Stability of viscoelastic plate in supersonic flow under random loading

The stability of a viscoelastic plate, subjected to a random load, in a supersonic flow is investigated. The stationary load is assumed in the form of Gaussian white noise. The relaxation kernel of the plate material is represented by a sum of exponents. The influence of such parameters as external damping, material viscosity, flow speed, and probabilistic characteristics of the load on the stability of the plate, in mean square form, is analyzed. Nomenclature D = bending stiffness of the plate k = coefficient of the external and aerodynamic damping / = width of the plate q = uniform external load R = relaxation operator R(t — T) = relaxation kernel t = time u = coefficient, depending on the flow speed v = speed of the flow w = transverse deflection of the plate x = coordinate 8 = thickness of the plate ae*, Lk = parameters of the kernel of the relaxation p = mass per unit of the plate volume

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