| This thesis is supported by the Doctor Subject Foundation of the Ministry of Education of China under Grant No. 98014106. Knowledge from different cross disciplines such as Physics of Crystals, Physics of Dielectrics, Theory of Elasticity, Theory of Potential and Group Theory is utilized in the investigation on the torsional effect of piezoelectrics. It is confirmed that the torsional effect of piezoelectrics does exist by the theoretical analysis and the test in this thesis. The connection between the torque and the polarized charges is established. The complicated stress distribution of piezoelectric beam under torsion is investigated first by utilizing the torsion theory of anisotropic beam. The governing equation and boundary conditions of torsion problem of piezoelectric beam are converted into the solvable form. Then the nonlinear electric polarization due to torsion is analyzed and the problems of electric field in torsional effect of piezoelectrics are converted into the inner and outer boundary value problems of partial differential equations according to the equivalent principle of electric field. Finite element method is used in the analysis of the electric field in torsional effect of quartz crystal. In the process of investigation on the torsional effect of quartz crystal, mirror symmetric conservative law is applied to ascertain the connection between the physical characteristics of leftwards spiral crystals and rightwards spiral crystals. A new method for torque measuring is established in this thesis by using a single piezoelectric beam. The method is testified by experiments on the leftwards spiral quartz beam, and the results of the experiments coincide well with the results of calculating. An optimizing method for the sensitivity in detection of torsional effect is modified at the end of the thesis. The optimized cutting angles of piezoelectric crystals are obtained by using unconstrained simplex minimization method ----Nelder-Mead method.
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