Multifield Coupling Analysis Of Piezoelectric Spherical Shell

Piezoelectric material has been extensively used in technological applications such as sensors, actuators, transformers, etc., for its unique electromechanical characteristics. It is important to analyze exactly the multifield coupling responses of laminated/functionally graded piezoelectric devices which are usually located in a complex environment, and the results should have a great value for the design and optimization of these devices. The developed analysis methods will be also useful for the analysis of other structures made of new-type functional materials.A three-dimensional analysis of pyroelectric responses of a multilayered piezoelectric hollow sphere is performed based on the state-space formalism, In particular, the effect of interfacial bonding imperfections is considered by introducing different weak interface models for different physical fields. Transfer matrices for interfaces are thus established, and the global transfer matrix is accordingly derived and exactly solved. The analysis, without any assumptions on deformation and with a high efficiency of computation, can be a means of comparison with any approximate solutions.Similar analysis is also proposed for a functionally graded piezoelectric material (FGPM) spherical shells subjected to various thermal boundary conditions applied on the inner and outer spherical surfaces. For FGPM spherical shells with its material properties varying along the radial coordinate according to a power law, a new set of state variables are introduced such that an exact three-dimensional solution can be obtained. Based on such an exact strategy, a modified laminate model has been proposed for FGPM spherical shells with arbitrarily varying properties along the thickness. In this model, the material properties in each divided layer are approximated as power functions of the radial coordinate, which can assure that the material properties at the interface between two successive layers are continuous. Thus, the new model overcomes the defect of material discontinuity occurring at the interfaces in the traditional approximate laminate model.Transient responses of pyroelectric spherical shells subjected to thermal shock are also investigated based on the generalized L-S theory, either in the time domain or in the frequency domain. Using the Laplace transform and the state-space formalism in the frequency domain along with the traditional approximate laminate model, the time-domain responses can be obtained numerically using inverse Laplace transform. This approach is simple and straightforward, can be easily applied to the thermal shock problem of laminated and functionally graded spherical shells. For the time-domain analysis, a combination of the separate variables method and the superposition method is adopted, which clearly avoids the numerical error induced by the numerical inverse Laplace transform. Numerical results indicate that the time-domain analysis can capture the wave front of thermal waves clearly.A three-dimensional analysis of the free vibration of a laminated piezoelectric hollow sphere filled with air or fluid is presented. No assumptions on deformation have been introduced except for the use of the conventional approximate laminate model. It is noted that, however, as the number of layers increases, the solution will gradually approach the exact solution.An exact solution of the radial vibration of functionally graded, arbitrarily thick, hollow sphere filled with an elastic medium is obtained. Here, the material properties vary along the thickness in power laws, but the gradient index of density can be different from that of other material parameters. Thus, the current model surmounts the limit that all gradient indices are assumed to be the same as in the literature, providing more choices to tune the resonant and anti-resonant frequencies of the spherical shell.