Abstract
We consider low-frequency vibrations of a vibroprotective system of rigid bodies consisting of a roller vibration suppressor and a movable carrying body under the action of an external harmonic excitation. We write out the dynamic equations of the common motion of the damper working body along the hinged roller and of the carrying body. We propose a graphical method for determining the optimal adjustment parameters of the roller damper, which is part of the vibroprotective system.
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References
V. P. Legeza, N. I. Bobyr’, and M. A. Martynenko, “Roller Damper of Forced Vibrations of High-Rise Structures,” Ukraine Patent No. 58981A (15 August 2003), F16 F7/10, E04 B1/98, Bulletin No. 8.
B. G. Korenev and I. M. Rabinovich (Editors), Dynamical Calculation of Buildings under Special Interactions. Designer’s Handbook (Stroiizdat, Moscow, 1981) [in Russian].
B.G. Korenev and I. M. Rabinovich (Editors), Dynamical Calculations of Special Engineering Buildings and Structures. Designer’s Handbook (Stroiizdat, Moscow, 1986) [in Russian].
I. M. Besprozvannaya, A. G. Sokolov, and G. M. Fomin, Action of the Wind upon Tall Continuous Structures (Stroiizdat, Moscow, 1976) [in Russian].
B. V. Ostroumov, Studies, Development, and Implementation of High-Rise Structures with Vibrodampers, Abstract of Doctoral Dissertation in Technical Sciences (ZAO Mel’nikov “TzNIIPSK,” Moscow, 2003) [in Russian].
B. G. Korenev, “Dynamical Dampers of Vibrations,” in Proc. of Intern. Symp. “Vibroprotection in Building,” Vol. 2 (Leningrad, 1984), pp. 7–17 [in Russian].
V. P. Legeza, Roller Vibrodamper of Forced Vibrations of High-Rise Structures, Patent of Ukraine No. 54033A (17 February 2003), F16 F7/10, E04 B1/98, Bulletin No. 2.
V. P. Legeza, “Plane Problem on a Heavy Ball Rolling in a Spherical Recess of an Inverted Pendulum,” Prikl. Mekh. 37(8), 131–135 (2001) [Int. Appl. Mech. (Engl. Transl.) 37 (8), 1089–1093 (2001)].
V. P. Legeza, “Analysis of the Dynamic Behavior of a New Absorber of Forced Vibrations of Tall Structures,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 31–38 (2003) [Mech. Solids (Engl. Transl.) 38 (5), 24–30 (2003)].
V. P. Legeza, “Rolling of a Heavy Ball in a Spherical Recess of a Translationally Moving Body,” in TranslationalMotion in Space,” Prikl. Mekh. 38(6), 135–142 (2002) [Int. Appl. Mech. (Engl. Transl.) 38 (6), 758–764 (2002)].
V. P. Legeza, “Numerical Analysis of Plane Motion of a Ball in a Cycloidal Cavity between Two Movable Supports,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 12–17 (2003) [Mech. Solids (Engl. Transl.) 38 (6), 8–12 (2003)].
V. P. Legeza, “Control and Stabilization of Periodic Motions of a Carrying Body by Means of the Cycloidal Damper of Forced Oscillations,” Probl. Upr. Inform. No. 5, 41–47 (2001) [J. Automat. Inform. Sci. (Engl. Transl.) 33 (12), 44–50 (2001)].
A. N. Shmyrev, V. A. Morenshil’dt, and S. G. Il’ina, Ship Stabilizers (Sudpromgiz, Leningrad, 1961) [in Russian].
P. Appel, Traité de Mécanique Rationnelle (Gauthier-Villars, Paris, 1953).
A. I. Lurie, Analytic Mechanics (Fizmatgiz, Moscow, 1961; Springer, Berlin, 2001).
Yu. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems (Nauka, Moscow, 1967; AMS, Providence, 1972).
N. A. Fufaev, “A Sphere Rolling on a Horizontal Rotating Plane,” Prikl. Mat. Mekh. 47(1), 43–47 (1983) [J. Appl. Math. Mech. (Engl. Transl.) 47 (1), 27–29 (1983)].
N. A. Fufaev, “Theory of the Motion of Systems with Rolling,” Prikl. Mat. Mekh. 49(1), 56–65 (1985) [J. Appl. Math. Mech. (Engl. Transl.) 49 (1), 49–53 (1985)].
N. A. Fufaev, “Rolling of a Heavy Homogeneous Ball over a Rough Sphere Rotating around a Vertical Axis,” Prikl. Mekh. 23(1), 98–101 (1987) [Int. Appl. Mech. (Engl. Transl.) 23 (1), 86–89 (1987)].
M. A. Abdelkader, “A Ball Rolling on a Rotating Plane,” ZAMM 66(11), 563–566 (1986).
J. A. Hermans, “Symmetric Sphere Rolling on a Surface,” Nonlinearity 8(4), 493–515 (1995).
A. V. Borisov, J. S. Mamaev, and A. A. Kilin, “Rolling of a Ball on a Surface. New Integrals and Hierarchy of Dynamics,” Regul. Chaotic Dyn. 7(2), 201–219 (2002).
L. G. Lobas, “On Rolling System,” Prikl. Mekh. 36(5), 139–144 (2000) [Int. Appl. Mech. (Engl. Transl.) 36 (5), 691–696 (2000)].
Yu. G. Panovko and I. I. Gubanova, Stability and Oscillations of Elastic Systems (Consultant Bureau, New York 1965; Nauka,Moscow, 1979).
K. Magnus, Schwingungen. Eine Einführung in die Theoretische Behandlung von Schwingungsproblemen (Teubner, Stuttgart, 1976; Mir,Moscow, 1982).
F. S. Tse, I. E. Morse, and R. T. Hinkle, Mechanical Vibrations (Allyn and Bacon, Boston, 1963; Mashinostroenie, Moscow, 1966).
S. P. Timoshenko, D. H. Young, and W. Weaver Jr., Vibration Problems in Engineering (Wiley, New York. 1974; Mashinostroenie, Moscow, 1985).
J. P. Den Hartog, Mechanical Vibrations (Mc Graw-Hill, New York, 1956; Fizmatgiz, Moscow, 1960).
Building Regulations (SNiP) 2.01.07-85. Loads and Actions. Design Standards (Gosstroi SSSR, Moscow, 1987) [in Russian].
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Original Russian Text © V.P. Legeza, 2010, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2010, No. 2, pp. 49–61.
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Legeza, V.P. Dynamic model and optimal setup of a vibroprotective system. Mech. Solids 45, 194–204 (2010). https://doi.org/10.3103/S0025654410020056
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DOI: https://doi.org/10.3103/S0025654410020056