 Calculation of the dependence of the spatial cantilever truss vibration frequency on the number of panelsстатья

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• Авторы:
• Журнал: Вестник МГСУ
• Том: 16
• Номер: 5
• Год издания: 2021
• Первая страница: 570
• Последняя страница: 576
• DOI: 10.22227/1997-0935.2021.5.570-576
• Аннотация: ntroduction. The first (lowest) frequency of natural vibrations of a structure is one of its most important dynamiccharacteristics. Analytical solutions supplement numerical ones; they can be efficiently used to perform a rapid assessmentof properties of structures, to analyze and optimize constructions and to test numerical results. A space cantilever trussconsisting of three planar trusses with a rectangular grid is considered in the article. The objective is to find the analyticaldependence between the frequency of natural vibrations of a structure and the number of panels. It is assumed that the truss mass is distributed among the joints. Only the vertical mass displacement is taken into account. Materials and methods. Forces, arising in cantilever rods, are calculated by the Maple software as symbolic expressions, and the method of joint isolation is used here. The stiffness matrix is identified using the Mohr integral. Rods are assumed to be elastic, they have identical stiffness. The lower value of the vibration frequency is determined using the Dunkerleymethod. The final calculation formula used to identify the value of the vibration frequency is derived using the method of induction applied to a series of analytical solutions developed for trusses with a consistently increasing number of panels.When common members of sequences are found, genfunc operators of the Maple system are used. The analytical solution is compared with the numerical solution in terms of the first frequency using the analysis of the system spectrum featuring many degrees of freedom. The eigenvalues of the characteristic matrix are identified using the Eigenvalues operator fromthe Linear Algebra package. Results. The comparison between the analytical values and the numerical solution shows that the Dunkerley method ensures the accuracy varying from 20 % for a small number of panels to 3 % if the number of panels exceeds ten. The size of the structure, the weight and stiffness of rods have little effect on the accuracy of the obtained values. Conclusions. The lowest value obtained using the Dunkerley method in the form of a fairly compact formula has goodaccuracy, its application to a space structure with an arbitrary number of panels has a polynomial form equal to the number of panels, and it can be used in practical calculations.
• Добавил в систему: Кирсанов Михаил Николаевич