Transient Responses And Characteristic Waves Of Layered Piezoelectric Structures

Piezoelectric materials, as ideal materials of sensors and actuators in intelligent structure systems, have the characteristics of piezoelectric and inverse piezoelectric effects, which can perceive and respond to environment. These materials, forming the laminated piezoelectric smart structure with the function of self-test, self-adaption and quick response, are always pasted on the surface or embedded in the internal part of base layer material in the form of clad layer and chip. With so many advantages, such as better receptivity and wider working frequency, piezoelectric laminated structure has higher specific strength and specific modulus applied into the aerospace, dynamometry, nondestructive testing and biomedicine. There is a significantly important point doing research on the application of electric elastic wave to design and manufacture of laminated piezoelectric smart structure.Because of the anisotropy matrices of composite material and piezoelectric materials, the interactive laying of materials and the coupling in piezoelectric media, laminated piezoelectric smart structure is dynamic system with discontinuous distribution, discontinuous material properties and electromechanical coupling. At present, a series of technical difficulties on numerical model of laminated piezoelectric structure’s dynamic response analysis and the balance between accuracy and efficiency. Therefore, based on the transient response of electromechanical coupling from the structure of piezoelectric laminated plate and shell, this paper tries to build an analysis system which can both consider the balance between accuracy and efficiency and describes precisely dynamic response of laminated piezoelectric smart structure. The corresponding work is as follow:(1) Based on the propagation characteristic of electric-elastic wave and three dimensional electric-elastic theory, a numerical model of laminated piezoelectric plate has been built based on piezoelectric layer element, which can deduce the deformation, transient distribution and response time of potential under the common action among force load, potential incentive and electromechanical coupling load. This method can solve structure transient response efficiently by associating several numerical methods such as Finite element method and overcome several difficulties in traditional method.(2) The transient problem of electric elastic wave has been for piezoelectric laminated cylindrical shell has been analyzed. On the radial direction of cylindrical shell, displacement field and electric potential field will be dispersed in the form of three nodes isoparametric element. The coupling physical field of piezoelectric laminated cylindrical shell can be fitted by the vector function of cylindrical element’s surface distribution and the scale and precision of calculation can be controlled by changing the density of cylindrical shell element. Based on Hamilton theory, the whole motion control equation of structure will be built after twice independent variational methods for node displacement and electric potential. In addition,, semi-analytical solutions of the wave number domain displacement and transient distribution of electric potential under several kinds of force-electric load are deduced. Bringing in equivalent load of the wave number domain and equivalent coupling stiffness matrix makes solving process more unified and it is convenient to analyze directly the influence of electrical coupling effect on laminated piezoelectric structure dynamic response. At the same time, this measurement will decrease the degree of freedom of control equation and workload of calculation. When the material properties of the piezoelectric layer and substrate layer meet certain conditions, motion control equation of the wave number domain and corresponding eigenvalue problem will be a real treatment increasing the calculation efficiency further.(3) Based on the modal analysis theory, researches about problems of the propagation and scattering characteristics have been done. Free vibration control equation has been built according to piezoelectric laminated structure mechanics model of single layer cell. Moreover, six concepts of characteristic face are used for expressing the influence of material anisotropy and piezoelectric effect on structure fluctuation characteristics.(4) Based on semi-analytical calculation model for laminated panels pressure dynamic response analysis, both transient responses of electric potential and displacement for loading parameters and the first-order sensitivity of the material constitutive parameters are deduced. Using properties of space domain-wave number domain transform, the first-order sensitivity of wave number domain response has been deduced from the control equation of wave number domain. The comparison between this method and finite difference method verifies advantages of efficiency and accuracy in this proposed method. Combing with interval structure analysis theory, a new method has been proposed for obtaining transient response border of displacement and electric potential quickly on the premise that there are many uncertain parameters and constraints.