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Three-dimensional pyroelectric analysis of
multilayered piezoelectric spherical shell |
| LIU Cheng-bin1, BIAN Zu-guang2, CHEN Wei-qiu3 |
1. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China; 2. Branch College of Civil
Engineering and Architecture, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
3. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China |
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Abstract A second-order homogeneous state equation was established from the equations governing the heat conduction in the spherical shell. It was solved by a successive use of series expansion technique and matrix theory. A transfer relation was obtained between the thermal state vectors at the inner and outer surfaces of the multilayered shell by using the continuity conditions at each interface, and the thermal field could be exactly determined once incorporating the prescribed surface temperatures into the relation. Based on the three-dimensional equations for a pyroelectric body in spherical coordinates, three displacement functions and two stress functions were introduced to obtain a second-order homogeneous state equation and a sixth-order inhomogeneous state equation. Exact solutions were obtained via a solution procedure similar to the thermal field. Through numerical examples, the steady-state responses of thin/thick single-layered piezoelectric spherical shells subject to prescribed temperatures at the inner and outer surfaces were given, and the difference in thermal response between a single-layered spherical shell and a multilayered one was discussed. It is shown that different thickness and structure style can obviously change the spherical shell’s pyroelectric effect.
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Published: 14 July 2011
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叠层压电球壳的三维热释电分析
从球壳热传导方程出发,建立一个关于温度场的二阶齐次状态方程,并采用级数展开技术和矩阵理论进行精确求解.利用界面连续条件导出叠层球壳内、外表面温度场状态矢量的传递关系,进而利用内、外表面的温度边界条件精确确定球壳内的温度分布.基于热释电弹性体的三维基本方程,引入3个位移函数与2个应力函数,导出1个二阶齐次状态方程和1个六阶非齐次状态方程,并采用几乎相同的求解策略得到了边界温度作用下球壳内精确的电弹性场.通过数值算例考察了单层薄/厚球壳在内、外恒定温度作用下的稳态响应，以及相同厚度的单层与叠层球壳的不同热释电响应,发现厚度与结构形式不同可以显著改变其热释电效应.
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