Sensitivity analyses of resonant frequencies and modal strain energy of damaged beams by perturbation method

G Chen,P Liang,P P Gong

doi:10.21595/jve.2018.19560

Abstract

A new perturbation method has been proposed to investigate the sensitivities of the eigen-parameters (frequencies and mode shapes) and the modal strain energy density of a damaged beam. The sensitivities were obtained via the Rayleigh quotient and Taylor series expansion. The damage was simulated by the reduction in the cross-sectional area of the beam. The theoretical relationships were established between the damage parameter and the variations of the frequency and modal strain energy. The analytical formulae explicitly reveal the underlying mechanism that, the frequency, which is closely related to the modal strain energy of the entire structure, is less sensitive to the local damage; the modal strain energy density, on the other hand, is able to reflect the local damage in a small region. The results of the perturbation analyses were validated with the finite element analyses and experimental tests of the beam models with 2 damage levels. The first resonant frequencies decrease slightly with the increases of the damage. When 30 % of the cross-sectional area is cut off in the damaged zone, the first resonant frequencies are still 95 % and 98 % those of the intact beam for the bending vibration around x-axis and around y-axis; meanwhile, the modal strain energy increases 94 % and 54 % in the damage zone, which closely correlates with the local damage parameters. The proposed perturbation method has the potential to assess the quality of damage indictors faster and more easily than FE and experimental methods.

Highlights

Detection and quantification of structural damages are of great importance to ensure the lifetime safety, prevent catastrophic events, and increase the service of structures
This paper aims to propose a perturbation method based on the Rayleigh quotient via a beam model to evaluate the sensitivities of the first frequency and the modal strain energy in a region
When the beam is cut off 10 % in the height in the damage zone, the bending stiffness is reduced 27 % around x-axis and 10 % around y-axis; which results in the frequency being reduced 2 % and 1 % respectively for the bending vibration around x-axis and y-axis

Summary

Introduction

Detection and quantification of structural damages are of great importance to ensure the lifetime safety, prevent catastrophic events, and increase the service of structures. Available damage detection methods include magnetic field methods, ultrasonic methods, eddy-current methods, and thermal field methods [1], which are localized experimental methods. Most of these experimental methods require that the damage location is approximately known in advance and accessible for inspection. The underlying idea behind the vibration-based technology is that, the changes in the physical properties (stiffness, mass, and damping) of a structure will cause detectable changes in its modal parameters (frequencies, modes, and strain energy) which are the functions of its physical properties [5, 6]. The changes in the modal parameters can be assumed as indictors for damage detection.

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