Research On Natural Characteristic And Nonlinear Vibration Behavior Of Hard-coating Plate

Thin plate structure is widely implemented in many engineering fields. Nowadays, the coating technology applying on thin plate is interested by many researchers because of its advantages of enhancing the strength or stiffness, especially improving dynamics characteristics of the integrated structure. At present, a novel damping coating technology is attracting more attention, which adopts special ceramic-substrate or metal-substrate coatings possessing high-damping capacity to increase the total damping capacity of thin plate structure; thus improves dynamics characteristic and reduces vibration. For hard-coating thin plate structure possessing high-damping capacity, the study on its dynamics and/or vibrations are becoming emerging research focus. Therefore, it has important theoretic significance and pressing engineering application value to investigate the typical natural characteristic and nonlinear vibration behaviors of hard-coating thin plate.In this dissertation, theoretical investigation, numerical simulation and experimental investigation are presented to analyze the natural characteristic and nonlinear vibration behaviors of hard-coating plate. The exact analytical solutions, numerical solutions and experimental test results of the natural characteristic of hard-coating plate are obtained based on the mechanic principle of multilayered plates, the mechanics of anisotropic materials and the nonlinear vibration theory of plates. Nonlinear vibration behaviors of hard-coating plate are analyzed considering the effects of material nonlinearity and large deflection, to further master the underlying principles of vibrations of hard-coating plate structure. Mainly, the following research contents are carried out in this dissertation:(1) On the base of elastic theory and the vibration theory of plate and shell, an analytical solution method used for composite laminate plate structure with magneto-electro-elastic (MEE) characteristic is studied to solve the hard-coating plate, and it is treated as theoretical base of dynamics analysis of hard-coating plate structure. After building the constitutive equations and governing equations, the state-vector and propagator matrix approach are utilized for solving the natural frequencies and vibration modes of MEE multilayered plate, and then the analytical solutions of natural characteristic of hard-coating plate.(2) The three-dimensional finite element (FE) model of anisotropy hard-coating plate is built by FE theory with magneto-electro effect and hard-coating material anisotropic characteristic. Numerical results of the natural characteristic of hard-coating plate are calculated, the first 8 orders natural frequencies and vibration modes are compared, with magneto-electro effect or not. The results indicate that hard-coating would cause the reduction of each order natural frequency of hard-coating plate considering piezoelectric effect, but the piezomagnetic hard-coating will correspondingly increase them, even cause the exchangement of certain modes (e.g. the 7th and 8th modes). The natural frequency values of hard-coating plate calculated by the FE method are bigger than calculated by the theory of multilayered plate, but in the same tendency.(3) Based on the theory of MEE multilayered plate and transition of material elastic coefficients, the effect of hard-coating parameters on structure natural frequency is analyzed by state-vector and propagator matrix approach. The natural frequencies of piezoelectric (PE) hard-coating plate are compared with bare plate at the same mode shapes, the results indicate that, The decrement ratios are up to 45% for the 1 st and 7th modes, and at least over 25% for the 4th and 8th modes. The hard-coating will change the mode shapes of the higher orders. The natural frequencies of bare plate calculated by analytical method have the same tendency with the results in FE method, but the calculated values are bigger. In contrast, the natural frequencies values of hard-coating plate calculated by analytical method are smaller than FE method.(4) Based on the theory of equivalent nonlinear ealsticity, it is studied on the natural characteristic problem of cantilever hard-coating plate, which made of anisotropic hard-coating material and isotropic metal material, by Galerkin method and small parameter method. First, nonlinear partial differential equations of motion are built considering geometrical linearity and material nonlinear elasticity of composite laminated cantilever plate. Then, these equations are transformed into nonlinear ordinary differential equations by Galerkin method. To solve these nonlinear ordinary differential equations, they are transformed into a series of linear differential equations by small parameter method, and approximate analytic solutions of nonlinear dynamic characteristic of cantilever hard-coating plate are obtained. The calculated natural frequencies by nonlinear analytical method and FE method are extremely close to the experimental test results, but the calculated values by linear analytical method have a comparatively big difference after the 3rd order.(5) The study on nonlinear vibration response of catilever hard-coating plate under transverse loading is proceeded. Based on the theories of von Karman and Reddy three-order shear deformation, the nonlinear dynamic equations of hard-coating plate are built by Hamilton variation principle. To obtain nonlinear governing equation of hard-coating plate under transverse load, these equations are discretized in Galerkin method. The system averaged equations with 1:2 and 1:3 internal resonances are obtained with the method of multiple scales, then nonlinear vibration response behavior of cantilever hard-coating plate under transverse loading could be presented.(6) The comparison test analysis is presented between cantilever bare plate and cantilever hard-coating plate under transverse harmonic base excitation. In several nonresonance intervals, with the increasing of excitation frequencies, the plate response presents alternately period and nonperiod vibration. Compare measured amplitude-frequency response amplitudes of bare plate in the resonance interval with hard-coating plate, the results indicate that the amplitudes of bare plate of the higher orders (from 5th to 8th) are 3-15 times more than hard-coating plate,which manifest the vibration attenuation effect in higher orders.In brief, aims at the demand of damping vibration attenuation, this dissertation presents theoretical analysis, numerical simulation and experimental test of natural characteristic and nonlinear vibration response of hard-coating plate, which adopts hard-coating damping technology. The results indicate the effect of hard-coating parameters on structural natural characteristic, hard-coating material nonlinearity, and the effect of geometric nonlinear characteristic on nonlinear vibration behavior. It establishes definite theoretical basis of mastering the dynamics and vibration mechanism of hard-coating plate, and realizing the rational design and optimization of this kind of new material structure.