BY THE DETERMINATION OF THE INTRINSIC FREQUENCY OF FREE OSCILLATIONS BEAMS
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Abstract
Considered in the paper, the method allows to determine for single-span beams with arbitrary fixing all the natural frequencies of free oscillations without setting up and solving differential equations. Free vibrations of beams are considered as forced oscillations of the free beam by reactions remote support connections. To describe these fluctuations by the recurrence formula is constructed so-called generalized dynamic Green’s function. The idea of its construction is that the dynamic Green’s function of the free beam series “corrected” in acceding to the reference link. Equating the “corrected” Dynamic Green’s functions are obtained equations to find the natural frequencies of the single-span beams with various fixed end. The above method of generalized dynamic Green’s function should be considered as an implicit acceptance of the determinant of disclosure necessary to obtain the frequency equation by force.
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References
Туровский, Л.М. Исследование свободных колебаний пластин с комбинированным «наполнением» / Л.М. Туровский, Г.П. Мудрый // Механика. Вып. 2. – Воронеж, 1974. – С. 23–31.
Тимошенко, С.П. Колебания в инженерном деле / С.П. Тимошенко. – М.: Физматгиз «Наука», 1967. – 442 с.
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