Thermoacoustic response of porous FGM cylindrical shell surround by elastic foundation subjected to nonlinear thermal loading

2020 ◽  
Vol 156 ◽  
pp. 106996 ◽  
Author(s):  
Tao Fu ◽  
Xing Wu ◽  
Zhengming Xiao ◽  
Zhaobo Chen
Keyword(s):  
Cylindrical Shell ◽  
Elastic Foundation ◽  
Thermal Loading

Dynamic thermo-elastic response of a discrete multi-layered cylindrical shell subjected to transient thermal loading

2008 ◽  
Vol 222 (4) ◽  
pp. 549-561 ◽  
Author(s):  
J Y Zheng ◽  
X D Wu ◽  
Y J Chen ◽  
G D Deng ◽  
Q M Li ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Elastic Response ◽  
Elastic Part ◽  
Dynamic Part ◽  
Layered Cylindrical Shell ◽  
Stress Boundary Conditions ◽  
Transient Thermal ◽  
Stress Boundary

Explosion containment vessels (ECVs) are used to fully contain the effects of explosion events. A discrete multi-layered cylindrical shell (DMC) consisting of a thin inner cylindrical shell and helically cross-winding flat steel ribbons has been proposed, which has obvious advantages of fabrication convenience and low costs. The applications of ECVs are closely associated with blast and thermal loads, and thus, it is important to understand the response of a DMC under transient thermal load in order to develop a design code and operation procedures for the use of DMC as ECV. In this paper, a mathematical model for the elastic response of a DMC subjected to thermal loading due to rapid heating is proposed. Based on the axisymmetric plane strain assumption, the displacement solution of the dynamic equilibrium equations of both inner shell and outer ribbon layer are decomposed into two parts, i.e. a thermo-elastic part satisfying inhomogeneous stress boundary conditions and a dynamic part for homogeneous stress boundary conditions. The thermo-elastic part is solved by a linear method and the dynamic part is determined by means of finite Hankel transform and Laplace transform. The thermo-elastic solution of a DMC is compared with the solution of a monobloc cylindrical shell, and numerical results are presented and discussed in terms of winding angle and material parameters.

Nonlinear stability of sandwich beams with carbon nanotube reinforced faces on elastic foundation under thermal loading

2018 ◽  
Vol 233 (5) ◽  
pp. 1701-1712 ◽  
Author(s):  
Yaser Kiani ◽  
Mostafa Mirzaei
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Material Properties ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Ritz Method ◽  
Numerical Results ◽  
Equilibrium Path ◽  
Sandwich Beams ◽  
Post Buckling

In this research, post-buckling response of sandwich beams with carbon nanotube reinforced face sheets subjected to uniform temperature rise loading and resting on a two-parameter elastic foundation is investigated. A single-layer theory formulation based on the first-order shear deformation beam theory is used. Material properties of the media are obtained according to a refined rule of mixtures approach which contains efficiency parameters. Suitable for the large deformations, von-Kármán strains are taken into consideration. The elastic foundation is modelled as the Pasternak model which takes into account the shear interaction of the springs. Material properties of the face sheets are considered to be position and temperature dependent. The governing equations of the system are obtained using the Ritz method for various combinations of clamped, simply supported and sliding supported edges. Post-buckling equilibrium path of the beam is obtained according to an iterative displacement control strategy. Numerical results of the present study are compared with the available data in the open literature. Then, the numerical results are provided to explore the effect of side-to-thickness ratio, volume fraction of carbon nanotube, distribution pattern of carbon nanotube, the ratio of face thickness-to-host thickness, boundary conditions and elastic foundation.

Effect of Porosity on Flexural Vibration of CNT-Reinforced Cylindrical Shells in Thermal Environment Using GDQM

2018 ◽  
Vol 18 (10) ◽  
pp. 1850123 ◽  
Author(s):  
Hamed Safarpour ◽  
Kianoosh Mohammadi ◽  
Majid Ghadiri ◽  
Mohammad M. Barooti
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
Flexural Vibration ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Equivalent Material

This article investigates the flexural vibration of temperature-dependent and carbon nanotube-reinforced (CNTR) cylindrical shells made of functionally graded (FG) porous materials under various kinds of thermal loadings. The equivalent material properties of the cylindrical shell of concern are estimated using the rule of mixture. Both the cases of uniform distribution (UD) and FG distribution patterns of reinforcements are considered. Thermo-mechanical properties of the cylindrical shell are supposed to vary through the thickness and are estimated using the modified power-law rule, by which the porosities with even and uneven types are approximated. As the porosities occur inside the FG materials during the manufacturing process, it is necessary to consider their impact on the vibration behavior of shells. The present study is featured by consideration of different types of porosities in various CNT reinforcements under various boundary conditions in a single model. The governing equations and boundary conditions are developed using Hamilton's principle and solved by the generalized differential quadrature method. The accuracy of the present results is verified by comparison with existing ones and those by Navier's method. The results show that the length to radius ratio and temperature, as well as CNT reinforcement, porosity, thermal loading, and boundary conditions, play an important role on the natural frequency of the cylindrical shell of concern in thermal environment.

Vibration of a Temperature-Dependent Thermally Pre/Postbuckled FGM Beam Over a Nonlinear Hardening Elastic Foundation

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
S. E. Esfahani ◽  
Y. Kiani ◽  
M. Komijani ◽  
M. R. Eslami
Keyword(s):  
Elastic Foundation ◽  
Small Amplitude ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Material ◽  
Fgm Beam ◽  
Generalized Differential ◽  
Nonlinear Hardening ◽  
Raphson Method

Small amplitude vibrations of a functionally graded material beam under in-plane thermal loading in the prebuckling and postbuckling regimes is studied in this paper. The material properties of the FGM media are considered as function of both position and temperature. A three parameters elastic foundation including the linear and nonlinear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The solution is sought in two regimes. The first one, a static phase with large amplitude response, and the second one, a dynamic regime near the static one with small amplitude. In both regimes, nonlinear governing equations are discretized using the generalized differential quadrature (GDQ) method and solved iteratively via the Newton–Raphson method. It is concluded that depending on the type of boundary condition and loading type, free vibration of a beam under in-plane thermal loading may reach zero at a certain temperature which indicates the existence of bifurcation type of instability.

scholarly journals Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 2: Numerical results and discussion

2017 ◽  
Vol 39 (4) ◽  
pp. 329-338
Author(s):  
Dang Thuy Dong ◽  
Dao Van Dung
Keyword(s):  
Elastic Foundation ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Shallow Shells ◽  
Nonlinear Dynamic Equations ◽  
Graded Material ◽  
Doubly Curved

In part 1, the governing nonlinear dynamic equations of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners on elastic foundation subjected to mechanical and thermal loading are established based on the first order shear deformation theory (FSDT) with von Kármán - type nonlinearity and smeared stiffener technique. In the present part, the fourth-order Runge-Kutta method is applied to investigate influences of models of the shells, FGM stiffeners, thermal environment, elastic foundation, and geometrical parameters on the natural frequencies and dynamic nonlinear responses of stiffened FGM sandwich doubly curved shallow shells.

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.

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