## Analytical calculation of the fundamental oscillation frequency of a multi-domeстатья

Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из перечня ВАК
• Автор:
• Журнал: Строительство уникальных зданий и сооружений
• Том: 109
• Год издания: 2023
• Номер статьи: 10906
• DOI: 10.4123/CUBS.109.6
• Аннотация: The object of the study is a spatial model of a statically determinate truss of a regular type,consisting of separate domed hexagonal trusses connected in a row. Truss eigenfrequencies areinvestigated. Method. The lower bound of the first natural frequency is sought in analytical form. The Dunkerley partial frequency method is used. The stiffness of the structure is calculated using the Maxwell – Mohr formula, assuming that the stiffnesses of the elements are the same. The partialfrequencies of the masses concentrated in the truss nodes are calculated from separate oscillationequations. Each mass is assumed to have three degrees of freedom. Several solutions for trusses witha successively increasing number of panels are generalized by induction to an arbitrary number ofpanels. For analytical transformations and calculation of common members of sequences ofcoefficients of the desired formula, operators of the Maple computer mathematics system are used. Innumerical form, the natural frequency spectra of a family of regular trusses are searched for andanalyzed. Result. The obtained dependence of the fundamental frequency on the number of panelshas coefficients in the form of polynomials of order not higher than the fourth. Comparison of theanalytical result with the first frequency of the entire frequency spectrum obtained numerically shows the high accuracy of the found formula. As the number of panels increases, the accuracy of theproposed solution increases. In the frequency spectrum, it is found that the highest frequency of natural vibrations does not depend on the order of the truss.
• Добавил в систему: Кирсанов Михаил Николаевич