Approximate Solution of Strongly Forced Nonlinear Vibrating Systems Which Vary With Time

Pinakee dey
2018 JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES  
Based on the combined work of extended Krylov-Bogoliubov-Mitropolskii method and harmonic balance (HB) method an analytical technique is presented to determine approximate solutions of nonlinear differential systems whose coefficients change slowly and periodically with time. Furthermore, a non-autonomous case also investigated in which an external force acts in this system. Formulation as well as determination of the solution is systematic and easier than the existing procedures. The method is
more » ... ures. The method is illustrated by suitable examples. 2 presented to determine periodic solutions of nonlinear differential equations by using a truncated Fourier series in which there exists a strongly nonlinear term based on the Harmonic balance (HB) method. Recently, Roy and Shamsul [V] found an asymptotic solution of a differential system in which the coefficient changes in an exponential order of slowly varying time. In this paper, we have used combining the methods of extended KBM [VIII], [VII], [X] and Harmonic balance (HB) method [I],[IX] to find the solution of strongly nonlinear non-autonomous differential system in which an external force acts.
doi:10.26782/jmcms.2018.10.00001 fatcat:s5zibgrbvvcydikrquzozyly7a