dynamic analysis of sdof structures with fractional order damping under harmonic excitation

in this paper, an effective scheme is provided to solve fractional order differential equation by using haar wavelet which governs in single-degree-of-freedom (sdof) structures. initially, the haar wavelet method and haar wavelet operational matrix are described. afterward, a well-known fractional differential equation has solved to verify and show the procedure. lastly, fractional order differential equations in sdof structures presented. the results have shown for three different values of derivative order. the root mean square of responses is presented. two performance indices introduced to evaluate the results. the results obtained are in good agreement with the existing ones in open literature, and it is shown that the procedure introduced in this paper is robust and easy to apply in the structures.