Nonlinear Dynamics Of Composite Laminated Cantilever Plate

Currently,composite laminated plates are being used extensively in aerospace, naval, transportation and civil engineering industries. They have many advantages such as light weight, high strength, and are easy to get different material characters by changing their structures. It is known that the linear theory can not solve the problems with large deflection in aeronautic and astronautic engineering. However, because of the material anisotropy and shear deformation, nonlinear analysis of composite laminated plates becomes more and more complex when the plates deform largely. Therefore, research on dynamical behavior of composite laminated plates considering higher-order transverse shear deformation is not only valuable to academic study but also to the engineering design.The nonlinear dynamics of composite laminated cantilever plates subjected to the in-plane and transversal excitations is investigated in this thesis. Based on the wing flutter on flying aircraft, considering the effects of higher-order transverse shear deformation and geometry deformation, the mathematical model of the composite laminated cantilever plates is presented. The main contents and innovative contributions of this thesis are as follows.(1) According to the Reddy's high-order shear deformation theory and the model of von Karman type equations for the geometric nonlinearity, the nonlinear governing partial differential equations of motion for composite laminated cantilever plate subjected to the in-plane and transverse excitations are derived by using the Hamilton's principle.(2) The Galerkin approach is utilized to transform the nonlinear partial differential governing equations of motion for composite laminated cantilever plate subjected to the in-plane and transverse excitations into a two-degree-of-freedom nonlinear system.(3) The method of multiple scales is employed to obtain the four-dimensional averaged equations of the composite laminated cantilever plate subjected to the in-plane and transverse excitations. The case of principal parametric resonance, 1/2 subharmonic resonance and 1:2 internal resonance is taken into account. The results of numerical simulation demonstrate that there exist the periodic, multi-periodic, quasi-periodic and chaotic motions of the system. The influence of the in-plane and transverse excitations on the nonlinear dynamics behaviors of the system is investigated.(4) Using the method of multiple scales, four-dimensional averaged equations of the system are derived under the case of principal parametric resonance, 1:3 internal resonance. The three-dimensional phase portraits, two-dimensional phase, oscillograms, and frequency spectrum graphs are obtained by numerical method. Moreover, the numerical simulation illustrates the existence of periodic and chaotic motions for the laminated cantilever plate with the changes of amplitude of forcing loads. The results indicate that the amplitude of the in-plane and transverse excitations is the primary controlling parameters of motion for the composite laminated cantilever plate.