Dynamic detection methods are based on the fact that damage influences the dynamic behaviour of structures, changing their mechanical characteristics [1]. Literature reviews present methods based on frequency shift [2], mode shapes and their derivatives [3] or on structural flexibility [4]. These methods generally use finite element models, involving a reduced number of elements; at the same time, few numbers of vibration modes are considered. This leads to difficulties in understanding the physical phenomenon which occurs as a result of the damage, as well as to precisely assess damage using these methods.

The proposed method takes into account the results of our previous research in which the dynamic behaviour of different beams was analysed, with a focus on frequency changes occurring as a result of damage [5]. This paper presents a relationship between frequency changes and damage location and severity, valid for all support types and mode numbers, containing only these two variables. Practically, the frequency shift is dependent on the beam characteristics considered represented by a constant, a term depending on the location (given by the square of the mode shape curvature of the undamaged beam) and one on the damage depth.

The first stage of the assessment algorithm consists in assigning the unit value to the term considering the damage depth; consequently, the relation depends just on the damage location. For any location along the beam one can determine, for the first ten vibration modes of the undamaged beam, a set of ten values representing the square of the respective mode shape curvatures for that location. This is a pattern characterizing the frequency changes for a damage placed at a certain location. By comparing measurement results with several patterns, one can determine the location.

Afterwards, by determing the term for the second variable, the depth can be assessed. Using continuous models and a large series of modes, the method is reliable (being successfully validated using numerous experiments) and ensures high precision, requiring only minimal data acquisition equipment.

1

A. Morassi, F. Vestroni, "Dynamic Methods for Damage Detection in Structures", CISM Courses and Lectures, 499, Springer Wien New York, 2008. doi:10.1007/978-3-211-78777-9

2

P. Cawley, R.D. Adams, "The location of defects in structures from measurements of natural frequencies", Journal of Strain Analysis, 14(2), 49-57, 1979. doi:10.1243/03093247V142049

3

A.K. Pandey, M. Biswas, M.M. Samman, "Damage detection from changes in curvature mode shapes", Journal of Sound and Vibration, 145, 321-332, 1991. doi:10.1016/0022-460X(91)90595-B

4

S.W. Doebling, C.R. Farrar, M.B. Prime, D.W. Shevitz, "Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review", Report No. LA 13070-MS, Los Alamos National Laboratory, Los Alamos, NM, 1996.

5

G.R. Gillich, Z.I. Praisach, "Robust method to identify damages in beams based on frequency shift analysis", SPIE Smart Structures/NDE, 8348-47, San Diego, California, USA, 2012. doi:10.1117/12.915158

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