Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method

This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM) to theoretically calculate its nature frequency and vibration response. First of all, strain dependent mechanical property of hard coating is briefly introduced and polynomial method is adopted to characterize the storage and loss modulus of coating material. Then, the principle formulas of inherent and dynamic response characteristics of the hard coating composite plate are derived. And consequently specific analysis procedure is proposed by combining ANSYS APDL and self-designed MATLAB program. Finally, a composite plate coated with MgO + Al2O3is taken as a study object and both nonlinear vibration test and analysis are conducted on the plate specimen with considering strain dependent mechanical parameters of hard coating. Through comparing the resulting frequency and response results, the practicability and reliability of FEIM have been verified and the corresponding analysis results can provide an important reference for further study on nonlinear vibration mechanism of hard coating composite structure.

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Vibration analysis of hard-coating laminated plate considering strain-dependent characteristic

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/1461348418781867 ◽

2018 ◽

Vol 37 (4) ◽

pp. 789-800 ◽

Cited By ~ 2

Author(s):

Wei Sun ◽

Xiaozhou Liu ◽

Jixiang Jiang

Keyword(s):

Composite Plate ◽

Nonlinear Behavior ◽

Coating Material ◽

Hard Coating ◽

Nonlinear Phenomenon ◽

Laminated Plate ◽

Lagrange’S Equation ◽

Calculation Results ◽

Material Nonlinear ◽

Strain Dependent

An analytical modeling method of hard-coating laminated plate under base excitation was studied considering strain-dependent characteristic of coating material (i.e. a kind of material nonlinear behavior). For convenience, the strain-dependent characteristic of hard-coating material was characterized by polynomial, and the material parameters were divided into two parts: linearity and nonlinearity. Hard coating was regarded as a special layer in the analysis and Lagrange’s equation was used to acquire nonlinear equation of motion of the hard-coating laminated plate. Based on Newton–Raphson method, the procedure of solving resonant response and resonant frequency of composite plate was presented. Finally, a T300/QY89l1 laminated plate with NiCoCrAlY + YSZ hard coating was chosen to demonstrate the proposed method, the linear and nonlinear vibrations of the composite plate were solved, and only the linear results were validated by ANSYS software. The results reveal that there is a big difference between the calculation results considering the nonlinearity of coating material and the linear results, which means the laminated plate displays soft nonlinear phenomenon because of depositing coating.

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Nonlinear vibration analysis of a hard-coating cylindrical shell with elastic constraints by finite element method

Nonlinear Dynamics ◽

10.1007/s11071-017-3849-7 ◽

2017 ◽

Vol 90 (4) ◽

pp. 2879-2891 ◽

Cited By ~ 7

Author(s):

Yue Zhang ◽

Wei Sun ◽

Jian Yang ◽

Qingkai Han

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Cylindrical Shell ◽

Nonlinear Vibration ◽

Vibration Analysis ◽

Hard Coating ◽

Elastic Constraints ◽

Element Method

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Nonlinear Vibration Response Analysis on a Composite Plate Reinforced With Carbon Nanotubes

Volume 3: Design, Materials and Manufacturing, Parts A, B, and C ◽

10.1115/imece2012-85856 ◽

2012 ◽

Author(s):

Xiang-Ying Guo ◽

Wei Zhang ◽

Qian Wang

Keyword(s):

