Research And Application Of The New Analysis Methods For Piezoelectric Smart Structures

Smart structures are widely used in the military aviation and aerospace engineering due to their superior properties, such as self-diagnosis, adaptive, self-repair, etc. With the development of thorough investigation and improving theory, applications of smart structures have been extended to civil engineering, shipbuilding, automobile and other industries. A good application prospect of smart structures has been unfolded for the structural health monitoring, damage self-healing and vibration, noise and shape control in the fields of aviation, aerospace, submarines, high-speed trains, automobiles, bridges, dams and architecture. In recent years, a great deal of attention has been paid to the research and application of smart structures in the world’s major developed countries, and therefore the research and application of smart structures has been classified as one of the priority development areas in terms of the21st century high-tech industries.Piezoelectric materials have a lot of advantages such as wide frequency response range, fast response, large compactness, high accuracy, good linear behavior, etc. and they can be used as not only sensors but also actuators. The smart control in structures can be realized by way of the unique direct and inverse piezoelectric effect of piezoelectric materials. Over the past decades, extensive studies have been carried out in the basic and applied research of piezoelectric smart structures and a wealth of research achievements have been made.At present, the studies of piezoelectric smart structures are mainly concerned with coupling theory, shape control, vibration control, noise control, optimization analysis, fault diagnosis and monitoring, analysis methods and experiment. Based on the spline meshless method and QR method founded by Professor Qin Rong in Guangxi University, new analysis models for piezoelectric smart laminated plates and piezoelectric frame structures are proposed to study the static deformation control, optimal shape control, active vibration control and parameter identification of piezoelectric material structures. The main work and innovations of the research in this paper are as follows:1. Based on Reddy’s third order plate theory and Hamilton variational principle, a new model of the static deformation control for piezoelectric smart composite plate is developed and the stiffness matrix is deduced by using spline meshless method. A model of the optimal shape control for piezoelectric smart composite plate is derived according to the sensitivity matrix which is based on the spline meshless discrete model with respect to the driving voltage and location of the actuator layer. By designing different piezoelectric actuators, various boundary conditions and different matrix materials, some numerical examples of open-loop control and closed-loop control are given. The numerical results show that the developed model is correct and effective for shape control. The spline meshless method has the advantages of high precision, simple input, high efficiency and concise boundary conditions.2. The study of the deformation control for piezoelectric smart laminated plate by the analytical method and the find of the electrical boundary conditions of piezoelectric layer in line with the unique features of direct and inverse piezoelectric effect. Based on the electrical balance equation and electrical boundary conditions, for the simply supported piezoelectric laminated plates considering the first shear impact, the deduced electric potential distribution is expressed as a hyperbolic function along the thickness. Numerical examples are given to analyze the deformation, electric potential distribution, open-loop and closed-loop control of the piezoelectric laminated plate under mechanical loads and electric loads. The results illustrate that the analytical solutions are cross-checked with those of spline meshless method and the agreement between them is satisfactory. Due to the insufficient controlling power of monolithic piezoelectric actuator, the analytical formula of driving force for the book-block piezoelectric actuator is derived to improve the driving efficiency. Moreover, the non-linear quantitative relationship between piezoelectric film layers (n) and the driving force of the piezoelectric actuators (Mxp) is established. Examples show that better control is obtained by the book-block piezoelectric actuator. So, it can be applied to the deformation control of piezoelectric laminated plate and steel frame structure.3. A new model for parameters identification of piezoelectric material. Based on the displacement modeled by the spline meshless method, the parameter identification problem is formulated as the problem of minimizing the objective function which is defined as a square sum of differences between the measured displacement and the computed displacement by the spline meshless method. The sensitivity matrix is calculated by the derivation of parameters to be identified. The calculation formula of sensitivity is deduced based on the displacement values obtained by the spline meshless method in line with the derivative of each material parameter. Levenberg-Marquardt method with the trust-region based techniques, is used to solve the minimization problem. In the process of parameter identification, the calculated results obtained by the spline meshless method using the true values of material parameters replace the measured data on displacements. However, normal distribution noises are added to simulate errors in measurement. For piezoelectric composite plate under the mechanical loads and electrical loads, the identification of matrix material parameter and piezoelectric parameter are investigated. Numerical examples show that the proposed method for parameter identification in this paper has high accuracy and good stability, and is effective.4. Based on Reddy’s third order theory, a new piezoelectric smart beam-column element is derived by considering the shear deformation effect, piezoelectric effect, initial geometric imperfection and P-A effect. When the shear effect and piezoelectric effect are not considered, the element geometric stiffness matrix derived in this paper for piezoelectric smart beam-column element derived can be degenerated to the one for the linear elastic case. With introducing its influence coefficient, the initial geometric imperfection is jointly analyzed with P-Δ effect and the corresponding element stiffness matrix is established. The correctness of this beam-column element is illustrated by some numerical examples. This work lays a theoretical foundation for the modeling of piezoelectric smart frame structure.5. Based on the piezoelectric smart beam-column element stiffness matrix derived in the above, the new dynamic analysis model for piezoelectric frame structure is developed by the spline QR method. The mode control theory and LQR optimal control method are used to establish the calculation model of active vibration control for piezoelectric frame structure. The influence of the P-A effect and initial geometric imperfection on the structural natural frequency and control power is discussed by way of laying piezoelectric stack actuators on the column. The simulation analysis of active vibration control for piezoelectric laminated beam and piezoelectric-steel frame structure is given and the results demonstrate that the vibration of the structure can be effectively suppressed by using this analysis model. With considering the P-Δ effect and initial geometric imperfection, the natural frequency of the structure decreases and the control voltage significantly increases. It is obvious that the influence of these two factors on the active vibration control can’t be ignored and its study is of great significance.By comparing with analytical solution and finite element solution, numerical results illustrate that the new model established by the proposed methods in this paper is correct and effective and those methods have a lot of advantages, such as simple input, high accuracy, good stability, clear physical concept, concise boundary conditions, less computation, run fast, etc. In this paper, the new methods are used to study shape control, vibration control, optimization analysis, and parameter identification for piezoelectric smart composite laminates and steel frame structures, which is of great significance in theory and practice. The proposed methods as well as the obtained conclusions have an important reference value.