State vector solutions for nonaxisymmetric problem of multilayered half space piezoelectric medium |
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Authors: | Jianguo Wang |
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Institution: | (1) Department of Civil Engineering, Hefei University of Technology, 230009 Hefei, China |
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Abstract: | A state space formulation is established for the nonaxisymmetric space problem of transversely isotropic piezoelectric media
in a system of cylindrical coordinate by introducing the state vector. Using the Hankel transform and the Fourier series,
the state vector equations are transformed into ordinary differential equations. By the use of the matrix methods, the analytical
solutions of a single piezoelectric layer are presented in the form of the product of initial state variables and transfer
matrix. The applications of state vector solutions are discussed. An analytical solution for a semiinfinite piezoelectric
medium subjected to the vertical point forceP
z, horizontal point forceP
x along x-direction and point electric charge Q at the origin of the surface is presented. According to the continuity conditions
at the interfaces, the general solution formulation forN-layered transversely isotropic piezoelectric media is given.
Project supported by the National Natural Science Foundation of China (Grant No. 59648001). |
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Keywords: | multilayered piezoelectric media transverse isotropy nonaxisymmetric problems state vector equations transfer matrix analytical solutions |
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