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Damage detection from the variation of parameter matrices estimated by incomplete FRF data
Salam Rahmatalla,은희창,이은택 국제구조공학회 2012 Smart Structures and Systems, An International Jou Vol.9 No.1
It is not easy to experimentally obtain the FRF (Frequency Response Function) matrix corresponding to a full set of DOFs (degrees of freedom) for a dynamic system. Utilizing FRF data measured at specific positions, with DOFs less than that of the system, as constraints to describe a damaged system, this study identifies parameter matrices such as mass, stiffness and damping matrices of the system, and provides a damage identification method from their variations. The proposed parameter identification method is compared to Lee and Kim’s method and Fritzen’s method. The validity of the proposed damage identification method is illustrated in a simple dynamic system.
Salam Rahmatalla,이은택,은희창 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.4
Assuming that the existence of the constraints yields the change of the inertia force, this study derives the time-varying mass matrix for describing the constrained dynamic equation. It is displayed that the results corresponds with the ones by Udwadia and Kalaba. The numerical results obtained by integrating the constrained dynamic equation of second-order differential equations yield the errors in the satisfaction of the constraints. Modifying the derived dynamic equation this study presents a numerical algorithm to reduce the errors and to compute more precise motion. It is illustrated that the proposed method can be more precisely utilized in constrained mechanical systems through two applications of constrained nonlinear robotic systems.
Damage detection by the distribution of predicted constraint forces
Salam Rahmatalla,이은택,은희창 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.4
Damage causes the deterioration of dynamic and static performance of intact structures. Regarding the measured static displacement or modal displacement data as constraints for describing damaged responses, this study derives analytical equations to estimate constraint forces in the satisfaction of constraints. The constraint forces are forces required for describing the flexural shape of the damaged beam under static and dynamic loadings. Based on the concept that the occurrence of damage causes the change of force mechanism, this work proposes an analytical method to detect damage from the distribution of constraint forces. When compared to the displacement curvature and the frequency response function (FRF) curvature methods using 2% noise, the results have shown that the proposed method is less sensitive to noise and is more effective in detecting multiple damaged areas in the beam of short span length and their intensity at low levels of damage.
Damage detection from the variation of parameter matrices estimated by incomplete FRF data
Rahmatalla, Salam,Eun, Hee-Chang,Lee, Eun-Taik Techno-Press 2012 Smart Structures and Systems, An International Jou Vol.9 No.1
It is not easy to experimentally obtain the FRF (Frequency Response Function) matrix corresponding to a full set of DOFs (degrees of freedom) for a dynamic system. Utilizing FRF data measured at specific positions, with DOFs less than that of the system, as constraints to describe a damaged system, this study identifies parameter matrices such as mass, stiffness and damping matrices of the system, and provides a damage identification method from their variations. The proposed parameter identification method is compared to Lee and Kim's method and Fritzen's method. The validity of the proposed damage identification method is illustrated in a simple dynamic system.
Estimation of parameter matrices based on measured data
Lee, Eun-Taik,Rahmatalla, Salam,Eun, Hee-Chang Elsevier 2011 Applied mathematical modelling Vol.35 No.10
<P><B>Abstract</B></P><P>Finite element structural updating based on measured data may inherent significant errors due to uncertainties in the updated physical parameter matrices. This study presents analytical equations to estimate the change in the physical parameter matrices based on the measured modal data of dynamic systems and the measured displacement data of static systems. The equations for the parameter estimation are derived by minimizing cost functions in the satisfaction of the eigenvalue equation, the mode shape orthogonality requirements for the dynamic system, and the satisfaction of the measured displacement data for the static systems. The proposed method utilizes the Moore–Penrose inverse for the inverse of the rectangular matrices without using Lagrange multipliers. Comparing the analytical results with Berman & Nagy’s method and Yang & Chen’s method, this study demonstrates that the derived equations take simpler forms and produce more accurate results. The proposed method can be widely utilized in predicting static or dynamic parameter matrices for the design and analysis of any structure.</P>