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- W2009096931 abstract "Recent discussions of parametrically excited oscillations seem to have overlooked an obvious question. How is energy transferred to a parametrically excited system to replace the energy lost to dissipative elements? The conventional analysis converts the linear differential equation representing the parametrically excited system into a Mathieu equation which is a lnear differential equation with a periodically varying coefficient, such as a periodically varying stiffness or length. This does not explain the physical mechanism involved in the energy transfer. To indicate how the energy is transferred, several systems are examined here, viz., (1) the simple pendulum where work is done when the length of the pendulum is varied periodically at half the period of the pendulum to increase the amplitude of its oscillation, (2) the taught string where work is done while sinusoidally varying the tension so as to excite transverse vibration at half the frequency of the varying tension, and (3) shape oscillations of gas bubbles in water excited by spherical volume pulsation at twice the frequency of the shape oscillation. These and other examples lead to the suggestion that more is required to excite parametric oscillation than being a solution of a Mathieu equation." @default.
- W2009096931 created "2016-06-24" @default.
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- W2009096931 date "2010-03-01" @default.
- W2009096931 modified "2023-09-24" @default.
- W2009096931 title "Parametrically excited oscillations: Where does the energy come from?" @default.
- W2009096931 doi "https://doi.org/10.1121/1.3384921" @default.
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