Uncertainty of the spectrum processing is estimated as the difference of the 2% extended spectrum from the 2% one at frequency of 6.81 Hz. Considering that the extension provides for 99% probability of non-exceedance (+2.33), we will get (at frequency of 6.81 Hz) by the lognormal distribution properties: . Damping The design frequency of the electric motor was 4.23 Hz corresponding to the acceleration 0.81g. It is considered that the 5% damping is median. However, when computing the damping coefficient and its uncertainty () one should first correct the frequency that changed due to the calculation update. Damping was taken into account when calculating the previous coefficient, therefore . Frequency 6.81 Hz is within the zone of response spectra intensification. In this zone, relations of the spectra (accelerations) with various attenuation coefficients (in fractions of the critical one) at the selected frequency are approximately inversely proportional to the square root of the relation of these attenuation coefficients. It is assumed that the 2% spectrum form the boundary corresponding to the standard deviation 2U , while the 5% spectrum is median (U = 0) (such assumption is suggested in the form of the expert evaluation). In this case: Modeling Possible decrease of the natural frequency due to change of damping and propagation of non-linear deformation is considered. are several methods of taking into account the change of loads on the elements due to the mentioned effects. Here the expert approach is used as the basis for such accounting. As mentioned above, the natural frequency 6.81 Hz is within the zone of response spectra intensification. When the natural frequency decreases, the load on the support structure will also decrease in accordance with the response spectrum. It is reasonably to suppose the decrease of the natural frequency by approximately 10% (median value) due to propagation of the non-linear deformations in the pre-failure
Uncertainty of the spectrum processing is estimated as the difference of the 2% extended spectrum from the 2% one at frequency of 6.81 Hz. Considering that the extension provides for 99% probability of non-exceedance (+2.33), we will get (at frequency of 6.81 Hz) by the lognormal distribution properties: . Damping The design frequency of the electric motor was 4.23 Hz corresponding to the acceleration 0.81g. It is considered that the 5% damping is median. However, when computing the damping coefficient and its uncertainty () one should first correct the frequency that changed due to the calculation update. Damping was taken into account when calculating the previous coefficient, therefore . Frequency 6.81 Hz is within the zone of response spectra intensification. In this zone, relations of the spectra (accelerations) with various attenuation coefficients (in fractions of the critical one) at the selected frequency are approximately inversely proportional to the square root of the relation of these attenuation coefficients. It is assumed that the 2% spectrum form the boundary corresponding to the standard deviation 2U , while the 5% spectrum is median (U = 0) (such assumption is suggested in the form of the expert evaluation). In this case: Modeling Possible decrease of the natural frequency due to change of damping and propagation of non-linear deformation is considered. are several methods of taking into account the change of loads on the elements due to the mentioned effects. Here the expert approach is used as the basis for such accounting. As mentioned above, the natural frequency 6.81 Hz is within the zone of response spectra intensification. When the natural frequency decreases, the load on the support structure will also decrease in accordance with the response spectrum. It is reasonably to suppose the decrease of the natural frequency by approximately 10% (median value) due to propagation of the non-linear deformations in the pre-failure
RB-123-17%20ENG.docx