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在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场.这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏.论文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题.采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程.给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏.同时,也讨论了厚度和边界条件对临界电压的影响.圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动.给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性.采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏.最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论.
When a voltage is applied to the inner and outer surfaces of the electroactive polymer cylindrical shell, the cylindrical shell will become thinner and elongate so that the same voltage will create a larger electric field in the cylindrical shell. This positive feedback may cause the cylindrical shell to become thinner in thickness, ultimately resulting in And its failure is destabilized.In this paper, the response and stability of electro-active polymer cylindrical shells under static and periodic voltages are studied.The nonlinear ordinary differential equations describing the surface movement of cylindrical shells are obtained by using the neo-Hookean material model. Cylindrical shell under different thickness and boundary conditions with the voltage applied to the deformation curve of the cylindrical shell, the results show that there is a critical voltage, when the applied voltage is greater than the critical value, the cylindrical shell will be destroyed at the same time, also discussed the thickness and boundary The influence of the condition on the critical voltage.The cylindrical shell under the action of sinusoidal periodic voltage changes with time is periodic or quasi-periodic nonlinear vibration.The calculation results of natural frequency of cylindrical shell vibration are given, The periodic solution of the vibration of the cylindrical shell is obtained and the stability of the periodic solution is studied numerically.The vibration amplitude of the cylindrical shell is obtained by numerical simulation The results show that the multi-frequency resonance occurs in the cylindrical shell, and the amplitude of the cylindrical shell jumps during resonance, resulting in the instability failure of the cylindrical shell. Finally, the vibration curve and phase diagram of the near resonance point are given, Vibration characteristics are discussed.