Size-dependent vibration and stability of multi-span viscoelastic functionally graded material nanopipes conveying fluid using a hybrid method

2017 ◽  
Vol 179 ◽  
pp. 590-600 ◽  
Author(s):  
Jiaquan Deng ◽  
Yongshou Liu ◽  
Zijun Zhang ◽  
Wei Liu
Keyword(s):  
Functionally Graded Material ◽  
Hybrid Method ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material ◽  
Conveying Fluid

Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
S. P. Pavlov ◽  
M. V. Zhigalov ◽  
V. A. Krysko
Keyword(s):  
Differential Equations ◽  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Stability Loss ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Timoshenko Beams ◽  
Size Dependent ◽  
Rigid Layer ◽  
Graded Material

The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state.

Stability of clamped-clamped periodic functionally graded material shells conveying fluid

2014 ◽  
Vol 21 (15) ◽  
pp. 3034-3046 ◽  
Author(s):  
Huijie Shen ◽  
Jihong Wen ◽  
Dianlong Yu ◽  
Xisen Wen
Keyword(s):  
Functionally Graded Material ◽  
Functionally Graded ◽  
Graded Material ◽  
Conveying Fluid

Dynamic behaviors of multi-span viscoelastic functionally graded material pipe conveying fluid

2016 ◽  
Vol 231 (17) ◽  
pp. 3181-3192 ◽  
Author(s):  
Jiaquan Deng ◽  
Yongshou Liu ◽  
Zijun Zhang ◽  
Wei Liu
Keyword(s):  
Functionally Graded Material ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Functionally Graded ◽  
Piping System ◽  
Pipe Conveying Fluid ◽  
Dynamic Behaviors ◽  
Graded Material ◽  
The Stability ◽  
Conveying Fluid

In this paper, the dynamic behaviors of a multi-span viscoelastic functionally graded material pipe conveying fluid are investigated by dynamic stiffness method. The material properties of the functionally graded material pipe are considered as graded distribution along the thickness direction according to a power-law. Several numerical examples are performed to study the effects of volume fraction exponent, fluid velocity, internal pressure, and internal damping on the stability and frequency response of the fluid-conveying functionally graded material pipe. It’s found that the viscoelastic functionally graded material pipe exhibits some special dynamic behaviors and it could increase the stability significantly when compared with the aluminum and steel pipes. The numerical results also demonstrate that by the introduction of the functionally graded material, the stiffness of the piping system could be modulated easily by designing the volume fraction function. Therefore, if the dominant frequency contents of the external loads are known, a preferable design of the functionally graded material pipe to reduce the vibration is possible.

A Hybrid Method for Transverse Vibration of Multi-Span Functionally Graded Material Pipes Conveying Fluid with Various Volume Fraction Laws

2017 ◽  
Vol 09 (07) ◽  
pp. 1750095 ◽  
Author(s):  
Jiaquan Deng ◽  
Yongshou Liu ◽  
Wei Liu
Keyword(s):  
Hybrid Method ◽  
Transverse Vibration ◽  
Present Method ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Functionally Graded ◽  
Graded Material ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

Both functionally graded materials (FGMs) and fluid-conveying pipes have wide applications in engineering communities. In this paper, the transverse vibration and stability of multi-span viscoelastic FGM pipes conveying fluid are investigated. Volume fraction laws including power law, sigmoid law and exponential law are introduced to describe the variations of material properties in FGM pipes. A hybrid method which combines reverberation-ray matrix method and wave propagation method is developed to calculate the natural frequencies, and the results determined by present method are compared with the existing results in literature. Then, a comparative study is performed to investigate the effects of fluid velocity, volume fraction laws and internal damping on transverse vibration and stability of the FGM pipes conveying fluid. The results demonstrate that the present method has high precision in dynamic analysis of multi-span pipes conveying fluid. It is also found that natural frequencies of FGM pipes can be adjusted by devising the volume fractions laws. This particular feature can be tailored to fulfill the special applications in engineering.

The beam-mode stability of periodic functionally-graded-material shells conveying fluid

2014 ◽  
Vol 333 (10) ◽  
pp. 2735-2749 ◽  
Author(s):  
Huijie Shen ◽  
Michael P. Païdoussis ◽  
Jihong Wen ◽  
Dianlong Yu ◽  
Xisen Wen
Keyword(s):  
Functionally Graded Material ◽  
Functionally Graded ◽  
Mode Stability ◽  
Graded Material ◽  
Beam Mode ◽  
Conveying Fluid

Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect

2015 ◽  
Vol 18 (2) ◽  
pp. 425-442 ◽  
Author(s):  
Fouzia Larbi Chaht ◽  
Abdelhakim Kaci ◽  
Mohammed Sid Ahmed Houari ◽  
Abdelouahed Tounsi ◽  
O. Anwar Beg ◽  
...  
Keyword(s):  
Functionally Graded Material ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material ◽  
Stretching Effect

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

2020 ◽  
Vol 234 (18) ◽  
pp. 3667-3688
Author(s):  
Ismail Bensaid ◽  
Ahmed Amine Daikh ◽  
Ahmed Drai
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material

The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

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