In this paper, a method to calculate the dynamic stress concentration around the triangular defect of piezoelectric material under electroelastic coupling is studied and applied to the promising barium calcium zirconate titanate. Firstly, the electroelastic governing equation is decomposed by decoupling technique, and the analytical solutions of elastic wave field and electric field are obtained by wave function expansion method. Then, the conformal transformation is used to simplify the triangle boundary into a circular boundary, and the corresponding modal coefficients are determined according to the simplified boundary conditions. Finally, the analytical solution of the dynamic stress concentration factor can be obtained according to the constitutive equation. Substitute the relevant material parameters of (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 and set different temperatures, Ce doping amount, and incident wave number for numerical simulation. The numerical results show that the incident wave number, piezoelectric properties, and the shape parameters and deflection angle of the triangular defect have a great influence on the dynamic stress around the defect, and some meaningful laws are summarized through analysis.

The vibration of flexible structures in spacecraft, such as large space deployable reflectors, solar panels and large antenna structure, has a great impact on the normal operation of spacecraft. Accurate vibration control is necessary, and the control of angular displacement is a difficulty of accurate control. In the traditional control method, the mode space control has a good effect on suppressing low-order modes, but there is control overflow. The effect of traveling wave control on low-order modes is worse than the former, but it has the characteristics of broadband control. It can better control high-order modes and reduce control overflow. In view of the advantages and disadvantages of the two control methods, based on Timoshenko beam theory, this paper uses vector mode function to analyze the modal of spacecraft cantilever beam structure, establishes the system dynamic equation, and puts forward an optimized traveling wave control method. As a numerical example, three strategies of independent mode space control, traditional traveling wave control and optimized traveling wave control are used to control the active vibration of beam angle. By comparing the numerical results of the three methods, it can be seen that the optimal control method proposed in this paper not only effectively suppresses the vibration, but also improves the robustness of the system, reflecting good control performance. An innovation of this paper is that the Timoshenko beam model is adopted, which considers the influence of transverse shear deformation and moment of inertia on displacement and improves the accuracy of calculation, which is important for spacecraft accessory structures with high requirements for angle control. Another innovation is that the optimized traveling wave control method is exquisite in mathematical processing and has good results in global and local vibration control, which is not available in other methods.

In this paper, the calculation method of dynamic stress concentration around piezoelectric ceramics containing regular n-sided holes under the action of electroelastic coupling wave was studied, and it was applied to promising barium calcium zirconate titanate material. First, electroelastic governing equations were decomposed by using the auxiliary function method, and the solution forms of the elastic wave field and electric field were obtained by using the wave function expansion method. Then, the triangular boundary was simplified to a circular boundary using the mapping function, and the corresponding modal coefficients were determined according to simplified boundary conditions. Finally, the dynamic stress-concentration factor was calculated to characterize the dynamic stress concentration. We performed numerical simulations with a correlation coefficient of (1 − x)[(Ba0.94Ca0.06) (Ti0.92Sn0.08)]-xSm2O3-0.06 mol% GeO2 (abbreviated as (1 − x)BCTS-xSm-0.06G). The numerical calculation results show that the incident wave number, piezoelectric properties, shape parameters of the hole, and deflection angle have a great influence on the dynamic stress around the defect, and some significant laws are summarized through analysis.

Sodium bismuth titanate (Bi0.5Na0.5TiO3, BNT) has attracted much attention because of its excellent dielectric, piezoelectric and electromechanical properties. The microstructure of sodium bismuth titanate-doped ferrum niobium material (Bi0.5Na0.5TiO3 doped (Fe0.5Nb0.5)4+, BNT-xFN) shows a triangle as its typical defect shape. Since piezoelectric devices usually operate under dynamic loads, they fail easily owing to dynamic stress concentration or dynamic fracture. Elastic waves can simulate many types of dynamic loads, and the dynamic stress concentration caused by an anti-plane shear wave is the basis for the calculation of the stress field strength factor of type Ⅲ-dynamic fractures. In this study, the electroelastic coupled-wave diffraction and dynamic stress concentration of BNT-xFN materials with triangular defects under the incidence of anti-plane shear waves were studied. Maxwell equations are decoupled by auxiliary functions, and the analytical solutions of the elastic wave field and electric field are obtained. Based on the conformal mapping method, the triangle defect was mapped to the unit circle defect, and the dynamic stress concentration coefficient around the triangle defect was obtained by calculating the undetermined mode coefficients in the expression through boundary conditions. The numerical calculation shows that the size of the triangular hole, the frequency of the applied mechanical load, the incidence angle of mechanical load and the amount of FN doping have a great influence on the stress concentration of BNT-xFN materials.