Piezoelectric Material Beam Stability Analysis And Research

The stability problems of rectangle-section beam made of transversely isotropic piezoelectric material subjected to two different loads are mainly discussed in this dissertation.Firstly, the beam is pin-pin supported and is polarized along the longitudinal direction of the beam. The electrical field and the constant load are applied along the same direction. The governing equations of buckling and the corresponding natural boundary conditions are derived according to variational principle. The solutions to these non-linear equations are obtained by perturbation method. The critical load (bifurcation point) as well as the postbuckling load is given. It is shown from the conclusions that the critical load and the postbuckling path of the piezoelectric beam are not relevant to the applied electric field, but the voltage between the two ends of the beam can be changed when the buckling occurs. Although the electric field cannot control the stability of the beam, it can detect whether the buckling occurs or not and the buckling degree.Secondly, a slender cantilever beam made of transversely isotropic piezoelectric material subjected to subtangential follower forces at the free end is considered. An independent parameter λ is introduced to reflect the ratio of the conservative and the non-conservative components of the load. Then the virtual work principle (the variational principle is used here) is employed to derive the governing equations and the corresponding natural boundary conditions. The linear solution to these governing equations shows that only when the independent parameter X changes in the range [0,0.5] do the equilibrium configuration exist for the subtangential follower force and the buckling load changes with the parameter λ. The perturbation solutions to these non-linear governing equations are given. The results reveal that the buckling load is determined only by the independent parameter λ and the characteristics of the material but does not relate to the electric field. The voltage between the two ends of the beam is not only determined by the buckling occurrence of the beam, but also strongly relevant to the independent parameter λ.Finally, the dynamic problem of the beam, described as previously, in case ofinfinitesimal deformation is primarily discussed.This dissertation is divided into five chapters. The research actuality of the related field is briefly introduced in the first section. And the work to be done, the research methods and its significance are also explained in this section. The piezoelectric constitutive equations and the physical methods used in this article are briefly introduced in chapter 2 and chapter 3, respectively. The stability problem of piezoelectric beam under three cases is studied and analyzed as an emphasis in the fourth section. The last chapter includes the summary and prospect.