Smart Materials, Boards, Arch Structure Strong Nonlinear Dynamic Characteristics Research

In this paper, the nonlinear dynamics acts of the smart structure, board structure and the arch structure are systematic studied by using rigorous theoretical analysis and numerical computation. The work are as follows:1 Overview the nonlinear dynamics researches of the smart structure, boardstrcuture and arch structure and review the strong nonlinear vibration theory.2 Set up the piezoelectric isotropic rectangular plate model, derive rectangular plate piezoelectric vibration nonlinear partial differential equations by Hamilton's principle. Use double Fourier series expansion method and Galerkin method to simplify differential equation into rectangular plate piezoelectric-line Vibration of the ordinary differential equation. Ues the initial transform method to solve three hard spring strongly nonlinear equations of Duffing, and the results obtained from the exact solutions, as well as LP, improved LP method were compared.The results showed that the initial transform method has better accuracy than LP and LP method, and has simpler solutions form.3 Establish nonlinear viscoelastic axisymmetric circular plate partial differential equations, use Galerkin method to simplify the differential equation into the second strongly nonlinear ordinary differential equations. Ues the initial transform method to solve second strongly nonlinear ordinary differential equations, and the results obtained from the exact solutions, as well as LP, improved LP method were compared. The results show that compared with the LP, and improved LP method, the initial transform not only has better accuracy, but also has wider application. LP and inproved LP method can onlysolve two types of equations when the initial transform method can solve three types of secondary nonlinear vibration equations4 Set up the weak nonlinear dynamics partial differential equations of arch structure, use Galerkin method to simplify the differential equation into ordinary differential equation both contained quadratic nonlinear item and thrid nonlinear item, derive based harmonic response and combined harmonic response.Mapping and analysis of the elastic arch structure with the phase plane trajectory, the time history, the Poincare map, through Melnikov function to identify the critical chaotic conditions.5 Take two degrees strong nonlinear spring system as an example, established a two degrees strong nonlinear coupled ordinary differential equations, use initial transform method to solve the coupled equation in different parameters of the system. The results obtained from initial transform method and Exact Solution (or numerical solution) were compared, and the results showed that the results obtained from the initial transform method and exact solutions (or numerical solution) good agreement.In summary, initial transform method is not only suitable for solving symmetric strong nonlinear vibration system, but also suitable for solving ansymmetric strong nonlinear vibration system. Using two harmonics can get high accuracy results.The initial transform method is not only suitable for solving one degree nonlinear vibration systems, but also suitable for multi degree strong nonlinear vibration system.The resonance control, nonlinear model analysis, bifurcation and chaotic study of multidegrees system by using initial transform method need to be further discussed.