Carbon Nanotubes ◽

Differential Equations ◽

Nonlinear Vibration ◽

Thin Plate ◽

Composite Plate ◽

Laminated Plates ◽

Vibration Response ◽

Response Analysis ◽

Rectangular Thin Plate ◽

Chaotic Motions

In order to compare nonlinear vibration response of the different enabled materials in the matrix of composites, the nonlinear vibrations of a composite plate reinforced with carbon nanotubes (CNT) are studied. In this paper, the carbon nanotubes are supposed to be long fibers. The nonlinear governing partial differential equations of motion for the composite rectangular thin plate are derived by using the Reddy’s third-order shear deformation plate theory, the von Karman type equation and the Hamilton’s principle. Then, the governing equations get reduced to ordinary differential equations in thickness direction with variable coefficients and these are solved by the Galerkin method. The case of 1:1 internal resonance is considered. The asymptotic perturbation method is employed to obtain the four-dimensional averaged equations. The numerical method is used to investigate the periodic and chaotic motions of the composite rectangular thin plate reinforced with carbon nanotubes. The results of numerical simulation demonstrate that there exist different kinds of periodic and chaotic motions of the composite plate under certain conditions. At last, the nonlinear vibration responses of the plate are compared with the same responses of angle-ply composite laminated plates.

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Analytical Modeling of Hard-Coating Cantilever Composite Plate considering the Material Nonlinearity of Hard Coating

Mathematical Problems in Engineering ◽

10.1155/2015/978392 ◽

2015 ◽

Vol 2015 ◽

pp. 1-14 ◽

Cited By ~ 9

Author(s):

Wei Sun ◽

Ying Liu ◽

Guangyu Du

Keyword(s):

Analytical Model ◽

Composite Plate ◽

Analytical Modeling ◽

Variable Stiffness ◽

Vibration Response ◽

Material Nonlinearity ◽

Hard Coating ◽

Resonant Frequencies ◽

Specific Calculation ◽

Coating Composite

Due to the material nonlinearity of hard coating, the coated structure produces the nonlinear dynamical behaviors of variable stiffness and damping, which make the modeling of hard-coating composite structure become a challenging task. In this study, the polynomial was adopted to characterize this material nonlinearity and an analytical modeling method was developed for the hard-coating composite plate. Firstly, to relate the hard-coating material parameters obtained by test and the analytical model, the expression of equivalent strain of composite plate was derived. Then, the analytical model of hard-coating composite plate was created by energy method considering the material nonlinearity of hard coating. Next, using the Newton-Raphson method to solve the vibration response and resonant frequencies of composite plate and a specific calculation procedure was also proposed. Finally, a cantilever plate coated with MgO + Al2O3hard coating was chosen as study case; the vibration response and resonant frequencies of composite plate were calculated using the proposed method. The calculation results were compared with the experiment and general linear calculation, and the correctness of the created model was verified. The study shows the proposed method can still maintain an acceptable precision when the material nonlinearity of hard coating is stronger.

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Identifying the Mechanical Parameters of Hard Coating with Strain Dependent Characteristic by an Inverse Method

Shock and Vibration ◽

10.1155/2015/487457 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 7

Author(s):

Wei Sun ◽

Zhuo Wang ◽

Mingwei Zhu ◽

Guangyu Du

Keyword(s):

Storage Modulus ◽

Loss Factor ◽

Inverse Method ◽

Equivalent Strain ◽

Hard Coating ◽

Mechanical Parameters ◽

Preparation Technology ◽

Coating Composite ◽

Plate Shape ◽

Strain Dependent

The mechanical parameters of hard coating, such as storage modulus and loss factor, are affected by preparation technology significantly and have the strain dependent characteristic. So the effective identification of these mechanical parameters becomes a challenge task. In this study, a hard-coating cantilever thin plate under base excitation was taken as the research object, and an inverse method was developed to identify these mechanical parameters. Firstly, the principles of identifying storage modulus and loss factor of hard coating were presented according to the inverse method. Then, from the need of parameters identification, the analytical model and calculation formula of equivalent strain for the hard-coating composite plate were derived. Next, also for parameter identification, the vibration experiments about the cantilever plate coated with NiCoCrAlY+ yttria-stabilised zirconia (YSZ) hard coating were performed. Finally, the mechanical parameters of NiCoCrAlY+YSZ hard coating with strain dependent characteristic were identified by the proposed method. The identification results show that the change rules of storage modulus and loss factor of hard coating with the strain amplitude are almost consistent with the results listed in the other similar references. However, the identification results herein can more directly serve for the dynamic modeling of hard-coating plate-shape composite structure.

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