scholarly journals Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation

Technologies ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 56
Author(s):  
Rosa Penna ◽  
Luciano Feo
Keyword(s):  
Elastic Foundation ◽  
Volume Fraction ◽  
Nonlinear Ordinary Differential Equation ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Geometric Imperfection ◽  
Winkler Elastic Foundation ◽  
Initial Geometric Imperfection ◽  
Closed Form Analytical Solution ◽  
The Galerkin Method

Nonlinear free vibrations of functionally graded porous Bernoulli–Euler nano-beams resting on an elastic foundation through a stress-driven nonlocal elasticity model are studied taking into account von Kármán type nonlinearity and initial geometric imperfection. By using the Galerkin method, the governing equations are reduced to a nonlinear ordinary differential equation. The closed form analytical solution of the nonlinear natural flexural frequency is then established using the Hamiltonian approach to nonlinear oscillators. Several comparisons with existing models in the literature are performed to validate the accuracy and reliability of the proposed approach. Finally, a numerical investigation is developed in order to analyze the effects of the gradient index coefficient, porosity volume fraction, initial geometric imperfection, and the Winkler elastic foundation coefficient, on the nonlinear flexural vibrations of metal–ceramic FG porous Bernoulli–Euler nano-beams.

scholarly journals Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory

2018 ◽  
Vol 18 (04) ◽  
pp. 1850049 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Pasternak Elastic Foundation

This paper deals with the free vibration and buckling analysis of functionally graded material (FGM) plates, resting on the Winkler–Pasternak elastic foundation. The higher order shear deformation plate theory (HSPT) is adopted for the realistic variation of transverse displacement through the thickness, using the power law distribution to describe the variation of the material properties. Both the effects of shear deformation and rotary inertia are considered. In the present model, the plate is discretised into [Formula: see text] eight noded serendipity quadratic elements with seven nodal degrees of freedom (DOFs). The validation study is carried out by comparing the calculated values with those given in the literature. The effects of various parameters like the Winkler and Pasternak modulus coefficients, volume fraction index, aspect ratio, thickness ratio and different boundary conditions on the behaviour of the FGM plates are studied.

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.

Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates

2017 ◽  
Vol 21 (3) ◽  
pp. 895-916 ◽  
Author(s):  
Sid Ahmed Belalia
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Material ◽  
Large Amplitude ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Nonlinear Frequency ◽  
Graded Material

In this paper, the geometrically nonlinear formulation based on von Karman’s assumptions is employed to study the large amplitude free vibrations of functionally graded materials sandwich plates. The functionally graded material sandwich plate is made up of two layers of power-law functionally graded material face sheet and one layer of ceramic homogeneous core. A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange’s equations. Employing the harmonic balance method, the equations of motion are converted from time domain to frequency domain and then solved iteratively using the linearized updated mode method. Results for linear and nonlinear frequency parameters of the simply supported functionally graded material sandwich plates are computed and compared with the published values, and an excellent agreement was found. The influence of the mechanical properties of the functionally graded material, thickness ratio of FGM layers, and volume fraction exponent on the backbone curves and on the nonlinear frequency parameters are investigated. The effects of the material properties of two different types of ceramics on the large amplitude vibration behaviors of the functionally graded material sandwich plates is also presented and discussed for the first time.

Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

2019 ◽  
Vol 19 (03) ◽  
pp. 1950028 ◽  
Author(s):  
S. J. Singh ◽  
S. P. Harsha
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Load Parameter ◽  
Various Boundary Conditions ◽  
Pasternak Elastic Foundation ◽  
Parametric Studies

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

FREE VIBRATION OF FUNCTIONALLY GRADED ARBITRARY STRAIGHT-SIDED QUADRILATERAL PLATES RESTING ON ELASTIC FOUNDATIONS

2011 ◽  
Vol 03 (04) ◽  
pp. 825-843 ◽  
Author(s):  
A. ALIBEYGI BENI
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Computational Domain ◽  
Fg Plates

The free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates rested on two-parameter elastic foundation and in thermal environment is presented. The formulation is based on the first-order shear deformation theory (FSDT). The material properties are assumed to be temperature-dependent and graded in the thickness direction. The solution procedure is composed of transforming the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. After studying the convergence of the method, its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for isotropic rectangular and FG rectangular and skew plates. Then, the effects of thickness-to-length ratio, elastic foundation parameters, volume fraction index, geometrical shape and the boundary conditions on the frequency parameters of the FG plates are studied.

scholarly journals THERMAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR PLATE RESTING ON THE PASTERNAK ELASTIC FOUNDATION VIA THE DIFFERENTIAL TRANSFORM METHOD

2017 ◽  
Vol 15 (3) ◽  
pp. 545 ◽  
Author(s):  
Fatemeh Farhatnia ◽  
Mahsa Ghanbari-Mobarakeh ◽  
Saeid Rasouli-Jazi ◽  
Soheil Oveissi
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Temperature Rise ◽  
Volume Fraction ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transform Method ◽  
Pasternak Elastic Foundation ◽  
Differential Transform

In this paper, we propose a thermal buckling analysis of a functionally graded (FG) circular plate exhibiting polar orthotropic characteristics and resting on the Pasternak elastic foundation. The plate is assumed to be exposed to two kinds of thermal loads, namely, uniform temperature rise and linear temperature rise through thickness. The FG properties are assumed to vary continuously in the direction of thickness according to the simple power law model in terms of the volume fraction of two constituents. The governing equilibrium equations in buckling are based on the Von-Karman nonlinearity. To obtain the critical buckling temperature, we exploit a semi-numerical technique called differential transform method (DTM). This method provides fast accurate results and has a short computational calculation compared with the Taylor expansion method. Furthermore, some numerical examples are provided to consider the influence of various parameters such as volume fraction index, thickness-to-radius ratio, elastic foundation stiffness, modulus ratio of orthotropic materials and influence of boundary conditions. In order to predict the critical buckling temperature, it is observed that the critical temperature can be easily adjusted by appropriate variation of elastic foundation parameters and gradient index of FG material. Finally, the numerical results are compared with those available in the literature to confirm the accuracy and reliability of the DTM to determine the critical buckling temperature.

Sign in / Sign up

Export Citation Format

Share Document