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Sub-resonant Response of a Mechanical System parametrically excited at its Resonant Frequency

Naturevolume 207page853 (1965) | Download Citation



IN the course of an attempt to improve the response of an inertial seismometer to very-low-frequency frame movements, it appeared worthwhile to investigate the response of a spring-mass system subjected to parametric excitation1. The parametric excitation or ‘pumping’ consisted of modulating the restoring force on the mass by means of an electromechanical spring2 driven from a sinusoidal current source. In the initial work the restoring force was varied at twice the resonant frequency of the system as is usually done in a degenerate parametric device. It was found both from theory3 and experiment that this will increase the relative motion between mass and frame only for inputs with a frequency at or near the resonant frequency, and that the input must bear the proper phase relationship to the pump. There is no improvement for frequencies much below resonance.

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  1. 1

    Blackwell and Kotzebue, Semiconductor-Diode Parametric Amplifiers (Prentice-Hall, Inc., 1961).

  2. 2

    Gilman, R., Report on Some Experimental Long-Period Seismographs, Bull. Seism. Soc. Amer., 50, 553 (1960).

  3. 3

    Rodgers, P. W., “Mechanical Parametric Amplifiers”, submitted to J. App. Mech.

  4. 4

    McLachlan, N. W., Theory and Application of Mathieu Functions (Dover, 1964).

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  1. Seismographic Station and Department of Electrical Engineering, University of California, Berkeley



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