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The couple stress-based nonlinear coupled three-dimensional vibration analysis of microspinning Rayleigh beams

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Abstract

The nonlinear coupled three-dimensional vibrations of microspinning Rayleigh beams are analytically studied utilizing the modified couple stress theory to take into account the small-scale effects. The considered nonlinearity is of geometrical type due to the mid-plane stretching. The rotary inertia and gyroscopic effects are both included in the formulation. Governing equations of motion are derived with the aid of the Hamilton Principle and then transformed into complex form. Then, the Galerkin and multiple scales methods are utilized to solve the nonlinear partial differential equation. Approximate analytical expressions for nonlinear natural frequencies of the spinning beams in forward and backward whirling motions are obtained. Numerical results illustrate that the length-scale value has a significant effect on linear and nonlinear natural frequencies as well as the critical rotational speeds of hinged–hinged and clamped–clamped microrotating beams.

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Authors and Affiliations

  1. Mechanical Engineering Department, Sharif University of Technology, Azadi Ave, Tehran, Iran

    M. Asghari & M. Hashemi

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  1. M. Asghari
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  2. M. Hashemi
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Correspondence to M. Asghari.

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Asghari, M., Hashemi, M. The couple stress-based nonlinear coupled three-dimensional vibration analysis of microspinning Rayleigh beams. Nonlinear Dyn 87, 1315–1334 (2017). https://doi.org/10.1007/s11071-016-3116-3

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  • DOI: https://doi.org/10.1007/s11071-016-3116-3

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