Thermal post-buckling and the stability boundaries of structurally damped functionally graded panels in supersonic airflows

2010 ◽  
Vol 92 (2) ◽  
pp. 422-429 ◽  
Author(s):  
Sang-Lae Lee ◽  
Ji-Hwan Kim
Keyword(s):  
Functionally Graded ◽  
Stability Boundaries ◽  
Post Buckling ◽  
The Stability

scholarly journals Nonlinear post-buckling of thin FGM annular spherical shells under mechanical loads and resting on elastic foundations

2014 ◽  
Vol 36 (4) ◽  
pp. 291-306 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Vu Thi Thuy Anh ◽  
Dao Huy Bich
Keyword(s):  
Mechanical Load ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Spherical Shells ◽  
Nonlinear Buckling ◽  
Geometrical Properties ◽  
Elastic Foundations ◽  
Approximate Analytical Solutions ◽  
Post Buckling ◽  
The Stability

This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for annular spherical shells are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form of load-deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the annular spherical shells.

scholarly journals Geometrical Influence on Stability of FGM Beams under Vibration

2020 ◽  
Vol 9 (4) ◽  
pp. 2027-2033
Keyword(s):  
Power Law ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Finite Element Analyses ◽  
Power Law Distribution ◽  
Rotating Beam ◽  
Stability Boundaries ◽  
Exponential Law ◽  
Graded Material ◽  
The Stability

In this paper the influence of geometry on the stability of a functionally graded material rotating beam is reported. The equation of motion is formulated using Hamilton’s principle in association with finite element analyses. Floquet’s theory was used for establishing the stability boundaries. The properties of functionally graded ordinary (FGO) and functionally graded sandwich (FGSW) beams under consideration are assumed to be graded following either power law or exponential law across the thickness of the beam. The effect of geometry in terms of slenderness parameter on the dynamic stability of both FGO & FGSW beams have been investigated. The increase in slenderness parameter enhances the stability of both the FGO and FGSW beams. Further it has been observed that exponential distribution of properties ensures better stability compared to power law distribution of properties.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

Electro-thermo-mechanical post-buckling of piezoelectric functionally graded cylindrical shells

2021 ◽  
Author(s):  
Shengbo Zhu ◽  
Zhenzhen Tong ◽  
Jiabin Sun ◽  
Qingdong Li ◽  
Zhenhuan Zhou ◽  
...  
Keyword(s):  
Cylindrical Shells ◽  
Functionally Graded ◽  
Post Buckling

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

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