Modal interaction activations and nonlinear dynamic response of shallow arch with both ends vertically elastically constrained for two-to-one internal resonance

2014 ◽  
Vol 333 (21) ◽  
pp. 5511-5524 ◽  
Author(s):  
Zhuangpeng Yi ◽  
Lianhua Wang ◽  
Houjun Kang ◽  
Guangya Tu
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Modal Interaction ◽  
Shallow Arch ◽  
Nonlinear Dynamic Response

scholarly journals Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Y. X. Hao ◽  
W. Zhang ◽  
X. L. Ji
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Internal Resonances ◽  
Third Order ◽  
Nonlinear Dynamic Response

The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle. Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm. The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.

Nonlinear Dynamic Response and Buckling of Damaged Composite Pipes Under Radial Impact

2006 ◽  
Author(s):  
Wenyong Tang ◽  
Tianlin Wang ◽  
Shengkun Zhang
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Nonlinear Dynamic ◽  
Shear Deformation Theory ◽  
Nonlinear Dynamic Response ◽  
Nonlinear Dynamic Equations ◽  
Geometric Deformation ◽  
Initial Geometric Imperfections ◽  
Set Up ◽  
Composite Pipes

In this paper, the nonlinear dynamic response and buckling of damaged composite pipes under radial impact is investigated. A model involving initial geometric deformation, delamination and sub-layer matrix damage is set up for theoretical analysis. Based on the first order shear deformation theory, the nonlinear dynamic equations of the composite pipe considering transverse shear deformation and initial geometric imperfections are obtained by Hamilton’s theory and solved by a semi-analytical finite difference method. The effects of damage on the dynamic response and buckling of composite pipes are discussed.

Nonlinear dynamic response and vibration of imperfect eccentrically stiffened sandwich third-order shear deformable FGM cylindrical panels in thermal environments

2017 ◽  
Vol 21 (8) ◽  
pp. 2816-2845 ◽  
Author(s):  
Nguyen D Duc ◽  
Ngo Duc Tuan ◽  
Phuong Tran ◽  
Tran Q Quan ◽  
Nguyen Van Thanh
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Geometrical Nonlinearity ◽  
Cylindrical Panel ◽  
Geometrical Parameters ◽  
Third Order ◽  
Nonlinear Dynamic Response ◽  
Elastic Foundations ◽  
Thermal Environments ◽  
Cylindrical Panels

This study follows an analytical approach to investigate the nonlinear dynamic response and vibration of eccentrically stiffened sandwich functionally graded material (FGM) cylindrical panels with metal–ceramic layers on elastic foundations in thermal environments. It is assumed that the FGM cylindrical panel is reinforced by the eccentrically longitudinal and transversal stiffeners and subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution. Based on the Reddy’s third-order shear deformation shell theory, the motion and compatibility equations are derived taking into account geometrical nonlinearity and Pasternak-type elastic foundations. The outstanding feature of this study is that both FGM cylindrical panel and stiffeners are assumed to be deformed in the presence of temperature. Explicit relation of deflection–time curves and frequencies of FGM cylindrical panel are determined by applying stress function, Galerkin method and fourth-order Runge-Kutta method. The influences of material and geometrical parameters, elastic foundations and stiffeners on the nonlinear dynamic and vibration of the sandwich FGM panels are discussed in detail. The obtained results are validated by comparing with other results in the literature.

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