Research On The Property Of Mechanics Of Piezoelectric And Functionally Graded Cylindrical Shells

Functionally graded materials (FGMs) are microscopically inhomogeneous composite materials. Material properties are graded in the thickness direction according to volume fraction power law distribution. Designers may obtain the desirable material properties adequate to the design purpose as they arrange the volume fractions of the constituents appropriately. The piezoelectric smart structure is a kind of adaptive structures, and integrated with composite base structure, piezoelectric sensor/actuator and controller units, which can observe the external disturbances by sensor, then change the structural state to adapt for environment's change by the actuator, through regulation of controller units. It hold very wide and bright prospect of application in the many fields, such as aerospace, chemical pipes, nuclear power, offshore, submarine structures, pressure vessels and civil engineering structures. Piezoelectric FGM structures will have the advantages of FGMs and piezoelectric materials linked together.The main work in the dissertation includes:(1) Based on the first-order shear deformation theory and the Hamilton's principle, the equations of motion, the eigen-equation, the static buckling equation and the dynamic stability equation of Mathieu-Hill type are obtained for functionally graded cylindrical shells in thermal environments, embedded in an elastic medium. From example calculations, effects of thermal environments, material composition, static axial loading, medium stiffness and shell geometry parameters on vibration, buckling and the parametric resonance are described.(2) A theoretical method is developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory considering shear deformation and rotary inertia. The Rayleigh-Ritz procedure is applied to obtain the frequency equation and the static buckling equation. The effects of stiffener's number and size on natural frequency of functionally graded cylindrical shells are investigated. Moreover, the influences of material composition, thermal loading and shell geometry parameters on buckling and vibration are studied.(3) Considering rotary, in-plane inertias, and fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived based on the first-order shear deformation theory and the Hamilton's principle. The equations of eigenvalue problem are obtained by using a modal expansion method. The response characteristics of fluid-conveying FGM cylindrical shells are obtained by using modal superposition and Newmark's direct time integration method. Effects of material composition, thermal loading, flow velocity, medium stiffness and shell geometry parameters on the free vibration characteristics are described. Numerical examples show that the dynamic characteristics of fluid-conveying FGM cylindrical shells are relate to the flow velocities, volume fraction exponents of FGMs, axial loads, excitation frequencies of the radial load and thermal environment of FGM shells conveying fluid.(4) Based on the first-order shear deformation theory and the Hamilton's principle, taking into account both the direct piezoelectric effect and the converse piezoelectric effect, and a layerwise quadratic distribution of the electric potential, the coupling equations to govern the electric potential and the displacements are obtained for the functionally graded cylindrical shell with surface-bonded piezoelectric layers. Constant-gain negative velocity feedback approach is used for active vibration control. The modal superposition and Newmark's integration method are used to calculate the displacements and sensory electric potential of the functionally graded cylindrical shell subjected to moving loads. The convergence of time response and critical velocities of moving loads are investigated. The influences of control gain, different piezoelectric materials and various loading forms on the active vibration control are described in the numerical results.In some special conditions, the obtained results have been compared with the analytical results of other researchers, which showed good agreement. Much research is published firstly in the above field. The present investigation will be expected to perfect theory and analytical method for functionally graded structures and functionally graded piezoelectric smart structures. The present work shows that some meaningful and interesting results presented in this paper are helpful for the application and the design of novel materials made of composite structures equipped with piezoelectric components.