Analytical Model of the Two-Mass Above Resonance System of the Eccentric-Pendulum Type Vibration Table
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Lviv Polytechnic National University, Institute of Engineering Mechanics and Transport, Department of Mechanics and Automation of Mechanical Engineering, Lviv, 79013, Ukraine
Lviv Polytechnic National University, Institute of Civil Engineering and Building Systems, Department of Strength of Materials and Structural Mechanics, Lviv, 79013, Ukraine
Lviv National Agrarian University, Faculty of Mechanic and Power Engineering, Department of Project Management and Occupational Safety, Lviv-Dubliany, 80381, Ukraine
Online publication date: 2020-11-26
Publication date: 2020-12-01
International Journal of Applied Mechanics and Engineering 2020;25(4):116-129
The article deals with atwo-mass above resonant oscillatory system of an eccentric-pendulum type vibrating table. Based on the model of a vibrating oscillatory system with three masses, the system of differential equations of motion of oscillating masses with five degrees of freedom is compiled using generalized Lagrange equations of the second kind. For given values of mechanical parameters of the oscillatory system and initial conditions, the autonomous system of differential equations of motion of oscillating masses is solved by the numerical Rosenbrock method. The results of analytical modelling are verified by experimental studies. The two-mass vibration system with eccentric-pendulum drive in resonant oscillation mode is characterized by an instantaneous start and stop of the drive without prolonged transient modes. Parasitic oscillations of the working body, as a body with distributed mass, are minimal at the frequency of forced oscillations.
Bednarski Ł. and Michalczyk J. (2017): Modelling of the working process of vibratory conveyors applied in the metallurgical industry. – Archives of Metallurgy and Materials, vol.62, No.2, pp.721-728.
Filimonikhin G. and Yatsun V. (2017): Conditions of replacing a single frequency vibro-exciter with a dual-frequency one in the form of passive auto-balancer.– Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, vol.1, pp.61-68.
Nadutyi V.P., Sukharyov V.V. and Belyushyn D.V. (2013): Determination of stress condition of vibrating feeder for ore drawing from the block under impact loads. – Metallurgical ---amp--- Mining Industry, vol.51, pp.24-26.
Babitsky V. (2013): Theory of vibro-impact systems and applications. – Springer Science ---amp--- Business Media.
Luo G., Zhang Y., Xie J. and Zhang J. (2007): Vibro-impact dynamics near a strong resonance point. – Acta Mechanica Sinica, vol.23, No.3, pp.329-341.
Sokolov I.J., Babitsky V.I. and Halliwell N.A. (2007): Autoresonant vibro-impact system with electromagnetic excitation. – Journal of Sound and Vibration, vol.308, pp.375-391.
Rajesh K. and Saheb K.M. (2018): Large amplitude free vibration analysis of tapered Timoshenko beams using coupled displacement field method. – Int. Journal of Applied Mechanics and Engineering, vol.23, No.3, pp.673-688. DOI: 10.2478/ijame-2018-0037.
Gharaibeh M.A., Obeidat A.M. and Obaidat M.H. (2018): Numerical investigation of the free vibration of partially clamped rectangular plates. – Int. Journal of Applied Mechanics and Engineering, vol.23, No.2, pp.385-400. DOI: 10.2478/ijame-2018-0022.
Joubaneh Eshagh F., Barry Oumar R. and Tanbour Hesham E. (2018): Analytical and experimental vibration of sandwich beams having various boundary conditions. – Journal of Sound and Vibration, vol.18. doi.org/10.1155/2018/3682370.
Xianjie Shi and Dongyan Shi (2018): Free and forced vibration analysis of T-shaped plates with general elastic boundary supports. – Journal of Low Frequency Noise, Vibration and Active Control, vol.37, No.2, pp.355-372. DOI: 10.1177/1461348418756021.
Mirzabeigy A. and Madoliat R. (2018): Free vibration analysis of a conservative two-mass system with general odd type nonlinear connection. – Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., vol.88, pp.145-156. https://doi.org/10.1007/s40010....
Panovko G. and Shokhin A. (2018): Experimental analysis of the oscillations of two-mass system with self-synchronizing unbalance vibration exciters. – Journal Vibroengineering PROCEDIA, vol.18, pp.8-13. doi.org/10.21595/vp.2018.19906.
Jia-Jang Wu (2006): Free vibration characteristics of a rectangular plate carrying multiple three-degree-of-freedom spring–mass systems using equivalent mass method. –International Journal of Solids and Structures, vol.43, No.3-4, pp.727-746. doi.org/10.1016/j.ijsolstr.2005.03.061.
Vera S.A., Febbo M., Mendez C.G. and Paz R. (2005): Vibrations of a plate with an attached two degree of freedom system. – Journal of Sound and Vibration, vol.285, No.1, pp.457-466. DOI: 10.1016/j.jsv.2004.09.020.
Gursky V. and Kuzio I. (2018): Dynamic analysis of a rod vibro-impact system with intermediate supports. – Acta Mechanica et Automatica, vol.12, No.2, pp.127-134. DOI 10.2478/ama-2018-0020.
Gorman D.J. (1995): Free vibration of orthotropic cantilever plates with point supports. – Journal of Engineering Mechanics, vol.121, No.8, pp.851-857.
Gorman D.J. (1999): Accurate free vibration analysis of point supported Mindlin plates by the superposition method. –Journal of Sound and Vibration, vol.219, No.2, pp.265-277.
Gorman D.J. and Singal R.K. (1991): Analytical and experimental study of vibrating rectangular plates on rigid point supports. – AIAA Journal, vol.29, No.5, pp.838-844.
Gorman D.J. (1992): A general analytical solution for free vibration of rectangular plates resting on fixed supports and with attached masses. – Journal of Electronic Packaging, vol.114, 239.
Gorman D.J. (1999): Vibration analysis of plates by the superposition method. – Vol.3, World Scientific.
Abrahams I.D. and Davis A.M.J. (2002): Deflection of a partially clamped elastic plate. – In IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity (pp.303-312). Springer Netherlands.
Abrahams I.D., Davis A.M. and Smith S.G.L. (2008): Matrix Wiener–Hopf approximation for a partially clamped plate. –Quarterly Journal of Mechanics and Applied Mathematics, vol.61, No.2.
Shatokhin V.M. (2008): Analysis and parametric synthesis of non-linear power transmission of machines: monograph. – Kharkiv: NU «KhPI», 456 p.
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