Research On Theory And Algorithms For Multi-fieles Coupling Of Mangetoelectroelastic Solids

Piezoelectirc,piezomagnetic materials which are used as sensor and actuator integrating with structure form a intelligent material system, which can also be called piezoelectric, piezomagnetic composite materials system. The primary work for the research in this kind of intelligent structures is to establish analytical model which can accurately indicate the interaction between piezoelectric, piezomagnetic sensor and actuator and body structure. This model is not only able to exhibit the internal of magneto-electro-elasticity coupling interaction in piezoelectric,piezomagnetic intelligent structure from the global aspect, but also easy to analyze and calculate with necessary mathematical tools.A general variational principle of magneto-electro-elastic composite structures is discussed which contains stress, strain, displacement, electric displacement, electric field, electric potential, magnetic displacement, magnetic field and magnetic potential as the independently assumed field variables. The stationary conditions of the functional are equivalent to all governing equations and boundary conditions in magneto-electro-elastic composite structures. Eight degenerated variational principles of magneto-electro-elastic composite structures are presented which are deduced from the general variational principle.In this paper, state variable formulation for free vibration of the laminated structures bonded and embedded actuators and sensors (piezoelectric and/or piezomagnetic) is established. The present mixed type formulation has the great advantage that the size of the system to be solved is independent of the number of layers and is of order three for free vibration of the laminate with bonded and embedded piezoelectric and/or piezomagnetic layers. Analytical solutions of 3D free-vibration of simply supported piezoelectric and piezomagnetic composite plates have been presented. The transfer matrices for either closed circuit or open circuit piezoelectric and piezomagnetic layers are derived. The special case of elastic layer is also treated. The assembly procedure is described for the different electric and magnetic surface conditions. Numerical examples are analyzed to study the vibration characteristics of smart laminate plates with different stacking sequence and different span to thickness ratio.The finite element equations are derived by application of Hamilton principle based on the classic electroelastic theory. Based on these equations, mechanical-electric coupled program has been developed by use of ANSYS/APDL language. Based on the analysis of a degraded model, we researched the influence for the beam's deflection and free vibration frequency caused by the change of the piezoelectricity's length(a) and position(b). One set and two sets of piezoelectricity with different boundary conditions have been presented. A conclusion has been derived to be advisory in designing piezoelectricity structure.Theoretical derivation,numeriacl method and FE modeling is used in the subject, the physical nature of magneto-electro-elasticity coupling action in piezoelectric, piezomagnetic composite materials is closely grasped, and mathematical physical model which is appropriate to piezoelectric,piecomagnetic structure is explored in this paper.These researches show important theoretical significance and practical application value not only for the basic theory study but also for the design and industrial application in the future about piezoelectric, piezomagnetic meterials and intelligent structure.