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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
An Improved Structural Damage Detection Method Based on Modal Strain Energy
G.J. He12, M. Yuan1 and L. Elfgren2
1Civil Engineering and Architecture College, Central South University of Forestry and Technology, Changsha, Hunan, P.R.China
G.J. He, M. Yuan, L. Elfgren, "An Improved Structural Damage Detection Method Based on Modal Strain Energy", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 294, 2006. doi:10.4203/ccp.83.294
Keywords: damage detection, modal strain energy, vibration, structures.
Based on modal strain energy, an improved structural damage detection algorithm is developed in this paper. By dividing the contribution of higher modes into two parts, i.e., the static and dynamic contributions, the static term can be expressed by lower modes and the dynamic term was approximately approached.
According to the structural modal methods, with a change of stiffness and mode shape, it can be assumed that,
where, is the change in the structural stiffness matrix resulting from damage; is the change in the th mode shape resulting from damage; is the total number of elements; is the total number of modes; is the number of low modes; , and are the coefficients defining a fractional change of the stiffness matrix and the mode shape vector.
The total contribution of lower and higher modes can be expressed as follows,
The modal strain energy change (MSEC) of the th element and th mode can be defined as
Substituting equation (61) into equation (62)
Selecting the values of MSE of elements (commonly ), and so damage coefficients of possible damaged elements can be calculated according to the following linear system of equations
Coefficient , can be expressed as
This approach could be applied to detect structural damage location and quantity by using only the first one or two modes.
The three numerical examples with different structures, but the same damaged case, are studied in present. The results illustrate that the present method is simple and effective with satisfactory precision both in locating the place of damage and estimating the magnitude of damage. The following conclusions have been obtained:
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