An Improved Method of Modal Superposition Based on Tchebyshev Polynomials

In the analysis of an aero-elastic system, the structural system is sometimes linear while the aerodynamic system is nonlinear. To solve such vibration response problem, the classic modal superposition method is an efficient choice usually. High-precision calculation accuracy depends on the number of frequencies used and sometimes the number is very high even over 50. This paper provides an improved method of modal superposition based on Tchebyshev polynomials. The essence of this work is to substitute Tchebyshev polynomials into Fourier series expressions and therefore the original basis functions has been changed. Finally, an example will illustrate how it works in details and the result will show that the number of modal vectors and modal coordinates in Tchebyshev polynomials form is more less than that in the classical modal superposition form. Using this improved method will has significantly improved the efficiency of any aero-elastic system analysis. Moreover, it is maybe not necessary to know all the frequencies information which will not be discussed in this article.