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The level of mitigation depends not only on the amount of eccentricity but also on the frequency ratio (the ration of translational frequency to rotational frequency).
Depending on the ratio of the torsional to the translational eigenfrequency, i.e. the torsional to translational frequency ratio (TTFR), of asymmetric structures, the following three scenarios can be distinguished: (1) torsionally flexible structures (TTFR<1.0), (2) torsionally intermediate stiff structures (TTFR=1.0), and (3) torsionally stiff structures (TTFR>1.0).
Depending on the ratio of the torsional to the translational eigenfrequency, i.e. the torsional to translational frequency ratio (TTFR), of asymmetric structures, the following cases can be distinguished: (1) torsionally flexible structures (TTFR<1.0), (2) torsionally intermediate stiff structures (TTFR=1.0), and (3) torsionally stiff structures (TTFR>1.0).
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If the magnitudes of all translational frequencies are <0.01 cm−1 and the magnitudes of all rotational frequencies are <10 cm−1, all vibrational frequencies are checked; otherwise, the analysis of vibrational frequencies is aborted and the ligand is considered not to be in its local minimum conformation.
If the magnitudes of all translational frequencies are <0.01 cm−1 and the magnitudes of all rotational frequencies are <10 cm−1, all vibrational frequencies are checked; otherwise, the analysis of vibrational frequencies is aborted and the guest is considered not to be in its local minimum conformation.
An accurate joint model should include translational and rotational frequency response functions (FRFs) and consider the joint's inertial properties.
Slug flow characteristics such as translational velocity, slug frequency, and slug length were experimentally measured using a 50.8 mm ID vertical pipe for six different high oil viscosities, namely 586, 401, 287, 213, 162, and 127 mPa s.
Empirical relationships were assessed by means of (a) areal changes of forests and logged areas, (b) spatio-temporal distribution of shallow translational landslides, (c) frequency ratios and (d) logistic regression analysis.
The inclusion of massive foundation and nonlinearity of soil effects leads to the amplification of higher modes of vibration and activates the high-frequency translational motion of the input ground motion and generates foundation-rocking responses.
The cut-offs for the gradient and the translational and rotational frequencies are obtained from reference 12, and are based on the fact that geometry cannot be optimized to a gradient of exact zero because of numeric truncations [12].
The cut-offs for the gradient and for the translational and rotational frequencies are obtained from reference 16 and based on the fact that geometry cannot be optimized to a gradient of exact zero because of numeric truncations [16].
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