Model-Aided Diagnosis of Mechanical Systems: Fundamentals, by Professor Dr. rer. nat. Dr. hc. Hans Günther Natke,

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By Professor Dr. rer. nat. Dr. hc. Hans Günther Natke, Professor Dr. habil. Czeslav Cempel (auth.)

Diagnosis of technical structures is necessary, referring to protection and economics. tracking and analysis, specially in handheld remote control structures, wishes holistic versions, as defined the following. This publication describes the basics for technical prognosis in addition to state-of-art instruments. Model-based analysis and information established analysis, basics in decision-making and evaluate are incorporated. the basis of prognosis for purposes is given. The publication is written for the specialist training engineer in study and business applications.

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Extra resources for Model-Aided Diagnosis of Mechanical Systems: Fundamentals, Detection, Localization, Assessment

Example text

8) The eigenvectors are linearly independent and form a basis set, so that the eigenvector changes IlU can be expressed as a linear combination of the nominal eigenvectors with a matrix A: dU:= UoA. 9) the linearized Eq. 10) 24 2. 13) indicates that, to first order parameter modifications, the eigenvalue changes are independent of the eigenvector changes, and depend only on the nominal modal quantities and on the parameter modifications. Taking into account that A is a diagonal matrix, the non-diagonal elements of Eq.

2. 001 RELATED SUSPENSION SPRING ; : /1 Fig. 5. :,. e:,. 2 ~fl ~f2 ~f3 ~f4 ~f5 -23% -21% -15% +15% +16% Fig. 6. 1. Damage, Faults and their Descriptions 23 relative to the eigenfrequency related to k2 -+ 00. The shifts for the five modes shown are relatively large. The curves show that the percentage changes of the eigenfrequencies of the lower modes are greater. Eigenfrequencies are not always as sensitive as indicated in these examples. This can be seen by taking the Rayleigh quotient and by modifying the stiffness and/or the mass distribution locally.

Wk(~) = 0, where the prime denotes differentiation with respect to f Comparing Eqs. Wk"(O = 0: the maximum modification of Wk(~) is asymptotically connected with the bending moment (the second 20 2. Review of Tools and Concepts of Diagnosis Fig. 3. Local stiffness reduction of a beam - x Fig. 4. One-sided elastically supported beam derivative) equal to zero, however with the shear force Qk(~) ~ wk'(~') =j=. o. It also follows that max~ wk({) does not correspond to the maximum amplitude Wk(O (w k({) = 0).

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