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Parametric pulse excitation in distributed mechanical systems with nonstationary boundaries


In a distributed system whose parameters vary with time the natural oscillation modes are interconnected and so it is possible to get parametric excitation of several synchronized harmonic modes simultaneously. If the natural oscillation spectrum of such a system consists of almost equally spaced lines, then a periodic change of the parameters with time can lead to the excitation of pulse-type oscillations [1]. This phenomenon can occur both in systems whose size varies with time and in systems whose boundary properties are nonstationary. The present paper is devoted to a study of the instability in these systems.

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Literature cited

  1. 1.

    A. I. Vesnitskii and A. I. Potapov, “Effective method of studying wave processes in systems whose size varies with time,” in: Dynamics of Systems [in Russian], No. 7, Gor'k. Univ., Gor'kii (1975).

  2. 2.

    Lord Rayleigh (J. W. Strutt), “On the pressure of vibrations,” Phil. Mag., Ser. 6,3, No. 15, 338 (1902).

  3. 3.

    E. L. Nikolai, “Transverse oscillations of a section of string whose length varies uniformly,” in: Papers on Mechanics [in Russian], GITTL, Moscow (1955).

  4. 4.

    O. A. Goroshko and G. N. Savin, Introduction to the Mechanics of One-Dimensional Deformable Bodies of Variable Length [in Russian], Naukova Dumka, Kiev (1971).

  5. 5.

    A. I. Vesnitskii and A. I. Potapov, “Some general properties of wave phenomena in a one-dimensional mechanical system of variable length,” Prikl. Mekh.,11, No. 4, 98 (1975).

  6. 6.

    V. N. Krasil'nikov and A. M. Pankratov, “Electromagnetic fields in resonators with oscillating boundaries,” in: Problems in Wave Diffraction and Propagation [in Russian], No. 8, Leningr. Univ., Leningrad (1968), p. 59.

  7. 7.

    A. I. Vesnitskii, L. A. Ostrovskii, V. V. Papko, and V. N. Shabanov, “Parametric pulse generation,” Zh. Éksp. Teor. Fiz., Pis'ma Red.,9, No. 5, 274 (1969).

  8. 8.

    D. A. Kabanov and S. M. Nikulin, “Generation of pulses in a transmission line with parametric diodes,” Radiotekh, Élektron.,17, No. 8, 1756 (1973).

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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 145–151, July–August, 1976.

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Vesnitskii, A.I., Krysov, S.V. & Shokhin, S.R. Parametric pulse excitation in distributed mechanical systems with nonstationary boundaries. J Appl Mech Tech Phys 17, 572–577 (1976).

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  • Mathematical Modeling
  • Mechanical Engineer
  • Industrial Mathematic
  • Mechanical System
  • Oscillation Mode