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
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.
［1］ MINDLIN R D. Equations of high vibrations of thermopiezoelectric crystal plates ［J］. International Journal of Solids and Structures, 1974, 10(6): 625-632. ［2］ NOWACKI W. Some general theorems of thermopiezoelectricity ［J］. Journal of Thermal Stresses, 1978, 1(1): 171-182. ［3］ IESAN D. On some theorems of thermopizeoelectricity ［J］. Journal of Thermal Stresses, 1989, 12(2): 209-223.
［4］ TAUCHERT T R. Piezothermoelastic behavior of a laminated plate ［J］. Journal of Thermal Stresses, 1992, 15(1): 25-37. ［5］ CHEN W Q, SHIOYA T. Piezothermoelastic behavior of a pyroelectric spherical shell ［J］. Journal of Thermal Stresses, 2001, 24: 105-120. ［6］ CHEN W Q, DING H J, XU R Q. Threedimensional static analysis of multilayered piezoelectric hollow spheres via the state space method ［J］. International Journal of Solids and Structures, 2001, 38: 4921-4936. ［7］ DING H J, CHEN W Q. Three Dimensional Problems of Piezolasticity ［M］. New York: Nova Science Publishers, 2001. ［8］ CHEN W T. On some problems in spherically isotropic elastic materials ［J］. Journal of Applied Mechanics, 1966, 33: 539-546. ［9］ HU Haichang. On the general theory of elasticity for a spherically isotropic medium ［J］. Acta Scientia Sinica, 1954, 3: 247-260. ［10］ 严宗达, 王洪礼. 热应力［M］. 北京: 高等教育出版社, 1993: 2-14. ［11］ PAUL H S, NELSON V K. Wave propagation in a pyroelectric cylinder of arbitrary cross section with a circular cylindrical cavity ［J］. Journal of the Acoustical Society of America, 1997, 102(1): 301-307.
