Flutter stability analysis of stochastic aeroelastic systems via the generalized eigenvalue-based probability density evolution method

Abstract

This paper proposes a generalized eigenvalue-based probability density evolution method for aeroelastic systems considering stochastic uncertainties in structural and aerodynamic parameters. Uncertain parameters in aeroelastic systems are characterized by stochastic model, and the flutter analysis model with stochastic parameters is established. The generalized eigenvalue-based probability density evolution method is then developed to capture the probability density function of the maximum real part of generalized eigenvalues. By introducing the virtual time parameter, the probability density evolution equation can be transformed into a standard form. Using the finite difference method and the total variation diminishing (TVD) scheme, the probability density function as well as the second-order statistical quantities of the maximum real part of generalized eigenvalues are predicted efficiently. Thus, the flutter stability of aeroelastic systems with stochastic parameters can be analyzed based on the probability distribution of the maximum real part of generalized eigenvalues. Two numerical examples demonstrate that the proposed method yields results consistent with Monte-Carlo simulation method and improves the computational efficiency.