A Sequential Quadratic Numerical Optimization Technique to Compute Critical Flutter Speeds

Abstract

A stable sequential quadratic numerical optimization technique is proposed to compute critical flutter speeds without resorting to complex algebra. The solution of the traditional eigenproblem stated in the frequency domain, and whose complex conjugate eigenvalues provide insights on the stability of the dynamic aeroelastic response, is avoided altogether. Instead, the technique relies on evaluation of the determinant of the dynamic matrix, which is certainly real (noncomplex). Since computation of the determinant of large, although banded (or sparse), nonsymmetric matrices is a computationally expensive routine, the procedure relies on a sequential quadratic polynomial approximation to the determinant in terms of natural frequency and free stream velocity, both properly scaled. The optimization technique is shown to be robust and to quickly converge when applied to beams and plates under supersonic flows modeled by piston theory. Two additional contributions of the paper are a method to scale the free stream velocity (essential for convergence) based on the stencil of the aeroelastic beam problem and a parallel algorithm to compute the determinant of the dynamic matrix (essential for fast computer processing).