Application of the dynamic stiffness matrix to the identification of cracks in beams and frames.

• Autorzy: Łukasiewicz, S.A. , Qian, E.R.

Warianty tytułu

PL

Zastosowanie dynamicznej macierzy sztywności do identyfikacji pęknięć w belkach i ramach.

• Języki publikacji: EN

Abstrakty

EN

The paper discusses the problem of the accuracy of the identification techniques detecting cracks and corroded members in vibrating beam and frame structures. The presence of the fatigue crack usually causes very small changes of the stiffness of the beam elements of the structure. To detect these changes it is necessary to apply the most precisely mathematical detection technique. The identification procedure based on the least squares technique uses finite elements models (FEM) of the structure and as a source of information the measured dynamic response and the natural frequencies. The application of the Dynamic Stiffness Matrix (DSM) for the representation of all constraints and model equations makes it possible to present the identification process in a very accurate and efficient mathematical form. The method of the detection of structural changes used in the present papaer was described in our previous paper. The Consistent Mass Matrieces (CMM) and Lump Mass Matrices (LMM) are very often used in the identification algorithms. It is shown that application of simplified approaches (CMM and LMM) can result in lower accuracy and poorer convergence of the identification algorithms. However, the application of CMM mass matrices does not introduce significant errors. The algorithms were tested on simulated numerical data for ten element beam frames.

PL

W artykule przedyskutowano problem dokładności wibracyjnych technik identyfikacji, stosowanych przy wykrywaniu pęknięć i skorodowanych członów konstrukcji belkowych i ramowych. Obecność pęknięć zmęczeniowych powoduje zwykle bardzo małe zmiany sztywności elementów belkowych konstrukcji. W celu wykrycia tych zmian niezbędne jest zastosowanie najbardziej precyzyjnych metod matematycznych. W procedurze identyfikacji opartej na metodzie najmniejszych kwadratów, stosuje się modele elementów skończonych (FEM) danej konstrukcji, a jako źródło informacji wykorzystuje się zmierzoną odpowiedź dynamiczną i częstotliwości drgań własnych. Zastosowanie Dynamicznej Macierzy Sztywności (DSM) do reprezentacji wszystkicj więzów i również modalnych pozwala na przedstawienie procesu identyfikacji w bardzo dokładnej i efektywnej formie matematycznej. Metoda detekcji zmian strukturalnych, użyta w przedstawionej pracy, była opisana w poprzedniej publikacji autorów. W algorytmach identyfikacji bardzo często używa się Macierzy Zgodnych Mas (CMM) i Macierzy Mas Skupionych (LMM). Jak wykazano, zastosowanie podejścia uproszczonego (CMM i LMM), może prowadzić do małej dokładności i słabej zbieżności algorytmów identyfikacji. Niemniej, zastosowanie macierzy mas typu CMM nie wprowadza istotnych błędów. Algorytmy były testowane na symulowanych danych numerycznych dla dziesięcioelementowych ram belkowych.

Słowa kluczowe

PL

identyfikacja; belka; rama; pęknięcie; macierz sztywności dynamicznej

EN

identification; vibration; drgania; beam; frame; crack; dynamic stiffness matrix

• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2004
• Tom: Vol. LI, nr 2
• Strony: 215-244
• Opis fizyczny: Bibliogr. 39 poz., rys., tab.

Twórcy

autor

Łukasiewicz, S.A.

• Department of Mechanical Engineering, The University of Calgary, Calgary Alberta, Canada,

autor

Qian, E.R.

• Department of Mechanical Engineering, The University of Calgary, Calgary Alberta, Canada

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