Nonlinear Dynamics Of Honeycomb Sandwich Plate

Honeycomb sandwich plate has many advantages such as low density, high strength ratio and high stiffness ratio. It is easy to obtain different mechanical characters by changing the structures of the honeycomb sandwich plate. Therefore, honeycomb sandwich plate is now widely used in aeronautic and astronautic engineering. It is known that the linear theory can't solve the problems with large deflection in aeronautic and astronautic engineering. For honeycomb sandwich plate, the transverse shear deformation can not be ignored and has important influence on their dynamic behaviors. Therefore, research on the nonlinear dynamics of honeycomb sandwich plate is significant in theory and application when considering higher-order transverse shear deformation.The nonlinear dynamics and chaotic motion of a simply-supported rectangular honeycomb sandwich plate are studied in this thesis. The main contents and contributions of this thesis are as follows.(1) Based on the Reddy's third-order shear deformation theory and the von Karman type equations, the governing equations of motion are established for the honeycomb sandwich plate subjected to the in-plane and transversal excitations by using the Hamilton's principle. The higher-order transverse shear deformation and damping are considered. The equivalent stiffness of the honeycomb core is calculated by using modified Gibson equation.(2) The Galerkin's approach is utilized to transform the nonlinear partial differential governing equations of motion for the honeycomb sandwich plate to a one-degree -of-freedom nonlinear system. Numerical simulation is used directly to investigate the nonlinear responses of the honeycomb sandwich plate. The results of numerical simulation demonstrate that there exist the periodic, multi-periodic, quasi-periodic and chaotic motions of the honeycomb sandwich plate. It is found that the motion of the system is period-1 or period-2 motions when parametric and external excitations are small. With the in-plane and transverse excitations increasing, the responses of the system change to the multi-periodic, quasi-periodic and chaotic motions.(3) The nonlinear partial differential governing equations of motion for the honeycomb sandwich plate are transformed to two-degree-of-freedom nonlinear systems by using Galerkin's approach when we choose two different mode functions. Numerical simulation is utilized to investigate the nonlinear responses of the two-degree-of-freedom nonlinear systems. The results of numerical simulation illustrate that there exist the periodic, multi-periodic, quasi-periodic and chaotic motions of the honeycomb sandwich plate.Comparing with single-degree-of-freedom nonlinear system, the two-degree-of- freedom nonlinear system has more complex nonlinear dynamics such as multi-periodic, quasi-periodic and chaotic motions when the smaller excitation is loaded in the honeycomb sandwich plate. It is indicated that the coupling of the first-order and the second-order modes has significant influence on the nonlinear responses of the honeycomb sandwich plate.(4) The method of multiple scales is employed to obtain the four-dimensional averaged equations of the honeycomb sandwich plate. The case of principal parametric resonance, 1/2 subharmonic resonance and 1:1 internal resonance is considered. Numerical simulation is used to analyze the nonlinear dynamics of the honeycomb sandwich plate based on the obtained averaged equations.We compare the results of numerical simulation obtained for the two-degree- of-freedom system without perturbation analysis with those obtained for the corresponding averaged equations. It is concluded that when the complex nonlinear dynamic phenomena, such as multi-periodic, quasi-periodic and chaotic motions, are analyzed, the magnitude of parametric excitation in the averaged equations is smaller than one in the two-degree-of-freedom nonlinear system.