In this paper, an improved probabilistic linearization approach is dev
eloped to study the response of nonlinear single degree of freedom (SD
OF) systems under narrow-band inputs. An integral equation for the pro
bability density function (PDF) of the envelope is derived. This equat
ion is solved using an iterative scheme. The technique is applied to s
tudy the hardening type Duffing's oscillator under narrow-band excitat
ion. The results compare favorably with those obtained using numerical
simulation. In particular, the bimodal nature of the PDF for the resp
onse envelope for certain parameter ranges is brought out.