scholarly journals Dynamic Stability of Bi-Directional Functionally Graded Porous Cylindrical Shells Embedded in an Elastic Foundation

2020 ◽  
Vol 10 (4) ◽  
pp. 1345 ◽  
Author(s):  
Farshid Allahkarami ◽  
Hasan Tohidi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Elastic Foundation ◽  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Practical Applications ◽  
Energy Devices ◽  
Various Boundary Conditions

This paper investigates the dynamic buckling of bi-directional (BD) functionally graded (FG) porous cylindrical shells for various boundary conditions, where the FG material is modeled by means of power law functions with even and uneven porosity distributions of ceramic and metal phases. The third-order shear deformation theory (TSDT) is adopted to derive the governing equations of the problem via the Hamilton’s principle. The generalized differential quadrature (GDQ) method is applied together with the Bolotin scheme as numerical strategy to solve the problem, and to draw the dynamic instability region (DIR) of the structure. A large parametric study examines the effect of different boundary conditions at the extremities of the cylindrical shell, as well as the sensitivity of the dynamic stability to different thickness-to-radius ratios, length-to-radius ratios, transverse and longitudinal power indexes, porosity volume fractions, and elastic foundation constants. Based on results, the dynamic stability of BD-FG cylindrical shells can be controlled efficiently by selecting appropriate power indexes along the desired directions. Furthermore, the DIR is highly sensitive to the porosity distribution and to the extent of transverse and longitudinal power indexes. The numerical results could be of great interest for many practical applications, as civil, mechanical or aerospace engineering, as well as for energy devices or biomedical systems.

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.

Dynamic Stability of Rotating FG-CNTRC Cylindrical Shells under Combined Static and Periodic Axial Loads

2018 ◽  
Vol 18 (12) ◽  
pp. 1850151 ◽  
Author(s):  
Yasin Heydarpour ◽  
Parviz Malekzadeh
Keyword(s):  
Dynamic Stability ◽  
Volume Fraction ◽  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Mechanical Stresses ◽  
Functionally Graded ◽  
Coriolis Acceleration ◽  
Axial Forces ◽  
Instability Regions

The dynamic stability behavior of rotating functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells under combined static and periodic axial forces is investigated. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells. The initial mechanical stresses due to the steady state rotation of the shell are evaluated by solving the dynamic equilibrium equations. The equations of motion under different boundary conditions are discretized in the spatial domain and transformed into a system of Mathieu–Hill type equations using the differential quadrature method (DQM) together with the trigonometric series. The influences of both the initial mechanical stresses and Coriolis acceleration are considered. Then, the parametric resonance is analyzed and the dynamic instability regions are determined by employing the Bolotin’s first approximation. After validating the approach, the effects of rotational speed, Coriolis acceleration, carbon nanotubes (CNTs) distribution in the thickness direction, CNTs volume fraction, length and thickness-to-mean radius ratios on the principal dynamic instability regions are examined in detail.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

Supersonic Aeroelasticity and Dynamic Instability of Functionally Graded Porous Cylindrical Shells Using a Unified Solution Formulation

2020 ◽  
Vol 20 (12) ◽  
pp. 2050132
Author(s):  
Mohammad Rahmanian ◽  
Masoud Javadi
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Dynamic Instability ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Computational Effort ◽  
Functionally Graded ◽  
Clear Understanding ◽  
Stability Margins ◽  
Graded Material

This study provides an overview on the effect of porosity on free vibrations and more importantly aeroelastic stability margins of cylindrical shells. A general formulation for cylindrical shells is first developed including the effects of shear deformation and rotary inertia along with Sander’s rigid body rotation modification. Two porosity distributions of even and uneven are considered for functionally graded shells. The most general form of power-law model which is known as four-parameter power-law is utilized to provide a clear understanding for the qualification of functionally graded material. A Ritz-based solution algorithm being capable of representing all combinations of symmetric and asymmetric boundary conditions by a penalty method is also introduced. In addition to the capability of satisfying all boundary conditions, the presented solution method is very fast in terms of convergence and computational effort. Various parametric studies are provided and practical results are reported.

On Free Vibration of Functionally Graded Mindlin Plate and Effect of In-Plane Displacements

2013 ◽  
Vol 29 (2) ◽  
pp. 373-384 ◽  
Author(s):  
A. Hasani Baferani ◽  
A.R. Saidi ◽  
H. Ehteshami
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Aspect Ratios

AbstractIn this paper, free vibration analysis of functionally graded rectangular plate is investigated based on the first order shear deformation theory and the effect of in-plane displacements on the natural frequencies of such plate is studied. The governing equations of motion are obtained, which are five coupled partial differential equations, without any simplification. Some mathematical manipulation leads us to decouple the equations. The decoupled equations are solved by the Levy's method for various boundary conditions. As the results show, in some boundary conditions the in-plane displacements cause a drastic change of frequencies. In other words, neglecting the in-plane displacement, which is assumed in some papers, is not proper for these boundary conditions. However, in the other boundary conditions, the natural frequencies are not significantly affected by the in-plane displacements. The results for various boundary conditions are discussed in detail and some interpretations for these differences are provided. Besides to the comparisons, the accurate natural frequencies of the plate for six different boundary conditions with several aspect ratios, thickness-length ratios and power law indices are presented. The natural frequencies of Mindlin functionally graded rectangular plates with considering the in-plane displacements are reported for the first time and can be used as benchmark.

Influence of Symmetrical Boundary Conditions on Free Vibration of Functionally Graded Cylindrical Shells With Ring Support

2009 ◽  
Author(s):  
M. R. Isvandzibaei ◽  
M. M. Najafizadeh ◽  
P. Khazaeinejad
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Third Order ◽  
Graded Materials ◽  
Ring Support

In the present work, the free vibration of thin cylindrical shells with ring support made of functionally graded materials under various symmetrical boundary conditions is presented. Temperature and position dependent material properties are varied linearly through the thickness of the shell. The functionally graded cylindrical shell has ring support which is arbitrarily placed along the shell and imposed a zero lateral deflection. The third order shear deformation theory is employed to formulate the problem. The governing equations of motion are derived using the Hamilton’s principle. Results are presented on the frequency characteristics and influence of the boundary conditions and the locations of the ring support on the natural frequencies. The present analysis is validated by comparing the results with those available in the literature.

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