Dynamic Response Analysis of Fractionally-Damped Generalized Bagley–Torvik Equation Subject to External Loads

• Published in: Russian journal of mathematical physics Vol. 27; no. 2; pp. 254 - 268
• Main Authors: Srivastava, H. M., Jena, Rajarama Mohan, Chakraverty, Snehashish, Jena, Subrat Kumar
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2020; Springer Nature B.V
• Subjects: Damping; Direct reduction; Dynamic response; Eigenvectors; Mathematical and Computational Physics; Physics; Physics and Astronomy; Step functions; Theoretical
• ISSN: 1061-9208; 1555-6638
• DOI: 10.1134/S1061920820020120

This article deals with the solution of a fractionally-damped generalized Bagley–Torvik (BT) equation whose damping characteristics are well-defined by means of the fractional derivative (FD) of the Riemann–Liouville and the Liouville–Caputo types. The Ho-motopy Analysis Method (HAM) is implemented for computing the dynamic response (DR) analysis. Two external forces or loads (namely, the unit step function and the unit impulse function) are considered for the analysis presented here. The FD is first defined and then used here in the Riemann–Liouville sense and the Liouville–Caputo sense. In order to show the efficiency, powerfulness, and validations of the present analysis, the obtained results are compared with the solutions derived earlier by Suarez and Shokooh (1997) who used the eigenfunction expansion method and by Podlubny (1999) who used fractional-order Green’s function.