Method of calculating natural frequencies and forms of free oscillations of mechanical systems based on a special combination of decomposition with condensation is proposed in this article. Condensation upon a frequency feature allows the use of only those equations of oscillations, natural frequencies and forms of which belong to a predetermined frequency range, that makes possible a substantial reduce of dimension of an original problem. Moreover, decomposition in combination with condensation lead to the account’s improved stability, as the condition of the matrix that determines the stability depends on the ratio of the highest natural frequency of the system to the lowest.
For the description of the movement of the conveyor Hamilton's principle — Ostrogradsky, including kinetic energy of fluctuations of a site of a cargo branch of a tape between rolikoopor and potential energy of elastic deformation of a tape is used. The variation of square functionality by a variation of an angle of rotation of a tubular tape, where turn corners — variations across Hamilton is calculated: the small; compatible to communications, isochronous. Equivalence of the variation principle of Hamilton — Ostrogradsky and a regional task is shown.
The site of the tape tubular conveyor in the form of two final elements containing three knots is considered. Matrixes of inertia and rigidity of separate final elements of a tape are made. Satisfying boundary conditions, are received the characteristic equation for determination of own frequencies of tortional fluctuations of a tape. Schedules of dependences of dimensionless lowest own frequency on tape speed at various values of distance between rolikoopor are submitted.
Issue number: 5
Year: 2017
ISBN:
UDK: 531.17.001.2
DOI: 10.25018/0236-1493-2017-7-0-93-102
Authors: Sazambaeva B. T., Akhmetova Sh. D., Kuanyshev G. I., Samogin Yu. N.
About authors: Sazambaeva B.T., Doctor of Technical Sciences,
Professor, e-mail: a.sazambaeva_t@mail.ru,
Kazakh National Research Technical University named after K.I. Satpayev,
050013, Almaty, Kazakhstan,
Akhmetova Sh.D., Candidate of Technical Sciences,
Assistant Professor, Head of Chair,
е-mаil: Ahmetona_sh_58@mail.ru,
Kazakh National Research Technical University named after K.I. Satpayev,
050013, Almaty, Kazakhstan,
Kuanyshev G.I., Candidate of Technical Sciences,
Assistant Professor, e-mail: gkuanishev@yandex.ru,
Kazakh National Research Technical University named after K.I. Satpayev,
050013, Almaty, Kazakhstan,
Samogin Yu.N., Candidate of Technical Sciences,
Assistant Professor, e-mail: samogin1812@yandex.ru,
National Research University «Moscow Power Engineering Institute»,
111250, Moscow, Russia.
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