In spite of its long history, and presence in a wide range of engineering structures, the approach to detect mode localization remains rather rudimentary in nature. The primary way is via a visual inspection of the mode shapes. For systems with complex geometry, the judgment of mode localization can become subjective as it would depend on visual ability and interpretation of the analyst. This paper suggests a numerical approach using modal data to quantify mode localization by utilizing the Modal Assurance Criterion (MAC) across all the modes due to changes in some system parameters. The proposed Modal Assurance Criterion Localization Factor (MACLF) gives a value between 0 to 1 and therefore gives an explicit value for the degree of mode localization. First-order sensitivity based approaches are proposed to reduce the computational effort. A two-degree-of-freedom system is first used to demonstrate the applicability of the proposed approach. The Finite Element Method (FEM) was used to study two progressively complex systems, namely, a coupled two-cantilever beam system and an idealized turbine blade. Modal data is corrupted by random noise to simulate robustness when applying the MACLF to experimental data to quantify the degree of localization. Extensive numerical results have been given to illustrate the applicability of the proposed approach.

Paper Availability

This material has been published in the Journal of Vibration and Acoustics, Vol. 138, No. 2, April 2016, 021002, Paper No: VIB-15-1115, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by ASME.

Link to paper using doi: 10.1115/1.4032032

Journal of Vibration and Acoustics