Nonlinear Thermal Flutter Analysis of Supersonic Composite Laminated Panels Using Differential Quadrature Method

2014 ◽  
Vol 14 (07) ◽  
pp. 1450030 ◽  
Author(s):  
Yaobin Niu ◽  
Zhongwei Wang ◽  
Weihua Zhang
Keyword(s):  
Temperature Distribution ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Composite Panel ◽  
Frequency Interval ◽  
Composite Panels ◽  
Quadrature Method ◽  
Average Temperature ◽  
Aspect Ratios ◽  
Temperature Load

In this paper, the differential quadrature method (DQM) was extended to deal with the nonlinear thermal flutter problem of supersonic composite laminated panel. Based on Hamilton's principle, the nonlinear thermal flutter model of composite panels was first established. The model adopted the von Karman large deflection plate theory for the geometrical nonlinearity, and the third order piston theory for the supersonic aerodynamic loads. Convergence and accuracy studies were carried out to verify the proposed approach. Finally, the nonlinear thermal flutter characteristics of a supersonic composite panel were studied. Uniform temperatures were first applied to the model in order to determine general heating effects on the stability of the composite panel. Owing to the varying structural stiffness of composite panels when subjected to thermal stresses, the thermal load reduced the frequency of composite panel, as well as the frequency interval between the first frequency and the second frequency; thereby hastening the flutter of composite panel. The nonlinear thermal flutter velocity ratio was decreased with respect to increasing temperature load for all aspect ratios. However, the influence of thermal loadings on flutter with various cross angles was different. Cases of unequal temperatures were considered. The average temperature load was kept constant which differs from the temperature gradient form of loading. The results show that the nonlinear thermal frequencies are affected in the presence of different temperature distributions. The changes in the temperature distribution have a slightly greater effect than changes in the average temperature. These effects due to temperature distribution changes do not have a substantial effect on the flutter dynamic pressure.

scholarly journals Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method

2012 ◽  
Vol 227 (4) ◽  
pp. 862-879 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Reza Kolahchi ◽  
Ali Akbar Mosallaie Barzoki ◽  
Mohammad Reza Mozdianfard ◽  
S Mosatafa Noudeh Farahani
Keyword(s):  
Aspect Ratio ◽  
Graphene Sheet ◽  
Temperature Difference ◽  
Frequency Ratio ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Graphene Sheets ◽  
Nonlinear Frequency ◽  
Quadrature Method ◽  
Aspect Ratios

In this article, transverse nonlinear vibration of orthotropic double-layered graphene sheets embedded in an elastic medium (spring and shear constants of the Winkler and Pasternak models) under thermal gradient is studied using nonlocal elasticity orthotropic plate theory. The equations of motion are derived based on application of Hamilton’s principles. These are coupled, two-dimensional and time-dependent equations, which cannot be solved analytically due to their nonlinear terms. Hence, differential quadrature method is employed to solve the governing differential equations for the two boundary conditions of simply and clamped support in all four sides. The plots for the ratio of nonlinear to linear frequencies versus maximum transverse amplitude for armchair and zigzag graphene sheet structures are presented to investigate the effects of nonlocal parameters, Winkler and Pasternak effects, temperature, and various aspect ratios. The study also indicates that the nonlinear effect represented by nonlinear frequency ratio is considerable at lower Winkler and Pasternak constants, length aspect ratio and thickness aspect ratio while it might be neglected for higher values of these parameters. Regarding the influence of temperature difference on support type, with increased temperature difference, nonlinear frequency ratio increases when the graphene sheet is simply supported, but for clamped one, no specific change in nonlinear frequency ratio is observed.

Dynamic stability of viscoelastic plates under axial flow by differential quadrature method

2017 ◽  
Vol 34 (4) ◽  
pp. 1240-1256 ◽  
Author(s):  
Mouafo Teifouet Armand Robinson ◽  
Sarp Adali
Keyword(s):  
Dynamic Stability ◽  
Differential Quadrature Method ◽  
Axial Flow ◽  
Single Mode ◽  
Viscoelastic Plate ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Content Type ◽  
Flutter Instability ◽  
Aspect Ratios

Purpose Cantilever plates subject to axial flow can lose stability by flutter and properties such as viscoelasticity and laminar friction affect dynamic stability. The purpose of the present study is to investigate the dynamic stability of viscoelastic cantilever plates subject to axial flow by using the differential quadrature method. Design/methodology/approach Equation of motion of the viscoelastic plate is derived by implementing Kelvin-Voigt model of viscoelasticity and applying inverse Laplace transformation. The differential quadrature method is employed to discretize the equation of motion and the boundary conditions leading to a generalized eigenvalue problem. The solution is verified using the existing results in the literature and numerical results are given for critical flow velocities Findings It is observed that higher aspect ratios lead to imaginary part of third frequency becoming negative and causing single-mode flutter instability. It was found that flutter instability does not occur at low aspect ratios. Moreover the friction coefficient is found to affect the magnitude of critical flow velocity, however, its effect on the stability behaviour is minor. Originality/value The effects of various problem parameters on the dynamic stability of a viscoelastic plate subject to axial flow were established. It was shown that laminar friction coefficient of the flowing fluid increases the critical fluid velocity and higher aspect ratios lead to single-mode flutter instability. The effect of increasing damping of viscoelastic material on the flutter instability was quantified and it was found that increasing viscoelasticity can lead to divergence instability.

Stability Analysis of Moving Printing Web With Sine Half-Wave Variable Density Based on Differential Quadrature Method

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Jimei Wu ◽  
Mingyue Shao ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Fan Zhao
Keyword(s):  
Flexible Electronics ◽  
Transverse Vibration ◽  
Differential Quadrature Method ◽  
Variable Density ◽  
Differential Quadrature ◽  
Printing Press ◽  
Quadrature Method ◽  
Half Wave ◽  
The Impact ◽  
Density Coefficient

The moving web is widely used to make printing and packaging products, flexible electronics, cloths, etc. The impact of the variable density on printing web dynamic behavior is considered. The density changes in the form of sine half-wave in the lateral direction. Based on the D'Alembert's principle, the transverse vibration differential equation of moving printing web with variable density is established and is discretized by using the differential quadrature method (DQM). The complex characteristic equation is derived. The impacts of the density coefficient and the dimensionless speed on the web stability and vibration characteristics are discussed. The results show that it is feasible to use the DQM to analyze the problem of transverse vibration of printing web with varying density; the tension ratio and the density coefficient have important impacts on the stability of moving printing web. This study provides theoretical guidance and basis for optimizing the structure of printing press and improving the stable working speed of printing press and web.

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