The Control Of Vibration And Thermo-elasticity Of The Composite Cicular (Annular) Plates With Embedded Shape Memory Alloys Fibers

Based on the Brinson's one dimensional thermomechanical constitutive relationship and the law of the mixture ratio of composite materials, equations governing the vibration and thermal post-buckling of composite circular/annular plates embedded with shape memory alloy wires in a temperature rise filed are derived. By using the shooting method, harmonic response of the vibration and thermal elastic stability of the SMA fiber reinforced composite circular/annular plates are investigated, and also the internal resonance of the annular plate is examined. The main contents of this thesis are as follows:1 Based on von Karman's theory of thin plates with large deflection, linear free vibration of the circular plates embedded with SMA fibers in the radial direction is studied in both the pre-buckling and post-buckling region. The results show that, after the SMA is activated, the first three frequencies of the circular plate can be adjusted in the inverse martensite transformation temperature domain of SMA. In the clamped boundary condition, the adjustment appears in the pre-buckling region, but in the simply supported boundary condition, it appears in the post-buckling region.2 Thermal elastic stability of the composite circular plates embedded with SMA fibers in radial direction is analyzed. The nonlinear governing equations are solved numerically by adopting a shooting method and the equilibrium paths of thermal post-buckling of the circular plates are obtained. Numerical results show that after activating the SMA fibers, the critical buckling temperature of the immovably clamped circular plates can be enhanced so that the occurrence of thermal buckling can be postponed;the activation of SMA doesn't has a significant effect on the critical temperature of the immovably simply supported circular plates, however, the post-buckling deformation of the circular plates can be controlled effectively in the inverse martensite transformation temperature domain.3 On the basis of the analysis of the thermal post-buckling, the modification of the bending deformation of the circular plate, subjected to mechanical load, are studied in the sense of AISEPT—Active Intergraded Strain Energy and Property Tuning and ASET—Active StrainEnergy Tuning. From the research results it can be found that the coefficient of thermal expansion of Matrix materials has a significant effluence on the control of the bending. By comparing the two control manners, the control effect of the latter is more effective than the former.4 Non-axisymmetrical linear vibration and the internal resonance of the annular plate embedded with SMA fibers in the radial and circumferential directions under C-C and S-S boundary conditions are studied. The results show that the radial embedment of SMA has a strong effect on the vibration with the lower order circumferential modes but a weak effect on that with the higher order ones. However, the circumferential embedment of SMA leads to an opposite phenomenon compared with the radial embedment. Moreover, the embedment of SMA also has a significant effect on the internal resonance of the annular plate. The internal resonance of the annular plate with embedded SMA fibers in the radial direction is more complicated than that of the annular plate with embedded SMA fibers in the circumferential direction. Because of embedment of SMA fibers, internal resonance phenomenon will appear in the S-S plate, but originally, in the isotropic annular plate there will be no any internal resonance.