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THE ENVELOPE OF RANDOM VIBRATION OF A LIGHTLY DAMPED NONLINEAR OSCILLATOR
MASSACHUSETTS INST OF TECH CAMBRIDGE
There are several ways in which the envelope of the stationary random response of a lightly damped oscillator can be characterized. Two characterizations which lead to the same first order probability distributions for systems with conservative nonlinear restoring forces are described. In such systems the envelope distributions are in general different from the distributions of peak amplitudes. The Duffing system is used to illustrate these general results. For the special case of a Gaussian oscillator an envelope characterization is given by Rice. It is shown that in this case the above envelope characterization has the same first order distribution as that given by Rice, but that the second-order probability distributions are in general, different.
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