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Analytical dependence of the natural oscillation frequency of the planar truss on the number of panelsстатья
- Авторы: Kirsanov M., Dai Q.
- Журнал: AlfaBuild
- Том: 27
- Год издания: 2023
- Издательство: Федеральное государственное автономное образовательное учреждение высшего образования "Санкт-Петербургский политехнический университет Петра Великого"
- Местоположение издательства: Санкт-Петербург
- Номер статьи: 2701
- DOI: 10.57728/ALF.27
- Аннотация: The object of the study is a regular statically determinate beam-type planar truss with double supports and a rise in the middle of the span. The truss lattice is triangular. The stiffness of all truss rods is assumed to be the same. Method. The problem of the lower limit of the fundamental frequency of natural oscillations is solved in analytical form for an arbitrary number of panels. It is assumed that the truss mass is located at the nodes of the truss. The solution of the problem was found in the Maple computer mathematical system using the induction method. The forces in the rods are determined by the method of cutting nodes. The stiffness of the structure is calculated by the Maxwell-Mohr formula. Results. Formulas are obtained for the boundaries of the fundamental frequency of a type polynomial in the number of panels. A distinctive feature of the obtained solution compared to similar solutions using the Dunkerley and Rayleigh estimates is its high accuracy. It is shown that the redistribution of masses along the truss belts little changes the value of the first frequency.
- Добавил в систему: Кирсанов Михаил Николаевич