Abstract
A task is decided about the axisymmetric natural oscillations of circular plate of linear-variable thickness by the method of symmetries in the new variant of his realization. Equalizations of frequencies and forms of natural vibrations are got for a circular axisymmetric plate with the hard fixing her on an internal contour. The first three frequencies are certain and the corresponding to them own forms of vibrations of plate are built. Flexibility of method of symmetries is shown for the decision of tasks of theory of vibrations for the plates of variable thickness on the example of new variant of his realization. Efficiency of the accepted approach is illustrated comparing of the known results to got in the real work. It is shown, in particular, that these results possess higher exactness and more reliable as compared to known. Reference 10, figures 3, tables 2.
Highlights
Решена задача о собственных осесимметричных колебаниях круговой пластинки линейно-переменной толщины методом симметрий в новом варианте его реализации
Получены уравнения частот и форм собственных колебаний для кольцевой осесимметричной пластинки с жестким закреплением ее по внутреннему контуру
UDC 517.9:534.1:620.178.3 К.A. Trapezon, Ph.D., A.G. Trapezon, Dr.Sc. 1National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy Avenue, 37, Kyiv-56, 03056, Ukraine
Summary
На примере нового варианта решения задачи, рассмотренной в работе [7] показать гибкость и многовариантность метода симметрий при решении прикладных задач теории колебаний для пластинок переменной толщины. Эффективность подхода иллюстрируется сравнением результатов работ [4,7] с полученными в статье
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