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**Nonlinear dynamics of an electrorheological sandwich beam with rotary oscillation.**
*(English)*
Zbl 1264.74146

Summary: The dynamic characteristics and parametric instability of a rotating electrorheological (ER) sandwich beam with rotary oscillation are numerically analyzed. Assuming that the angular velocity of an ER sandwich beam varies harmonically, the dynamic equation of the rotating beam is first derived based on Hamilton’s principle. Then the coupling and nonlinear equation is discretized and solved by the finite element method. The multiple scales method is employed to determine the parametric instability of the structures. The effects of electric field on the natural frequencies, loss factor, and regions of parametric instability are presented. The results obtained indicate that the ER material layer has a significant effect on the vibration characteristics and parametric instability regions, and the ER material can be used to adjust the dynamic characteristics and stability of the rotating flexible beams.

### MSC:

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74H55 | Stability of dynamical problems in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

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\textit{K. Wei} et al., J. Appl. Math. 2012, Article ID 659872, 17 p. (2012; Zbl 1264.74146)

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### References:

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