Indirect Time Integration Scheme for Dynamic Analysis of Space Structures Using Wavelet Functions

Abstract

In this paper, an indirect and numerical time integration approach is proposed for dynamic analysis of space structures by using comprehensive wavelet functions. For this purpose, the proposed scheme is implemented on the second-ordered differential equation of motion governing single-degree-of-freedom (SDOF) systems and subsequently for multi-degrees-of-freedom (MDOF) systems. In this way, two different types of free-scaled wavelet functions have been utilized, namely the simple Haar wavelet functions and the complex Chebyshev wavelet functions. Accordingly, for the proposed procedure, a simple formulation has been derived from the adaptive approximation of external loadings and responses by free-scaled wavelet functions. It is deduced that the proposed method lies on unconditionally stable scheme. From an optimization point of view, the error and computation time involved have been comparatively evaluated. Finally, it is demonstrated that the time history analysis of space structures is optimally accomplished by lesser computational time and high accuracy of responses, particularly in the large-scaled systems for broad-frequency content loadings.