Comparison of different methods of assessing the free oscillatory characteristics of aeroelastic systems

Abstract

Different approximate methods of determining the eigenvalues of the integro-differential matrix equation of a simple aeroelastlc system are compared. It is shown that methods which use an approximate second order differential matrix equation with constant coefficients can give large errors in the values of complex eigenvalues, though the errors are usually small at airspeeds below the critical flutter speed, if the frequency parameter of each particular eigenvalue is lined-up with the value used to determine the aerodynamics. An improved method of solution using a finite series approximation to the indicial aerodynamics yielded in some cases an additional complex eigenvalue with a frequency of the same order as the other natural frequencies.