Nonlinear Mechanical Behaviour And Active Control Research On Piezoelastic Laminated Structures Including Interfacial Damage Effects

In this thesis, considering piezoelectric plates and piezoelastic laminated plates/shells composed by the piezoelectric membranes and fibre-reinforced composite laminated plates as the subjects investigated, the analysis of inter-laminar stresses and electric potential, nonlinear dynamic response, nonlinear vibration behaviors as well as the nonlinear active vibration control of piezoelectric structures / piezoelastic plates with interfacial imperfections are systematically studied, and the essential character of the mechanical property can be illustrated precisely.However, the establishment of the constitutive relations for piezoelectric materials with interfacial damage and corresponding mechanical modeling is very difficult. Limited investigation have been conducted for piezoelectric laminates with interfacial damage due to the difficulties in description of coupled electromechanical bonding conditions on damaged interfaces, and the study on interfacial damage in piezoelectric laminates is still at its early stages. Moreover, the geometric nonlinearity, damage effects and piezoelectric effects will make the governing equations and boundary conditions more complicated, and the new analytical methods and computational methodology are necessary to solve this problem. Due to the above reasons, there is little research on this field. The problem is investigated in this thesis, and some achievements are obtained on several aspects such as the establishment of the constitutive relations with interfacial damage, the construction of the mechanical modeling and the sake of efficient computational method, etc. The research results are significant not only in the academic but also in the practical engineering. The main results contain as follows.For the inter-laminar interfacial problem of composite laminated structures, based on the new method developed by Soldatos, for the general six-degrees-of-freedom plate theory towards the accurate stress analysis, and 3-D nonlinear elastic theory,using the variation principle and the equivalent strain theory in damage mechanics, considering the damage effect of the intra-layers and the inter-laminar interface, the non-linear equilibrium differential equations for composite laminated structures with interfacial imperfections are derived. Then, an analytical solution is presented by using the finite difference method to obtain the inter-laminar stresses for composite laminated beam, plate and shallow shells, respectively. In numerical examples, the effect of different damage, load forms, the number of layers on the displacements and inter-laminar stresses of composite laminated structures are investigated, and the effect of pure shear slip and delamination on the damaged interfaces are also researched.With respect to the interfacial potential analysis of piezoelectric material laminated plate, considering the geometric nonlinearity, damage effect on the piezoelectric interfaces and piezoelectric effect, upon employing the general solution about three equilibrium equations and the conservation of charge to determine the shape functions accounted for the discontinuity of displacement and electric potential on the interfaces, the three-dimensional nonlinear equilibrium differential equations of simply supported piezoelectric material laminated plates with interfacial damage are derived. Then, the effects of different damage values, load models and electric boundary conditions on the inter-laminar stress and electric potential profile of piezoelectric laminated plate with interfacial imperfections are investigated.Taken the problem of nonlinear dynamic response for piezoelectric composite laminated plate with interfacial damage into consideration, under the interfacial damage in such an initial stage, based on the Von Kármán's nonlinear theory and the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelectric composite laminated plates considering the damage effect of the intra-layers and the inter-laminar interface are derived. The intra-layer material damage evolution law is characterized by the Kachanov damage evolution equations. Through applying the finite difference method, Newmark method and iterative procedure, the above governing equations are solved. The effects of different damage models, damage evolution, amplitude and frequency of electric loads on the nonlinear dynamic response of piezoelectric laminated plate with interfacial imperfections are discussed in detail.Then, for the analysis of nonlinear free vibration for piezoelectric composite laminated plate with interfacial damage, based on the above three-dimensional nonlinear dynamic equations for piezoelectric composite laminated plates considering the damage effect of the intra-layers and the inter-laminar interface, by employing the Galerkin method, the nonlinear partial differential equations are changed into nonlinear ordinary differential equations about time-functions. In numerical examples, the damage evolution equation proposed by Kachanov is still taken, under the close-circuit condition, the effects of different damage models, the thickness of piezoelectric layer, the side-to-thickness ratio and the length-to-width ratio on the natural frequencies and non-linear amplitude-frequency response characteristics of the simply-supported piezoelastic laminated plates with interfacial imperfections are discussed, respectively.Additionally, assuming a symmetric cross-ply composite laminated plate with piezoelectric sensory/active devices on the upper and lower surfaces for nonlinear active vibration control purpose, considering the mass and stiffness of piezoelectric layers and the damage effect of the intra-layers and inter-laminar interface, upon employing active control of damping to the above derived three-dimensional nonlinear dynamic equations, a simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to realize the active control and damage detection of the piezoelectric smart laminated plates through a closed control loop. Numerical examples for simply supported rectangular laminated plates with interfacial imperfections are presented, and the influences of feedback control gain and the locations of the piezoelectric layers on the vibration control are investigated. Also, the effects of the degree and location of the damage on the sensor output voltage are discussed, and a way of damage detection is introduced.