Abstract
A calculation method for a mechanical system with delay in quasi-harmonic oscillatory conditions is proposed as the first-order approximation, on the assumption that the dry sliding-friction force is approximated polynomially by a finite number of components of the Taylor-series expansion; Pisarenko's hypothesis is adopted in taking energy dissipation into account.
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References
I. M. Babakov,Theory of Oscillation [in Russian], Nauka, Moscow (1968).
N. N. Bogolyubov and Yu A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Oscillation [in Russian], Nauka, Moscow (1974).
B. M. Zhirnov, “Self-oscillation of a mechanical system with two degrees of freedom, in the presence of delay,”Prikl. Mekh.,9, No. 10, 83–87 (1973).
B. M. Zhrinov, “Internal resoance of frictional self-oscillatory system with two degrees of freedom, in the presence of dalay,”Prikl. Mekh.,10, No. 10, 102–109 (1974).
B. M. Zhirnov, “Single-frequency conditions of frictional self-oscillatory system with two degrees of freedom, taking account of imperfect elasticity of material,”Probl. Prochn, No. 9, 110–113 (1977).
B. M. Zhirnov, “Single-frequency resonant oscillations of frictional self-oscillatory system with delay, in the presence of an external perturbation,”Prikl. Mekh.,14, No. 9, 102–109 (1974).
B. M. Zhirnov, “Nonresonant oscillation of frictional self-oscillatory system with one degree of freedom in the presence of external perturbation, taking account of imperfect elasticity of material,”Probl. Prochn., No. 11, 81–83 (1985).
B. M. Zhirnov, “Single-frequency oscillations of frictional mechanical self-oscillatory system, taking account of delay and energy scattering, in the presence of an external periodic perturbation,”Dinam. Prochn. Mash.,31, 68–77 (1980).
B. M. Zhirnov, “Self-oscillations of load on moving transportational belt,”Dinam. Prochn. Mash.,51, 48–55 (1990).
N. L. Kaidanovskii, “Mechanical self-oscillations in dry friction,”Zh. Tekh. Fiz.,19, No. 9, 985–996 (1949).
I. P. Mel'nichenko and B. M. Zhirnov, “Single-frequency self-oscillations of frictional mechanical system withN degrees of freedom, taking account of delay,”Prikl. Mekh.,10, No. 2, 120–125 (1974).
Yu A. Mitropol'skii,Nonsteady Processes in Nonlinear Oscillatory Systems [in Russian], Izd. AN UkrSSR, Kiev (1955).
G. S. Pisarenko,Oscillation of Mechanical Systems, Taking Account of Imperfect Elasticity of the Material [in Russian], Naukova Dumka, Kiev (1970).
N. L. Plakhtienko, “Estimating the self-oscillation parameters of a two-mass system in the presence of dry friction,”Prikl. Mekh.,32, No. 8, 87–94 (1996).
V. P. Rubanik,Oscillations of Quasi-Linear Systems with Delay [in Russian], Nauka, Moscow (1969).
S. L. Sobolev,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1966).
Additional information
Ukrainian Transportation University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 90–97, February, 1999.
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Zhirnov, B.M. Resonant processes in a mechanical self-oscillatory system with delay. Int Appl Mech 35, 195–203 (1999). https://doi.org/10.1007/BF02682155
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DOI: https://doi.org/10.1007/BF02682155