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Numerical-analytical method for calculating the oscillations of regular structures

Grishanina T.V., Shklyarchuk F.N.

#### Abstract:

Dynamics of elastic large-sized space structures is of grate interest for design of orbital stations, large radio antennas, radio telescopes, satellites with large solar panels. Special place among space structures is occupied by truss systems consisting of many thousands of elements. They can be used for future large antenna reflectors, platforms, strength frameworks. As a rule, such systems for convenience of assembling in space have a regular structure, i.e. they consist of the same type of sections (modules) connected in series with each other. When calculating the dynamic characteristics of such structures, the finite element method or other similar numerical methods can be used. But when they are used for systems with a large number of sections, difficulties arise due to the large dimension of the tasks being solved. Then the calculation can be very time-consuming. Therefore, it is of interest to develop effective models and methods based on the use of regularity properties of such structures. This paper presents a numerical-analytical method for calculating natural oscillations or harmonic forced oscillations of regular systems, the complexity of which does not depend on the number of modules of the same type and is determined by the number of degrees of freedom of one section. To assess the complexity and accuracy of the proposed calculation method, the problem of the flexural vibrations of a freely supported homogeneons beam is solved and the solution obtained on its basis is compared with the results of the exact solution and the direct solution based on the finite element method. From the calculations given in the article, it can be seen that the described method allows you to get results that are quite close to exact. Moreover, convergence improves with an increase in the number of elements of the same type included in the regular system. Thus, this method can be effective in dynamic calculations of regular structures consisting of a large number of sequentially connected modules of the same type.

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