Stochastic dynamic stiffness for damped taut membranes

Abstract

An analytical stochastic dynamic stiffness formulation is developed for the dynamic analysis of damped membrane structures with parametric uncertainties. First, the exact general solution of a biaxially taut membrane in the frequency domain is derived, which is used as the frequency-dependent shape function. Both the material properties and the tension fields of the membrane are modelled as 2D random fields with an exponential autocorrelation function in both x and y directions. Then, the random fields are decomposed by Karhunen-Loève (KL) expansion. After a formulation procedure like the finite element method, the stochastic stiffness, and mass elemental matrices are derived based on the frequency-dependent shape function and the KL expansion, subsequently forming the stochastic dynamic stiffness matrix. The developed stochastic dynamic stiffness elements can be assembled to model membrane assemblies with general boundary conditions considering uncertainties. The proposed method can be utilized as a feasible technique for the efficient and accurate stochastic dynamic analysis in the whole frequency domain. The current research paves the way for stochastic dynamic stiffness formulation for other two-dimensional structures like plates and shells.