Computational Technology Resources - CCP

Keywords: structural damage detection, non-destructive testing, vibration test, system analysis and identification, modal analysis, frequency response function, coordinate incompatibility, noise.

Summary

Modern engineering structures such as aircrafts, offshore oil platforms, transmission towers, are regularly monitored and maintained in order to avoid catastrophic failure. In spite of our best efforts, sporadic failures, which may have disastrous consequences in terms of human life and resources, still occur. It is therefore desirable to be able to detect invisible structural damage at an early stage so that appropriate measures can be taken to ensure the reliability of the structures. Non-destructive testing methods using ultrasound, X ray, dye penetrants, magnetic particle, acoustic emission, have been used to detect structural damage invisible to the unaided eyes. They are often limited to observation in a limited area and rely on a presumption of the likely area of damage A structural damage detection method using frequency response functions (FRF) data obtained from vibration test is presented. The method can locate damage and determine extent of damage in a structure. By using the abundance of FRF data, it can overcome the problem of coordinate incompatibility between the theoretical model and the experimental model by using dynamic expansion to evaluate the FRF data that cannot be obtained by experiments.

The basic equation of structural damage detection proposed here is:

$\displaystyle \{d(\Omega)\} = [Z(\Omega)]_{UD} \{\Delta\alpha (\Omega)\}_k$

(117.1)

where $\{d(\Omega)\}$ is the damage location vector (DLV), the subscript refers to the undamaged or virgin structure, $[Z(\Omega)]$ is the dynamic stiffness matrix, $[\alpha(\Omega)]$ is the receptance frequency response function (RFRF) at a particular frequency $\Omega$ and a column of this matrix is denoted by $\{\alpha(\Omega)\}_k$ . DLV can be evaluated at any frequency $\Omega$ and plotted against frequency range and degree of freedom (DOF), provided that the dynamic stiffness matrix $[Z(\Omega)]_{UD}$ of the undamaged structure and a column of the FRF of the damaged structure are available. In this method, the former is given by a FEM model, the latter is obtained from a vibration test, followed by Dynamic Expansion to overcome the problem of coordinate incompatibility. The method is called Damage Location Plot (DLP).

DLP was applied to the NASA 8 bay space truss structure and a plate structure. For the space truss structure, damage and noise were numerically simulated, the dynamic stiffness matrix and the FRF matrix were obtained from a computer program to assemble the truss elements for the FEM model and an algorithm using MATLAB was used to carry out the matrix operations. Cases involve either coordinate incompatibility or noise, or both were investigated. Similar steps were carried out for the plate structure. Simple discrete Kirchoff's theory (DKT) plate element was used for FEM model. Both numerically simulated damage as well as damage by saw cuts were used. For actual damage by saw cuts, vibration modal analysis using impact hammer was carried out to obtain FRF. These FRF with measurement noise were used in DLP to detect damage. Preliminary results show that this method of Damage Location Plot can overcome the problems of coordinate incompatibility and noise.

References

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