The monoreactive multibody floating-frequency oscillator

Abstract

BACKGROUND: The study is related to the machine science field and to oscillating mechanical systems in particular. The study relevance is explained with the fact that oscillations of inertial masses can be found all-around.

AIM: Development of the mathematical model of the monoreactive multibody floating-frequency oscillator.

METHODS: It is proved that points x₁, x₂, …., x_n, which are coordinates of the end of the random vector R in the coordinate system 0x_z1, 0x_z2, …., 0x_zn, are vertexes of a regular polygon. Shape and size of the polygon are not related to coordinates of the vector R, so they are constant. The center of the regular polygon always coincides with the middle of the vector R. In the considered (idealized) case, the polygon with the oscillating bodies with the mass m located at vertexes belongs to the plane Z. In technical applications, bodies should not impede motion of each other, so each body should have an own plane, and all planes should be in parallel (alike the multipiston mechanism).

RESULTS: The condition of occurrence of natural harmonic oscillations is equal-zero full energy of the system, which is exclusively kinematic in the considered case and which ensures monoreactive behavior of the oscillator. In the considered multidimensional planar monoreactive oscillator, free harmonic oscillations of bodies can occur.

CONCLUSIONS: Only kinetic energy takes part in energy exchange. There is no necessity in spring elements. The oscillator does not have fixed value of natural oscillation frequency. The frequency depends on initial velocities and location of bodies. The regular polygon x₁, x₂, …., x_n executes double rotation: around the point 0 and around the point r. Meanwhile, bodies execute linear harmonic oscillations with the amplitude of R. Use of either a slider-crank mechanism or a rod-crank mechanism helps to make bodies move in parallel. The obtained results can be used in development and study of mechanisms executing reciprocating motion in piston engines, in mechatronics and robotic systems, in hydraulic machines, vacuum and compressor machinery, in hydraulic and pneumatic systems, in on-ground transport and technological means and facilities.

Keywords

polygon / oscillating body / free oscillations / monoreactive system / frequency

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