Numerical analysis of non-linear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance

Abstract

Abstract. Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance, resulting in modal interaction, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential equations of the second order are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitudeand-phase modulations for the case of the combinational internal resonance. A good agreement in results is declared.

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

“…Shitikova and Ajarmah [29,30] performed a numerical study on the nonlinear vibration of fractionally damped cylindrical shells under the additive combinational internal resonance. Rossikhin et al [31] studied the nonlinear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance. Mokhtari et al [32,33] studied the vibration and aeroelastic flutter of sandwich cylindrical shells with fractionalorder viscoelastic core and isotropic face sheets, and Permoon et al [34] performed the same analysis for the vibration of sandwich conical shells with fractional core.…”