Study On Dynamics Of The Composite And Piezoelectric Material Laminated Plates And Shells

Based upon the Hamilton systematic methodology, the Hellinger-Reissner (H-R) mixed variational principle for general elastic materials was introduced into analyzing the dynamic problems of general composite structures with viscous damping force, piezoelectric and thermoelastic structures. The application area of the Hamilton canonical equation theory was extended. The main work could be outlined as follows:1. A modified mixed variational principle for general composite materials with viscous damping force was established and the corresponding state-vector equation was reduced. Combining the precise integration method and Muller method, a new solution for the harmonic vibration of simply supported open cylindrical laminates was proposed. The general solutions for the free vibration of underdamping, critical damping, overdamping of cylindrical laminates was simply given in terms of the linear damp vibration theory. The effect of viscous damp on the vibration of open cylindrical laminates was investigated.2. A numerical method for the inversion of Laplace transform was developed and its accuracy was shown through a lot of examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates was deduced from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate was given. For multilayered hybrid plates, the solution in terms of the propagator matrices was derived. The techniques not only accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, but also the rotary inertia of laminate and the transverse shear deformation are considered in the general equation of structure. As an application of the numerical inversion of Laplace transform presented in this paper, the problems of harmonic vibration and transient response were proposed and discussed, and we obtained the highly accurate numerical results.3. According to the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then, the numerical responses of the laminated piezothermoelastic plates and shells under thermal and dynamic load were studied; the effects of temperature and viscous damp on the vibration of laminated plate were also investigated when we studied the response problems of the thermoelastic composite laminated plates.