When vibration of the structure is unrecognized we call it random vibrations which their analysis is very important in space structures because these structures are exposed to acoustic forces or forces produced by turbulence of the atmosphere when a spacecraft is launched. Also in the aviation field, the random vibration analysis use to examine the response of the aircraft and missile structures to atmospheric turbulence and gust. In this research dominated equations of a truncated conical axisymmetric shell structure with linearized approximation of Love’s equations under uniform pressure is utilized. Considering displacements in the form of Frobenius series expansion the frequencies and...