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| THE DYNAMICS RESPONSE AND STABILITY OF A DIELECTRIC ELASTOMER CYLINDRICAL SHELL UNDER STATIC AND PERIODIC VOTAGE |
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Abstract Abstract：When a voltage is applied between the internal and external surface of a dielectric elastomer cylindrical shell, it thins down, and the same voltage will produce an even higher electric field. The positive feedback may make the dielectric elastomer cylindrical shell to thin down drastically, causing an electrical breakdown. We study the dynamics response and stability of the cylindrical shell which is under static and periodic voltage in this article. We get the ordinary differential equation which describes the movement of cylindrical shell using the neo-Hookean material model. The voltage curves as a function of the deformation with different thickness and different boundary conditions are given, and the critical voltage is found. The cylindrical shell will be destroyed if the applied voltage is greater than the critical value. Addition, we also discuss the thickness and boundary conditions influence on the critical voltage. When a periodic voltage is applied, the movement of the shell is cyclical or intending to cyclical nonlinear vibration. We calculate nature frequency of the cylindrical shell, and get the periodic solutions using the shooting method, analyze the stability of the periodic solutions using the numerical method. The vibration amplitude curves as a function of the incentive frequency of periodic voltage are given. The cylindrical shell occur mutirate resonance, the vibration amplitude jumps at the point of resonance which may cause the cylindrical shell destroyed. We give the time history curves and phase diagrams of the resonance points, and discuss the characteristics of the vibration.
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Received: 07 September 2011
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Corresponding Authors:
Youhe Zhou
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2012, Vol. 33 
