Wave localization in randomly disordered periodic layered piezoelectric structures

Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS WITH INITIAL STRESS

The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon.

Extended State to Localization in Random Aperiodic Chains

The electronic states in Thus-Morse chain （TMC） and generalized Fibonacci chain （GFC） are studied by solving eigenequation and using transfer matrix method. Two model Hamiltonians are studied. One contains the nearest neighbor （n.n.） hopping terms only and the other has additionally next nearest neighbor （n.n.n.） hopping terms. Based on the transfer matrix method, a criterion of transition from the extended to the localized states is suggested for CFC and TMC. The numerical calculation shows the existence of both extended and localized states in pure aperiodic system. A random potential is introduced to the diagonal term of the Hamiltonian and then the extended states are always changed to be localized. The exponents related to the localization length as a function of randomness are calculated. For different kinds of aperiodic chain, the critical value of randomness for the transition from extended to the localized states are found to be zero, consistent with the case of ordinary one-dimensional systems.

Prediction of Maximum Section Flattening of Thin-walled Circular Steel Tube in Continuous Rotary Straightening Process

Cross-sectional ovalization of thin-walled circular steel tube because of large plastic bending,also known as the Brazier effect,usually occurs during the initial stage of tube′s continuous rotary straightening process.The amount of ovalization,defined as maximal cross section flattening,is an important technical parameter in tube′s straightening process to control tube′s bending deformation and prevent buckling.However,for the lack of special analytical model,the maximal section flattening was determined in accordance with the specified charts developed by experienced operators on the basis of experimental data;thus,it was inevitable that the localized buckling might occur during some actual straightening operations.New normal strain component formulas were derived based on the thin shell theory.Then,strain energy of thin-walled tube（per unit length）was obtained using the elastic-plastic theory.A rational model for predicting the maximal section flattening of the thin-walled circular steel tube under its straightening process was presented by the principle of minimum potential energy.The new model was validated by experiments and numerical simulations.The results show that the new model agrees well with the experiments and the numerical simulations with error of less than 10%.This new model was expected to find its potential application in thin-walled steel tube straightening machine design.