Frequency/Laplace domain methods for computing transient responses of fractional oscillators

Although computing the transient response of fractional oscillators, characterized by second-order differential equations with derivatives for damping term, to external loadings has been studied, most existing methodologies have dealt cases either restricted orders or simple loadings. In this paper, considering complicated irregular, but deterministic, acting on oscillators any order between 0 and 1, efficient frequency/Laplace domain methods getting responses are developed. The proposed based pole-residue operations. frequency approach, “artificial” poles located along imaginary axis complex plane designated. Laplace “true” extracted through two phases: (1) a discrete impulse function (IRF) is produced taking inverse Fourier transform corresponding (FRF) that readily obtained from exact transfer (TF), (2) exponential signal decomposition method, i.e., Prony-SS invoked extract residues. Once poles/residues system known, those can be determined Sequentially, time history obtained. Two single-degree-of-freedom (SDOF) rational irrational derivatives, respectively, subjected sinusoidal earthquake loading presented illustrate procedure verify correctness method. verification conducted comparing results both approaches numerical Duhamel integral Furthermore, method applied 3-DOF also demonstrated.