Authors
Tyapin A.G.

Тяпин Александр Георгиевич Tyapin A.G.
Dr.Sci.Tech., JSC Atomenergoproject. Moscow, Russian Federation


Publications

Equation of planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov
Issue:
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The author derives the equation of planar vibrations of rigid structure resting on kinematical pendulum supports with planar bottom (after A.M. Kurzanov). Both support and the surface below are assumed rigid; no sliding assumed. One of the coefficients in the equation (i.e. coordinate of the rotation center) proves to be piece-wise constant. The equation is of the hyperbolic type with parametric terms. Even linearization of this equation does not bring it to the conventional equation of the SDOF oscillator. Principal difference is that the free vibration period depends on the amplitude. The equation is checked for free and forced vibrations. Similar problem is for the seismic response of the unanchored items. For the further research the experimental data about damping are of great importance: both for rotation and the gap closing.

Combination of modal responses in linear spectral method: comparison of different formulae for correlation coefficients
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Linear-spectral method (LSM) is still the common method for the seismic design analysis. "One-component one-mode" responses, obtained by static analysis in the conventional variant of LSM, are combined twice: first for different modes but for each single excitation component separately, then for the different excitation components. In the alternative LSM variant presented in the Russian code SP 14.13330, first one chooses the "most dangerous" direction of the one-component excitation for each mode; then calculates the "one-mode" response for this excitation, and finally these responses are combined. In both cases the combination is performed using the complete quadratic combination (CQC) rule. Different documents suggest different formulae for the correlation coefficients. In the paper different formulae are compared to each other. The goal is to limit the number of calculated coefficients and decrease the amount of calculations.

Planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov
Issue: #6 2020
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The author carries out parametric studies for the equation of planar vibrations of rigid structure resting on kinematical rolling supports with planar bottom (after A.M. Kurzanov). Both support and the surface below are assumed rigid; no sliding assumed. Varied parameter is the width of the bottom. Horizontal structural acceleration is studied. Three variants of the possible behavior are shown: (i) minor rocking with little decrease in response accelerations as compared to the initial excitation; considerable rocking with considerable decrease in the response accelerations; intensive rocking leading to the overturn of the supports. In vertical direction there appear shocks (infinite accelerations) during gap closings of the supports. The importance of the problem for the seismic response analysis of the unanchored items is noted. The author gives recommendations for the experimental program, aimed to obtain data about damping both for rotation and for the gap closing, and also about the impact of the flexibility of the supports and underlying surface. 

PLANAR VIBRATIONS OF RIGID STRUCTURE ON KINEMATIC SUPPORTS: GENERAL GEOMETRY
Issue: №4 2020
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The author derives
the equation of planar vibrations for kinematical rolling supports of varying
curvature radius. Both support and the surface below are assumed rigid; no
sliding assumed. Generalization means arbitrary geometry of the support and
rolling surface (the building is attached to the supports by hinges, as
previously). The equation of motion developed is checked with free and forced
vibrations of the support with two curvature radii (great radius in the central
part and small radius in the side parts). Such a support in the limit case
(when great radius goes to infinity, and small radius goes to zero) models the
support after A.М.
Kurzanov with planar bottom and finite size in plan. 

Planar Vibrations of Rigid Structure Resting on Kinematical Supports of Yu. D. Cherepinsky
Issue: №3 2020
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The author derives the equation of motion for a structure resting on kinematical pendulum supports of Yu.D.Cherepinsky. Both structure and supports are assumed to be rigid; no
sliding is assumed during rolling. Two components of seismic excitation are considered (horizontal one and vertical one). Equation of motion for free vibrations looks like that of the free vibrations for massive pendulum support standing alone (it was studied earlier). It is fact the equation of motion for pendulum, but center of rotation, inertia moment and stiffness are varying with time. This equation may be simplified to the linear one by skipping the second
order terms. The equation of motion for seismic response after linearization is the extension of the Mathieu-Hill’s equation, where horizontal component is responsible for the right-hand part (in the conventional Mathieu-Hill’s equation it is zero), and vertical component creates parametric excitation in the left-hand part. In fact, vertical seismic acceleration modifies gravity acceleration g, which controls the effective natural frequency for pendulum.
Thus, there might appear dynamic instability (though without infinite response due to the finite duration of excitation). The author presents numerical example.

Free Vibrations of Rigid Kinematic Support of Yu.D. Cherepinsky
Issue: №2 2020
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The author derives the equation of free vibrations for kinematical rolling support of Yu.D.Cherepinsky. Both support and the surface below are assumed rigid. It is shown that Lagrange equation is similar to the equation of motion for rotational oscillator where the rotation centre, rotational inertia and stiffness are changing every moment, depending on displacements. This equation can be further simplified to the linear form with the error proportional to the second degree of displacements. This equation looks somewhat like the equation for classical pendulum, but effective length in our case is controlled by curvature radii of support and of the rolling surface, as well as by the position of vertical load relative to the centre of the support. Non-linear characteristic is soft. The main nonlinearity is in the inertial term, and not in the stiffness term.

Site Response Analysis for “Side” Soil Profiles
Issue: №1 2020
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The authors suggest a new procedure of Site Response Analysis (SRA) for the so-called “side” (or additional) soil profiles – Low Boundary (LB) and Upper Boundary (UB). Standards require the analyses of these profiles in addition to the Best Estimate profile (BE) to account for the uncertainty in the input data about soil properties. The authors suggest stopping using the same input time history for all three profiles as a control motion at the surface, because it corresponds to the different physical seismic excitations coming form the depth. This is not in line with the ideology of Standards. Instead the authors suggest using the same time history as a control motion at the outcropped surface of the underlying half-space. This is also not completely correct, because for these three profiles (BE, UB and LB) the underlying half-spaces are also different. However, due to the physical considerations if all half-spaces are stiff enough, the error should not be so important. The effect of the 
proposed change is demonstrated on a particular site. The changes in the velocity and damping profiles have proved to be negligible, but the difference in the resulting response spectra at the outcropped surface of the foundation mat has proved to be significant. Generally, the response spectra for the “side” profiles came closer to spectrum for the BE profile. This result reflects the real world logic.


Issue: №5 2018
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