Flutter of geometrical imperfect functionally graded carbon nanotubes doubly curved shells

2021 ◽  
Vol 164 ◽  
pp. 107798
Author(s):  
Ali AminYazdi
Keyword(s):  
Carbon Nanotubes ◽  
Functionally Graded ◽  
Doubly Curved Shells ◽  
Functionally Graded Carbon Nanotubes ◽  
Doubly Curved

Thermomechanical nonlinear stability of pressure-loaded functionally graded carbon nanotube-reinforced composite doubly curved panels with tangentially restrained edges

2019 ◽  
Vol 233 (16) ◽  
pp. 5848-5859 ◽  
Author(s):  
Le Thi Nhu Trang ◽  
Hoang Van Tung
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Nonlinear Load ◽  
Reinforced Composite ◽  
Doubly Curved ◽  
Curved Panels

Geometrically nonlinear response of doubly curved panels reinforced by carbon nanotubes exposed to thermal environments and subjected to uniform external pressure are presented in this paper. Carbon nanotubes are reinforced into isotropic matrix through uniform and functionally graded distributions. Material properties of constituents are assumed to be temperature dependent, and effective elastic moduli of carbon nanotube-reinforced composite are determined according to an extended rule of mixture. Basic equations for carbon nanotube-reinforced composite doubly curved panels are established within the framework of first-order shear deformation theory. Analytical solutions are assumed, and Galerkin method is used to derive closed-form expressions of nonlinear load–deflection relation. Separate and combined effects of carbon nanotube distribution and volume fraction, elasticity of in-plane constraint, elevated temperature, initial imperfection, geometrical ratios and stiffness of elastic foundations on the nonlinear stability of nanocomposite doubly curved panels are analyzed through numerical examples.

CHAOTIC VIBRATIONS IN FUNCTIONALLY GRADED DOUBLY CURVED SHELLS WITH INTERNAL RESONANCE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250047 ◽  
Author(s):  
F. ALIJANI ◽  
M. AMABILI
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Maximum Lyapunov Exponent ◽  
Harmonic Load ◽  
Chaotic Vibrations ◽  
Doubly Curved Shells ◽  
Excitation Frequencies ◽  
Doubly Curved

Chaotic vibrations of functionally graded doubly curved shells subjected to concentrated harmonic load are investigated. It is assumed that the shell is simply supported and the edges can move freely in in-plane directions. Donnell's nonlinear shallow shell theory is used and the governing partial differential equations are obtained in terms of shell's transverse displacement and Airy's stress function. By using Galerkin's procedure, the equations of motion are reduced to a set of infinite nonlinear ordinary differential equations with cubic and quadratic nonlinearities. A bifurcation analysis is carried out and the discretized equations are integrated at (i) fixed excitation frequencies and variable excitation amplitudes and (ii) fixed excitation amplitudes and variable excitation frequencies. In particular, Gear's backward differentiation formula (BDF) is used to obtain bifurcation diagrams, Poincaré maps and time histories. Furthermore, maximum Lyapunov exponent and Lyapunov spectrum are obtained to classify the rich dynamics. It is revealed that the shell may exhibit complex behavior including sub-harmonic, quasi-periodic and chaotic response when subjected to large harmonic excitations.

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