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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**PLANAR VIBRATIONS OF RIGID STRUCTURE ON KINEMATIC SUPPORTS: GENERAL GEOMETRY**

**Issue:** №4 2020

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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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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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**Site Response Analysis for “Side” Soil Profiles**

**Issue:** №1 2020

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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.

**“Old” and “New” Nodes in Modeling of Complicated Soil Environment**

**Issue:** №6 2019

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is hard enough, this difference is negligible: “new nodes” approach will not give new results. But in case of soft substituting soil this “residual” stiffness can spoil the results of the “old nodes” approach. In such cases the “new nodes” approach is justified in spite of the increase of the problem size. Combined Asymptotic Method (CAM) is extended for the case of the “new nodes” approach; the capability of CAM is further extended. The topic is important because of the implementation of the upgraded soil pads under the base mats of the heavy structures in seismic regions.

**Some Comments on the New Generation of Standards in Earthquake Engineering. Part I: General Requirements and Seismic Input. Part II: Seismic Forces in Linear-spectral Method.**

**Issue:** №5 2019

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The author submits certain recommendations on the description of the linear-spectral analysis. Principal text is accompanied by the Comments. The author suggests the following changes. Matrix equations are introduced, as matrix calculations correspond to the current level of analysis. Mass matrix is populated (and not diagonal, as previously used). Residual mode is introduced as an alternative to the achievement of 95% total mass by the accumulation of modal masses. Seismic excitation is three-component without non-physical “dangerous directions” concept. Normalized spectra, responsibility coeffient, modifid damping coeffient are explained explicitly. Coeffient of non-linear response is applied to certain parts, and not to the whole structure. In the combination of modal responses the inter-correlation of the low-frequency modal responses is explicitly accounted for. If the suggested terms are fulfiled, the linear-spectral analysis should give the results like the time-domain analysis (provided response spectra are calculated from the actual components used in the time domain analysis). At the same time there is a certain smooth transition from the previous codes.

**“Dangerous Directions of Seismic Excitation” and Combination of the Close Modal Responses in Linear Spectral Analysis**

**Issue:** №4 2019

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**«Dangerous Directions of Seismic Excitation» in Linear Spectral Analysis**

**Issue:** №3 2019

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**Operational Basis Earthquake and Design Basis Earthquake: Normal and Abnormal Relations**

**Issue:** №2 2019

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**Linear Spectral Seismic Analysis of High-rise Building**

**Issue:** №1 2019

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**Seismic Isolation Under the Base Mat of Structure Interacting With Soil. Part I. One‑Dimensional Linear Model**

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**Non-Classical Damping in the Soil-Structure System and Applicability of the Linear-Spectral Method to the Calculation of Forces**

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**“Normal” and “Abnormal” Effect of Damping on the Dynamic Response of Linear System**

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**Modal Damping Considering Soil Foundation**

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