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On the application of the locality principle in structural dynamics

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Summary

A complicated mechanical structure as an assemblage of substructures is considered. A method which enables us to find the exact vibrational state of any substructure within the whole structure will be offered. In order to achieve this aim a particular element will be under precise consideration, while the rest of the structure will be described integrally. It is shown that the vibration of a certain particular element of the structure depends mainly upon the composition of the element itself and upon certain generalized properties of the remote elements of the structure, and does not depend upon details of its composition. As a result of a consideration of two examples, the effect of backward influence of the vibration of a particular element on the general vibrational state of a whole structure will become evident. This means that the usual methods of neglecting the existence of a whole structure, and investigating a simplified problem such as a particular element under excitation are not correct in the general case.

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Author notes

  1. A. K. Belyaev

    Present address: Department of Mechanics and Control Processes, Leningrad Polytechnical Institute, 195251, Leningrad, USSR

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    1. A. K. Belyaev
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    Belyaev, A.K. On the application of the locality principle in structural dynamics. Acta Mechanica 83, 213–222 (1990). https://doi.org/10.1007/BF01172982

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