Size-dependent vibration of rotating rayleigh microbeams with variable cross-section in complex environments

Authors

1 Assistant Professor of Mechanical Eng, Department of Engineering, Imam Ali University, Tehran,Iran

2 department of aerospace engineering, faculty of flight and engineering, Imam Ali university, Tehran, Iran

3 department of engineering, Imam Ali University, Tehran, Iran,

4 Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

Abstract

For the first time in the present study, the vibration of embedded rotating macro/microbeam in the Winkler-Pasternak foundation with the variable cross-sectional area and various boundary conditions in hygro-thermal-magnetic environments under axial and follower forces based on the Rayleigh beam model is studied. In this investigation, a parametric study is performed to clarify the impacts of various parameters such as boundary conditions, cross-sectional profile, foundation coefficients, rotary inertia factor, environmental conditions and size-dependent effects on the natural vibrational frequencies of the system. Couple stress theory is utilized to model the system. First, the dynamical equations of the system are derived using the Hamilton principle. To discretize the dynamical equation, the Galerkin method has been used, and the natural frequencies of the system are obtained by solving the eigenvalue problem. The results of the present study are compared and validated with the results presented in the technical literature. The results show that in high-temperature and low-temperature environments, the system has different dynamical behavior. It is observed that compared to the Euler-Bernoulli beam theory, the Rayleigh beam has lower frequencies. It is also concluded that in contrast to the effects of axial and follower forces, increasing the elastic and shear coefficients of the substrate improves the dynamical behavior of the system. Meanwhile, the vibrational frequencies of the structure increase by increasing the width ratio parameter. The results of the present study can be useful in the design of advanced structures such as microturbines and micromotors.

Keywords

References

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Journal of Solid and Fluid Mechanics
Volume 11, Issue 6
January and February 2022
Pages 159-171

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