The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.
Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation
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Bucciarelli, L. L., Jr., and Kuo, C. (September 1, 1970). "Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation." ASME. J. Appl. Mech. September 1970; 37(3): 612–616. https://doi.org/10.1115/1.3408588
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