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**On the transient response of plates on fractionally damped viscoelastic foundation.**
*(English)*
Zbl 1474.74108

Summary: This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin-Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

### MSC:

74S40 | Applications of fractional calculus in solid mechanics |

74D05 | Linear constitutive equations for materials with memory |

26A33 | Fractional derivatives and integrals |

74K20 | Plates |

### Keywords:

fractional viscoelasticity; plate vibration; fractional damping; viscoelastic foundation; step load
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\textit{R. K. Praharaj} and \textit{N. Datta}, Comput. Appl. Math. 39, No. 4, Paper No. 256, 20 p. (2020; Zbl 1474.74108)

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### References:

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