Almost-sure stochastic stability of viscoelastic plates in supersonic flow

The dynamic stability of a viscoelastic plate in a supersonic gas flow and subjected to a stochastically fluctuating axial thrust is performed within the concept of the Lyapunov exponent. The constitutive relation is modeled in an integral form by using the Boltzmann superposition principle. The pis ton theory as a quasi-first-order approximation is used to represent the ae rodynamic loading on the plate. The stochastic averaging method is used and the Khasminskii's technique [Khasminskii, R, A., "Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic System," Theo ry of Probability. and Its Application, Vol. 12, No. 1, 1967, pp, 144-147 ( English translation)] is employed to obtain the stability boundaries. The i nfluence of the various plate and flow parameters and the random loading sp ectral densities on the stability are investigated.