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.

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.

scholarly journals Dynamics of axially functionally graded conical pipes conveying fluid

2021 ◽  
Vol 37 ◽  
pp. 318-326
Author(s):  
Yuzhen Zhao ◽  
Dike Hu ◽  
Song Wu ◽  
Xinjun Long ◽  
Yongshou Liu
Keyword(s):  
Natural Frequency ◽  
Critical Velocity ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Reduction Factor ◽  
Functionally Graded ◽  
Function Type ◽  
Pipes Conveying Fluid ◽  
Volume Fraction Function ◽  
Conveying Fluid

Abstract In this paper, the dynamics of axially functionally graded (AFG) conical pipes conveying fluid are analyzed. The materials are distributed along the conical pipe axis as a volume fraction function. Either the elastic modulus or the density of the AFG conical pipe is assumed to vary from the inlet to the outlet. The governing equation of the AFG conical pipe is derived using the Hamiltonian principle and solved by the differential quadrature method. The effects of the volume fraction index, volume fraction function type and reduction factor on the natural frequency and critical velocity are analyzed. It is found that for a power function volume fraction type, the natural frequency and critical velocity increase with increasing volume fraction index and clearly increase when the volume fraction index is within the range (0, 10). For an exponential function volume fraction type, the natural frequency and critical velocity change rapidly within the range (−10, 10), besides the above range the relationship between the natural frequency, critical velocity and volume fraction index is approximate of little change. The natural frequency and critical velocity decrease linearly with increasing reduction factor.

scholarly journals Frequency Analysis of Functionally Graded Curved Pipes Conveying Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Liang ◽  
Xiao-Dong Yang ◽  
Ri-Dong Bao ◽  
Wei Zhang
Keyword(s):  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Sensitivity Study ◽  
Functionally Graded ◽  
Opening Angle ◽  
Curved Pipes ◽  
Free Vibration Frequency ◽  
Pipes Conveying Fluid ◽  
Curved Pipes Conveying Fluid ◽  
Conveying Fluid

The curved pipe made of functionally graded material conveying fluid is considered and the in-plane free vibration frequency of the resulting composite pipe is investigated. The material properties are assumed to distribute continuously along the pipe wall thickness according to a power law and the effective mass, flexural rigidity, and mass ratio are used in the governing equations. The natural frequencies are derived numerically by applying the modified inextensible theory. The lowest four natural frequencies are studied via the complex mode method, the validity of which is demonstrated by comparing the results with those in available literatures. A parametric sensitivity study is conducted by numerical examples and the results obtained reveal the significant effects of material distribution gradient index, flow velocity, fluid density, and opening angle on the natural frequencies of the FGM curved pipes conveying fluid.

ON VIBRATION OF FUNCTIONALLY GRADED PLATES ACCORDING TO A REFINED TRIGONOMETRIC PLATE THEORY

2005 ◽  
Vol 05 (02) ◽  
pp. 279-297 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Series Representation ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Functionally Graded ◽  
Graded Material

The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lamé's coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.

Effects of pores on nonlinear vibration and post buckling behavior of functionally graded material pipes conveying fluid

2021 ◽  
pp. 095440622098201
Author(s):  
Nan Li ◽  
Hongyan Zhang ◽  
Changqing Bai
Keyword(s):  
Dynamic Behavior ◽  
Functionally Graded Material ◽  
Primary Resonance ◽  
Functionally Graded ◽  
Pore Distribution ◽  
Buckling Behavior ◽  
Graded Material ◽  
Post Buckling ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

Functionally graded material (FGM) has an important application prospect in aircraft engineering, especially in smart aircraft. The dynamic behavior of FGM has been widely investigated so far but more work is needed for the porous FGM pipes conveying fluid. In this paper, a sensible pore distribution function related with the volume fraction of metal and ceramic is proposed for the dynamic modeling of porous FGM pipes conveying fluid. The maximum porosity and its corresponding position are taken into account in the present mechanical model. The material properties of the porous pipes are temperature dependent and can be affected by pore distribution. The governing equation of the porous FGM pipe is derived and then the exact solution of post buckling is obtained. The nonlinear primary resonance is determined by the multiple scale method. It is shown that the effect of the pore distribution is very significant on the post buckling behavior and nonlinear primary resonance of the porous FGM pipes. The current work is very helpful in understanding the influence of pore distribution on static and dynamic behavior of pores FGM structures in engineering practice.

scholarly journals A New Method Based on Laplace Transform and Its Application to Stability of Pipe Conveying Fluid

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
H. B. Wen ◽  
Y. R. Yang ◽  
P. Li ◽  
Y. D. Li ◽  
Y. Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Present Method ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Transformation Method ◽  
Critical Flow ◽  
Pipe Conveying Fluid ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

A new differential transformation method is developed in this paper and is applied for free vibration problem of pipes conveying fluid. The natural frequencies, critical flow velocities, and vibration mode functions of such pipes with several typical boundary conditions are obtained and compared with the results predicted by Galerkin method and finite element method (FEM) and with other results archived. The results show that the present method is of high precision and can serve as an analytical method for the vibration of pipes conveying fluid.

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