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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.

Various techniques are currently used to simulate a shock environment. The authors investigate the validity of simulating the shock environment due to a pyrotechnic firing by means of a nonstationary transient formed by modulating a stationary broad band random signal with an exponentially decaying pulse.

The stability of a radially constrained, complete, circular ring subjected to thermal stress and of a similarly restrained portion of a circular ring under circumferential end load is investigated. The effect of three types of initial geometric imperfections on the buckling behavior is determined. Results obtained, employing shallow arch approximations, show that this behavior depends on the assumed form of imperfection. In one case, no bifurcation or limit point exists at finite load level; in the second case, bifurcation and snap buckling may occur; in the third case, the system admits of a limit point. A design curve is proposed which can be used to estimate the stability limit of a circular ring exhibiting a certain “out-of-roundness.”