Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation

2020 ◽  
Vol 252 ◽  
pp. 112672 ◽  
Author(s):  
Bo Zhu ◽  
Qi Xu ◽  
Ming Li ◽  
Yinghui Li
Keyword(s):  
Elastic Foundation ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Nonlinear Elastic Foundation ◽  
Free And Forced Vibrations ◽  
Pipes Conveying Fluid ◽  
Nonlinear Elastic ◽  
Conveying Fluid

Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation

2017 ◽  
Vol 24 (11) ◽  
pp. 2327-2343 ◽  
Author(s):  
Rasool Moradi-Dastjerdi ◽  
Hamed Momeni-Khabisi
Keyword(s):  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Free And Forced Vibrations ◽  
Mesh Free ◽  
Pasternak Elastic Foundation

In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

Nonlinear thermomechanical buckling of sandwich FGM oblique stiffened plates with nonlinear effect of elastic foundation

2020 ◽  
pp. 089270572093595
Author(s):  
Dang Thuy Dong ◽  
Vu Hoai Nam ◽  
Nguyen Thoi Trung ◽  
Nguyen Thi Phuong ◽  
Vu Tho Hung
Keyword(s):  
Elastic Foundation ◽  
Geometrical Nonlinearity ◽  
Shear Deformation Theory ◽  
Equation System ◽  
External Pressure ◽  
Functionally Graded ◽  
Geometrical Properties ◽  
Nonlinear Elastic Foundation ◽  
The Galerkin Method ◽  
Nonlinear Elastic

In this article, the nonlinear thermomechanical buckling behaviors of sandwich functionally graded plates subjected to an axial compression and external pressure are analytically analyzed resting on nonlinear elastic foundation. Assuming that the plates are reinforced by oblique stiffeners and rested on nonlinear elastic foundation. The formulations are established using the higher-order shear deformation theory taking into account the geometrical nonlinearity of von Kármán. The Lekhnitskii’s smeared stiffener technique is developed for shear deformable oblique stiffener system using the coordinate transformation technique with both mechanical and thermal terms. The Galerkin method is utilized to obtain the nonlinear algebraically equation system, then, solve it to determine the explicit expressions of critical buckling loads and postbuckling load–deflection curves. Numerical results show the effects of temperature, nonlinear elastic foundation, stiffeners, and material and geometrical properties on nonlinear behaviors of plates.

Nonlinear Static and Dynamic Buckling Analyses of Imperfect FGP Cylindrical Shells Resting on Nonlinear Elastic Foundation Under Axial Compression

2020 ◽  
Vol 20 (07) ◽  
pp. 2050074
Author(s):  
Kamran Foroutan ◽  
Habib Ahmadi
Keyword(s):  
Elastic Foundation ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Porosity Distribution ◽  
Nonlinear Elastic Foundation ◽  
Special Cases ◽  
Nonlinear Static ◽  
Nonlinear Elastic

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

Large Amplitude Dynamic Analysis of FGM Cylindrical Shells on Nonlinear Elastic Foundation Under Thermomechanical Loads

2017 ◽  
Vol 09 (07) ◽  
pp. 1750105 ◽  
Author(s):  
Abbas Hadi ◽  
Hamid Reza Ovesy ◽  
Saeed Shakhesi ◽  
Jamshid Fazilati
Keyword(s):  
Elastic Foundation ◽  
Shell Thickness ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Governing Equations ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Dynamic Characteristics ◽  
Linear And Nonlinear ◽  
Nonlinear Elastic

Nonlinear dynamic characteristics of functionally graded material (FGM) cylindrical shells surrounded by nonlinear elastic foundation under axial static and lateral dynamic loads in thermal environment are investigated in the current paper. The main emphasis is on the simulation of the elastic foundation model and thermal loads. Nonlinear tri-parametric elastic foundation including linear and nonlinear parameters is used to model the reaction of the elastic foundation on the cylindrical shell. Different thermal loading scenarios are applied to the system to study the effects of thermal environment, including uniform, linear and nonlinear temperature distribution across the shell thickness. Governing equations are derived based on the Donnell’s thin shell theory. Material properties of the FGM are assumed to be variable through the shell thickness according to a power law function. Discretization of the obtained governing equations is performed using the Galerkin’s method. An averaging method and the Runge–Kutta method are applied to obtain the frequency–amplitude relation and time–deflection relation, respectively. Comprehensive numerical results are given for investigating the effects of thermo-mechanical loads, material and geometrical properties and nonlinear elastic foundation parameters on nonlinear dynamic characteristics of the functionally graded cylindrical shells (FGCSs). Present formulations are validated by comparing the results with the published data for some specific cases.

Large amplitude flutter analysis of functionally graded carbon nanotube reinforced composite plates with piezoelectric layers on nonlinear elastic foundation

2017 ◽  
Vol 233 (2) ◽  
pp. 533-544 ◽  
Author(s):  
Ali A Yazdi
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Large Amplitude ◽  
Composite Plates ◽  
Functionally Graded ◽  
Governing Equations ◽  
Nonlinear Elastic Foundation ◽  
Reinforced Composite ◽  
Piezoelectric Layers ◽  
Nonlinear Elastic

This paper presents a study of geometrical nonlinear flutter of functionally graded carbon nanotube-reinforced composite plates embedded with piezoelectric layers subjected to supersonic flow on nonlinear elastic foundation. The governing equations of the system are obtained using the classical plate theory and von Karman geometric nonlinearity. The linear piston theory is utilized to evaluate the aerodynamic pressure. Galerkin method is used to reduce the governing equations to an ordinary differential equation with respect to time in the form of Duffing equation. The homotopy perturbation method is employed to study the effect of large amplitude on the nondimensional flutter pressure. It is assumed that carbon nano-tubes are distributed along thickness in two different manners namely uniform distribution and functionally graded. The effects of volume fraction of carbon nanotubes, large amplitude, different distribution types, piezoelectric layers, and applied voltage on flutter pressure are studied.

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