Damage Identification in Continuum Structures From Vibration Modal Data
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ABSTRACT A novel procedure for damage identification of continuum structures is proposed, where both the location and the extent of structural damage in continuum structures can be correctly determined using only a limited amount of measurements of incomplete modal data. On the basis of the exact relationship between the changes of structural parameters and modal parameters, a computational technique based on direct iteration and directly using incomplete modal data is developed to determine damage in structure. Structural damage is assumed to be associated with a proportional (scalar) reduction of the original element stiffness matrices, equivalent to a scalar reduction of the material modulus, which characterises at Gauss point level. Finally, numerical examples for plane stress problem and plate bending problem are utilised to demonstrate the effectiveness of the proposed approach. INTRODUCTION Nondestructive damage evaluation methods using modified modal properties are highly attractive. Since they allow early damage detection at a relatively low cost, recently several researchers proposed various methods for damage identification [3-7]. Typically, a large amount of modal information associated with the damaged structure has to be employed to correctly identify damage in structures. Due to practical testing limitations, the dimension of the experimental eigenvectors is often significantly less than that of the analytical eigenvectors. To compare the undamaged analytical model and the damaged test model for the purpose of damage detection, both models need to have mode shape information with the same order of DOFs. Usually, either the order of the analytical model has to be reduced or the order of test results has to be expanded. However, any model reduction process introduces errors in the analytical model, while the mode shape expansion process introduces errors in the expanded mode shapes. Both sources of errors affect the accuracy in damage prediction, especially for structures experiencing serious damage. Therefore, a process capable of identifying structural damage while at the same time expanding the mode shapes would be desirable. Here, a computational technique based on a Direct Iteration which directly utilise the incomplete set of modal data is presented. It is demonstrated that the proposed method performs very well for structural damage detection even when only a limited number of sensors are placed. TECHNIQUES BASED ON CHARACTERISTIC EQUATIONS The governing equations, which represent the exact relationship between the change of structural parameters and the change of modal parameters, have been developed in Ref [1,2], and are now outlined as follows. From the spectral decomposition, the characteristic equations for the damaged structure can be rewritten as 281
Mat. Res. Soc. Symp. Proc. Vol. 503 © 1998 Materials Research Society
NC 0kT k=I
Xi
KOI*
-xk i
k
where NC represents the number of available modes for the original structure; Xi and ýj are the jph eigenvalue and the corresponding mode
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