By Tomasz Krysinski
This ebook offers a learn of the soundness of mechanical structures, i.e. their unfastened reaction after they are faraway from their place of equilibrium after a brief disturbance. After reviewing the most analytical equipment of the dynamical balance of platforms, it highlights the basic distinction in nature among the phenomena of pressured resonance vibration of mechanical structures subjected to an imposed excitation and instabilities that represent their loose reaction. It particularly develops instabilities bobbing up from the rotor–structure coupling, instability of keep an eye on structures, the self-sustained instabilities linked to the presence of inner damping and instabilities on the topic of the fluid–structure coupling for fastened and rotating buildings. For an unique procedure following the research of instability phenomena, the ebook offers examples of ideas received through passive or lively methods.Content:
Chapter 1 Notions of Instability (pages 1–90):
Chapter 2 Rotor/Structure Coupling: Examples of flooring Resonance and Air Resonance (pages 91–152):
Chapter three Torsional approach: Instability of Closed?Loop structures (pages 153–200):
Chapter four Self?Sustaining Instability for Rotating Shafts (pages 201–243):
Chapter five Fluid?Structure interplay (pages 245–333):
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Example text
It corresponds to the plot of the transfer locus in the complex plane, the Cartesian coordinates of which are Re(ω) and Im(ω). The curve is always oriented in the increasing ω direction. The Nyquist criterion resulting from the Cauchy’s theorem is used to study the zeros of the denominator of transfer function H(ω). We propose to use the simplified left-hand criterion. By representing the Nyquist locus of the open-loop transfer function, we can know the stability of the closed-loop system. 39 while checking that, for each pole, the curve passes on the right of point (-1,0) in the Nyquist plane, known as critical point.
9. 9. Transfer Function for Several Damping Ratio Values By definition, resonance frequency Ωr corresponds to the transfer function maximum (if any). 9. These amplitudes are not divergent. However, if damping is low, excessively large vibration amplitudes may lead to system breakage. The structure behavior to resonance can be interpreted by using a representation in the complex plane, similar to the notion of Fresnel rotating vector. 10. 10. 1. Behavior Before Resonance Significantly before resonance, the excitation frequency is such that: Ω<<ωp.
29. 48] The poles of the transfer system correspond to eigenvalues si of A. Simply observe the position of the poles in the complex plane to derive the system stability. Demonstrated in Chapter 2, the result shows that there are dominant poles. 8 Hz for the modes with a high lag component. 29. The dominant poles can be determined in this case by studying the mode deformation. Thus, for each eigenvalue si, the associated eigenvector Vi can be determined. 49] In order to determine the dominant poles, look at the amplitude of the eigenvector associated with each parameter.
