Optimum dynamic analysis of 2D frames using free-scaled wavelet functions

Abstract

This paper presents a wavelet-based scheme for dynamic analysis of 2-dimensional (2D) frames. In the proposed approach, free-scaled wavelet functions are developed for Multi-Degrees-of-Freedom (MDOF) structures, particularly, complex Chebyshev and simple Haar wavelets are implemented. A simple step-by-step and explicit algorithm is presented to calculate the time history response of 2D frames. The validity of the proposed procedure is demonstrated with two examples compared with several common numerical integration procedures such as family ofNewmark-β, Wilson-θ and central difference method. Finally, it is shown that dynamic analysis of 2D frames is optimally accomplished by lesser computational time and high accuracy of results.

Keywords

• Optimum structural dynamics
• explicit integration method
• numerical approximation
• free-scaled wavelet functions
• Chebyshev wavelet
• Haar wavelet