MATHEMATICAL MODELING OF A MULTI-INERT OSCILLATORY MECHANISM
Keywords:
oscillator, inert, harmonic, reactivity, spatial shift, phase shift, kinetic energyAbstract
It is noted that the free harmonic vibrations of a classical pendulum are due to the mutual conversion of the kinetic energy of the load intothe potential energy of the spring. Oscillators with a different nature of energy exchange have been developed, for example, by converting the kinetic energy of a load into the energy of a magnetic field of a solenoid or the energy of an electric field of a capacitor. All these oscillatory systems and the like were a prerequisite for the creation of a biinert oscillator,in which the acceleration of one load occurs due to the braking of another, i. e. only kinetic energies are exchanged. The aim of the work is mathematical modeling of a multi-inert oscillatory mechanism. The main research methods in the framework of this work are methods of mathematical modeling and analysis. The methods used make it possible to obtain a reliable description of the studied objects. Inthe proposed multi-inert oscillator, inert bodies of mass m each carry out harmonic oscillations due to the mutual exchange of kinetic energy.
The potential energy of the springs is not requiredfor this. Body vibrationsare free. A feature of a multi-inert oscillator is that the frequency of itsfree oscillations is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self-neutralization of mechanical reactive (inertial) power. n-gon, formed by inert bodies, carries out complex motion – orbital rotation around the center of coordinates and spin rotation around its axis passing through the center of the n-gon. Moreover, each load performs linear harmonic oscillations along its guide. With the arrangement of the guiding weights not in the form of a star, but in parallel to each other, the angles between the corresponding cranks must be 360/n degrees.
References
Dönmez D., Koca E. Variational Iteration Method for Transverse Vibrations of the Elastic, Tensioned Beam. International Journal of Materials, Mechanics and Manufacturing, 2017, vol. 5, no. 3, pp. 187–190. DOI: 10.18178/ijmmm.2017.5.3.315
Popov I.P. [Differential Equations of Two Mechanical Resonances]. Applied Physics and Mathematics, 2019, no 2, pp. 37–40. (in Russ.) DOI: 10.25791/pfim.02.2019.599
Platovskikh M.J., Vetyukov M.M. Self-Oscillations of Machines and Mechanisms. St. Petersburg, University of Mines Publ., 2017, pp. 87–103.
Finnveden S., Birgersson F., Ross U., Kremer T. A Model of Wall Pressure Correlation for Prediction of Turbulence-Induced Vibration. Fluids and Structures, 2005, no. 20, pp. 1127–1143. DOI: 10.1016/j.jfluidstructs.2005.05.012
Birgersson F., Finnveden S., Nilsson C.-M. A Spectral Super Element for Modelling of Plate Vibration. Part 1: General Theory. Sound and Vibration, 2005, no. 287, pp. 297–314. DOI: 10.1016/j.jsv.2004.11.012
Birgersson F., Finnveden S. A Spectral Super Elementfor Modelling of Plate vibration. Part 2: Turbulence Excitation. Sound and Vibration, 2005, no. 287, pp. 315–328. DOI: 10.1016/j.jsv.2004.11.011
Hambric S.A., Hwang Y.F., Bonness W.K. Vibrations of Plates with Clamped and Free Edges Excited by Low-Speed Turbulent Boundary Layer Flow. Fluid and Structures, 2004, no. 19, pp. 93–110. DOI: 10.1016/j.jfluidstructs.2003.09.002
Newland D.E. An Introduction to Random Vibration and Spectral Analysis. New York, Longman, 1984.
Rennison D.C., Piersol A.G., Wilby J.F., Wilby E.G. A Review of the Acoustic and Aerodynamic Loads and the Vibration Response of the SpaceShuttle Orbiter Vehicle – STS-1 Dynamics Verification Assessment. BBN, Report 4438 for NASA, Jet Propulsion Laboratory, 1980.
Kondakov S.V., Kromsky E.I., Asfandiyarov M.A.[Substantiation of the Parameters of the Shock-Vibration Mechanism for Compacting a Concrete Mix for a Caterpillar-Type Concrete Paver] All-Russian Scientific-Practical Conference. Chelyabinsk, South Ural Institute of Management and Economics Publ., 2018, pp. 148–156. (in Russ.)
Iskakov Zharilkassin, Bissembayev Kuatbay The Nonlinear Vibrations of a Vertical Hard Gyroscopic Rotor with Nonlinear Characteristics. Mech. Sci., 2019, no. 10, pp. 529–544. DOI: 10.5194/ms-10-529-2019
Sandalov V.M., Sergeev Yu.S. [Dynamic Model of Switched Reluctance Vibratory Drive]. Russian Electrical Engineering, 2012, vol. 83, no. 8, pp. 24–27. (in Russ.) DOI: 10.3103/S1068371212080111
Sergeev Yu.S. Privody vibracionnyh mashin na baze ventil'nyh induktornyh dvigatelej. Avtoref. dis. kand. tekhn. nauk[Drives of Vibration Machines Based on Switched Reluctance Drive. Abstract of сand. sci. diss.]. Chelyabinsk, 2011. 22 p.
Zhang Z. Design and Optimization of Comb Drive Accelerator for High Frequency Oscillation. Modern Mechanical Engineering, 2018, no. 8, pp. 1–10. DOI: 10.4236/mme.2018.81001
Sergeev S.V., Reshetnikov B.A., Gordeev E.N., Sergeev Yu.S., Gogolev V.P., Zakirov R.G., Mikryukov A.A., Irshin A.V. Sposob vozbuzhdeniya kolebaniy[Method of Excitation of Oscillations]. Patent RF 2533743, no. 2013121307/28; decl. 07.05.2013; publ. 20.11.2014, Bul. no. 32. 12 p.
Chen X., Hu Q., Xu Z., Zhu Ch. Numerical Modeling and Dynamic Characteristics Study of Coupling Vibration of Multistage Face Gearsplanetary Transmission. Mech. Sci., 2019, no. 10, pp. 475–495. DOI: 10.5194/ms-10-475-2019
Sergeev S.V., Reshetnikov B.A., Zakirov R.G. Vibracionnye rotornye privody mashin[Vibratory Rotary Machine Drives]. Chelyabinsk, South Ural St. Univ. Publ., 2007. 133 p.
Sergeev S.V., Reshetnikov B.A., Mikryukov A.A. [Investigation of the Shape of the Motion Trajectory of the Rotor Inertial Vibro Drive Operator]. Nauka YuUrGU. Materialy 67-y nauchnoy konferentsii[Science of SUSU. Materials of the 67th Scientific Conference], 2015, pp. 1261–1264. (in Russ.)
Efimtsov B.M. [Vibration of the Cylindrical Panel in the Field of Turbulent Pulsations of Pressure]. Soviet Physics – Acoustics, 1986, vol. 32, no. 4, pp. 536–538. (in Russ.)
Efimtsov B.M., Kudisova L.Y., Lebedev A.A. [Experimental Investigation of Fluctuations and Acoustic Radiation of Plates in the Field of Turbulent Pulsations of Pressure at Supersonic Speeds of a Stream]. Soviet Physics – Acoustics, 1984, vol. 30, no. 5, pp. 714–715. (in Russ.)
