Annotation:
In the work of Kurbatsky E.N., Mondrus V.L. «Dynamic Coefficients or Response Spectra of Structures to Earthquake?» with the reference to the norms of the technically developed countries, as well as to the monographs of the famous foreign scientists, an erroneous statement was put forward that during earthquakes the ground parts of structures are not subject to the influence of any external forces, and that the internal stresses and deformations in the elements of structures are created exclusively due to dynamic reactions to movement of their bases. It does not state that the cancellation of the action of gravity is associated with the inadequacy (incompleteness) of the mathematical models of the interaction of foundations and structures, but argues that if the force of gravity is clearly absent in the vibration equations, then it does not act on the structure. This incompleteness of ideas is present in the equation of horizontal vibrations in translated and domestic works, but in them, unlike the reviewed works, it is not stated that during earthquakes the ground parts of structures are not subject to the influence of any external forces.
The main reasons for the incompleteness (inadequacy) of the mathematical models of foundations and structures and their interaction was identified, which are that the center of gravity of the structure is located at the level of the base, and also that when deriving the equations for horizontal and vertical vibrations of the structure, the incomplete (selective) deformability of the base is used. But the selective deformability of the base when deriving the classical equations of horizontal and vertical vibrations does not allow rocking vibrations of the structure to occur under only horizontal or only vertical seismic influences, and this is a significant drawback of the mathematical modeling of the vibration processes of structures on a completely deformable base.
To eliminate this shortcoming, the work presents differential equations for translational and rocking plane-parallel vibrations of a rigid structure on a completely yielding foundation, including the effects of gravity. From them, in particular, it follows that as the height of the center of gravity tends to zero, these equations turn into classical linear equations of oscillations in the horizontal and vertical directions.
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