Stochastic microvibration response analysis of a magnetorheological viscoelastomer based sandwich beam under localized magnetic fields

Significance Statement

In many fields, precise apparatuses with disturbance sensitivity require completely steady operation surroundings, and then stochastic microvibrations need to be controlled effectively. Composite structures with smart materials are an alternative for the stochastic microvibration control by broad energy dissipation. Magnetorheological viscoelastomer (MRVE) is a new sort of smart materials which has the advantageous properties of magnetorheological fluids and viscoelastic substrate materials such as stiffness and damping adjustable by applied magnetic fields. The dynamics of magnetorheological viscoelastomer sandwich beams and plates have been studied recently including the periodic vibration, frequency response characteristics, dynamic stability and sound transmission characteristics. However, those researches considered only deterministic periodic dynamics. The research on stochastic microvibration responses of magnetorheological viscoelastomer sandwich beams and plates considered completely homogeneous magnetic fields. The homogeneous magnetic field covering completely large structures is not so realistic and may not be optimum. The stochastic microvibration response of magnetorheological viscoelastomer composite structures under localized magnetic fields needs to be studied further. The localized magnetic field covers incompletely composite structures and then the magnetorheological viscoelastomer core has dynamic characteristics varying in space. The corresponding vibration equations are partial differential equations with spatial parametric variation and temporal randomness so that the microvibration problem is more complicated than the previous.

  In this paper, the stochastic microvibration of a horizontal magnetorheological viscoelastomer based sandwich beam with a supported mass under random support disturbances and localized magnetic fields is studied to verify its control effectiveness. The localized magnetic field covering incompletely the beam results in the magnetorheological viscoelastomer properties varying in space. The effects of the localized magnetic field distribution on the microvibration are considered in the analysis. The vibration equations with spatial parametric variation and temporal randomness of the beam system under the localized magnetic field are derived, and then solved by the modal transformation and frequency spectrum analysis. The expressions of the frequency response function, response spectral density and root-mean-square velocity criterion for microvibration are obtained, where the non-homogeneous magnetorheological viscoelastomer modulus is considered due to the localized magnetic field. The stochastic microvibration control effectiveness of the beam system and the effects of the localized magnetic field intensity and placement on the microvibration responses are illustrated with numerical results. The study has a significance of the optimum design on the microvibration control of magnetorheological viscoelastomer composite structures with localized magnetic fields. The proposed analysis method can be applied to other composite structures with viscoelastic cores under random disturbances.

Figure legend: RMS velocity response spectra show the remarkable microvibration mitigation of a sandwich beam by using magnetorheological viscoelastomer.

Stochastic microvibration response analysis of a magnetorheological viscoelastomer based sandwich beam under localized magnetic fields. Advances in Engineering

 

Journal Reference

Z.G. Ying1, Y.Q. Ni2, R.H. Huan1. Applied Mathematical Modelling, Available online 22 January 2015.

[expand title=”Show Affiliations”]
  1. Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
  2. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
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Abstract

The microvibration of a horizontal magnetorheological viscoelastomer (MRVE) based sandwich beam with supported mass under random disturbances and localized magnetic fields is studied to verify its control effectiveness. The localized magnetic field covering incompletely the beam results in the magnetorheological viscoelastomer properties varying in space. The effects of the localized magnetic field distribution on the microvibration are considered in the analysis. The vibration equations with spatial parametric variation and temporal randomness of the beam system under the localized magnetic field are derived, and solved by the modal transformation and frequency spectrum analysis. Then the expression of the root-mean-square velocity criterion for microvibration is given, where the non-homogeneous magnetorheological viscoelastomer modulus is considered due to the localized magnetic field. The proposed analysis method can be extended to other random excited composite structures with viscoelastic cores. The stochastic microvibration control effectiveness of the beam system and the effects of the localized magnetic field intensity and placement on the microvibration response are verified by numerical results.

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