scholarly journals Investigation on vibration of the functionally graded material–stepped cylindrical shell coupled with annular plate in thermal environment

2021 ◽  
pp. 146134842110393
Author(s):  
Zhengxiong Chen ◽  
Ailun Wang ◽  
Bin Qin ◽  
Qingshan Wang ◽  
Rui Zhong
Keyword(s):  
Cylindrical Shell ◽  
Functionally Graded Material ◽  
Annular Plate ◽  
Thermal Environment ◽  
Current Method ◽  
Displacement Function ◽  
Functionally Graded ◽  
State Response ◽  
Annular Plates ◽  
Graded Material

This article is concerned with thermal vibration behaviors of the functionally graded material–stepped cylindrical shell coupled with annular plate, including free vibration, transient response, and steady state response. The stepped cylindrical shell is divided into N s segments at locations of thickness and radius variations, which is coupled with N p annular plates. The boundary and coupling conditions are achieved by introducing the artificial virtual spring technology. Under the framework of FSDT, the displacement function of arbitrary shell segment and annular plate is expanded with Chebyshev polynomials and Fourier series for circumferential direction. Compared with results obtained by the finite element method and the references, a series of numerical examples and validations are presented to verify the convergence and accuracy of the current method. The effects of the relevant parameters containing the geometric parameters, boundary conditions, various loadings, and the thermal environment are investigated in detail.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

Free Vibration and Elastic Critical Load of Functionally Graded Material Thin Cylindrical Shells Under Internal Pressure

2018 ◽  
Vol 18 (11) ◽  
pp. 1850138 ◽  
Author(s):  
Yueyang Han ◽  
Xiang Zhu ◽  
Tianyun Li ◽  
Yunyan Yu ◽  
Xiaofang Hu
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Internal Pressure ◽  
Critical Load ◽  
Natural Frequency ◽  
Functionally Graded Material ◽  
Present Method ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Graded Material

An analytical approach for predicting the free vibration and elastic critical load of functionally graded material (FGM) thin cylindrical shells filled with internal pressured fluid is presented in this study. The vibration of the FGM cylindrical shell is described by the Flügge shell theory, where the internal static pressure is considered as the prestress term in the shell equations. The motion of the internal fluid is described by the acoustic wave equation. The natural frequencies of the FGM cylindrical shell under different internal pressures are obtained with the wave propagation method. The relationship between the internal pressure and the natural frequency of the cylindrical shell is analyzed. Then the linear extrapolation method is employed to obtain the elastic critical load of the FGM cylindrical shell from the condition that the increasing pressure has resulted in zero natural frequency. The accuracy of the present method is verified by comparison with the published results. The effects of gradient index, boundary conditions and structural parameters on the elastic critical load of the FGM cylindrical shell are discussed. Compared with the experimental and numerical analyses based on the external pressure, the present method is simple and easy to carry out.

scholarly journals Vibration of Functionally Graded Material Plates with Cutouts & Cracks in Thermal Environment

2013 ◽  
Vol 560 ◽  
pp. 157-180 ◽  
Author(s):  
Ahmad Akbari Rahimabadi ◽  
Sundararajan Natarajan ◽  
Stephane Pa Bordas
Keyword(s):  
Functionally Graded Material ◽  
Effective Properties ◽  
Thermal Environment ◽  
Flexural Vibration ◽  
Partition Of Unity ◽  
Functionally Graded ◽  
Discontinuity Surface ◽  
Heaviside Function ◽  
Graded Material ◽  
Plate Geometry

In this paper, the effect of a centrally located cutout (circular and elliptical) and cracksemanating from the cutout on the free flexural vibration behaviour of functionally graded materialplates in thermal environment is studied. The discontinuity surface is represented independent of themesh by exploiting the partition of unity method framework. A Heaviside function is used to capturethe jump in the displacement across the discontinuity surface and asymptotic branch functions areused to capture the singularity around the crack tip. An enriched shear flexible 4-noded quadrilateralelement is used for the spatial discretization. The properties are assumed to vary only in the thicknessdirection. The effective properties of the functionally graded material are estimated using the Mori-Tanaka homogenization scheme and the plate kinematics is based on the first order shear deformationtheory. The influence of the plate geometry, the geometry of the cutout, the crack length, the thermalgradient and the boundary conditions on the free flexural vibration is numerically studied.

Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

2016 ◽  
Vol 28 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Mohammadreza Saviz
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Virtual Work ◽  
Electrical Potential ◽  
Axial Direction ◽  
Functionally Graded ◽  
Radial Coordinate ◽  
Graded Material

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezo-rings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

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