Variant of method of symmetries in a task about the vibrations of circular plate with a decreasing thickness by law of concave parabola
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Abstract
The decision of task is got about the vibrations of circular plate with a decreasing thickness by law of concave parabola. For the decision of differential equalizations of IV of order, that describe the axisymmetric vibrations of plates of variable thickness the methods of symmetries and factorization are used. The first are found three natural frequencies and the corresponding to them forms of vibrations are built for a circular plate with the hard fixing of internal contour. The results of calculation confirmed reliability of the worked out methodology and satisfactory exactness offered approach for tasks about the vibrations of plates of disk-type. Reference 11, figures 3, tables 1.
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References
Bichiashvili Z. D. (1983), “Opredelenie sobstvennich chastot i form svobodnich kolebaniy osesimmetrichnich plastinok metodom nachalnich parametrov : dis. kandidata nauk”. M., P. 186 (Rus)
Anikina T.A., Vatuljan A.O., Uglich P.S. (2012), “Ob opredelenii peremennoj gestkosti krugloj plastini” Computing Technology, Vol. 17, No. 6, pp. 26-35. (Rus)
Kuznecova E.V. (2006), “Izgib plastin : uchebno-metodicheskoe posobie k recheniju zadach k laboratornomu praktikumu po issledovaniju progibov pri nagrugenii prjamougolnich I kruglich plastin”. Perm PGTU, P. 32. (Rus)
Trapezon K.A. (2012) “Method of symmetries at the vibrations of circular plates of variable thickness” Electronics and Communications, No. 6, pp. 66-76. (Rus)
Trapezon K.A. (2012) “Generalized method of symmetries at the study of vibrations of resilient elements” Electronics and Communications, No. 2, pp. 31-34. (Rus)
Trapezon K.A. (2014) “The decision of task about the axisymmetric natural vibrations of circular plate with a thickness decreasing from a center on a concave parabola” Electronics and Communications, Vol. 19, No. 5, pp. 98-106. (Rus)
Timoshenko S.P., Vojnovskiy-Kriger S. (1963), “Plates and shells”. M. Phismatgiz, P. 636. (Rus)
Abramoviz M., Stigan I. (1979), “Reference book on the special functions”. M. Nauka, P. 832. (Rus)
Babakov I.M. (2004), “Teorija kolebanij”. M. Drofha, P. 591.(Rus)
Kollatz L. (1968), “Zadachi na sobstvennie znachenija s technicheskimi prilogenijami”. M. Nauka, P. 504. (Rus)
Timoshenko S.P. (1967), “Kolebanija v ingenernom dele”. M. Nauka, P. 444. (Rus)
