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S21 Vibrações e Análise Modal |
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Title:
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THE USE OF CONVEX SETS IN DAMAGE DETECTION
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Summary :
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ABSTRACT. DAMAGE DETECTION IN A CANTILEVER EULER-BERNOULLI BEAM IS INVESTIGATED. THE MATHEMATICAL MODEL FOR THE SYSTEM IS OBTAINED USING THE FINITE METHOD AND STATIC CONDENSATION. IN THIS PAPER, DAMAGE IS CONSIDERED A REDUCTION IN THE STIFFNESS OF ANY PARTICULAR ELEMENT OF THE MODEL. THE DETECTION SCHEME IS BASED ON ESTABLISHING FAILURE SETS WHICH PREDICT THE NATURAL FREQUENCY CHANGES IN THE BEAM DUE TO DAMAGE AT A GIVEN ELEMENT LOCATION. THESE FAILURE SETS ARE COMPARED WITH THE ACTUAL BEAM S RESPONSE USING AN EUCLIDEAN NORM. THE MODEL IS RESTRICTED TO A CONSERVATIVE SYSTEM THAT IS DESCRIBED BY A POSITIVE DEFINITE MATRIX CAPABLE OF BEING TRANSFORMED INTO A DIAGONAL JORDAN CANONICAL FORM. THE RESTRICTION OF THE MATHEMATICAL MODEL ENABLES THE FORMULATION OF A STANDARD EIGENVALUE PROBLEM. THIS REPRESENTATION HAS A GEOMETRIC INTERPRETATION OF A N-DIMENSIONAL ELLIPSOID THAT IS A CONVEX SET. AN EXAMPLE OF A TWO-DEGREE OF FREEDOM MODEL IS ESTABLISHED TO EXAMINE THE EFFECT DAMAGE HAS ON THE GEOMETRIC REPRESENTATION OF THE EIGENVALUE PROBLEM. THE GEOMETRIC REPRESENTATION OF THE EIGENVALUE PROBLEM OF THE DAMAGED STATE IS THE CONVEX HULL OF THE BEAM S PREVIOUS EXISTING CONDITION. THIS LEADS TO THE MATHEMATICAL VALIDATION OF THE ABOVE MENTIONED DAMAGE DETECTION SCHEME. EXPERIMENTAL VERIFICATION IS PERFORMED FOR SEVERAL CASES OF THE SIMPLIFIED MODEL. THE RESULTS SHOW THAT THE METHOD IS EASY TO USE AND DOES NOT REQUIRE A RIGOROUS AMOUNT OF INSTRUMENTATION FOR OBTAINING THE EXPERIMENTAL DATA REQUIRED BY THE DAMAGE DETECTION SCHEME.
KEYWORDS: DAMAGE DETECTION, CONVEX SETS, EULER-BERNOULLI BEAM
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Author :
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Agosto, Frederick A. J.
Hendricks, Scott L.
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Paper View :
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