Please wait a minute...
浙江大学学报(工学版)
JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE)
Civil Engineering     
Analysis of cut off frequencies for functionally graded fluid saturated materials
ZHOU Feng xi1,2, ZHANG Jia qi1, CAO Xiao lin1
1.Department of Geotechnical Engineering, Lanzhou University of Technology, Lanzhou 730050, China;2. The Western Civil Engineering Disaster Prevention and Mitigation Engineering Research Center of the Ministry of Education, Lanzhou 730050, China
Download:   PDF(570KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

The analytical expression for the cut off frequencies of the horizontal shear waves (SH wave) and Lamb waves (P SV wave) in a functionally graded inhomogeneous fluid saturated media was deduced by applying the WKB (Wentzel Kramers Brillouin) method based on Biot’s theory of poroelastic medium. In the process of solving, the cut off frequencies of SH wave and P SV wave were obtained with the limiting condition of the wave number approaching zero by simplifying the governing equation. The solution to the problem revealed that the cut off frequencies were closely associated with the physico mechanical properties and the heterogeneity of the material. The material parameter of the fluid saturated poroelastic plate changing along the thickness direction as an exponential form was considered. The changing regularity of the elastic plane wave’s cut off frequencies in the inhomogeneous fluid saturated porous plate was analyzed by numerical examples. The numerical results showed that the cut off frequencies were related to the material properties of the fluid saturated material, including thickness of the plate, porosity, gradient index and permeability. The accuracy of the numerical solution was validated.

Published: 01 April 2016
CLC:  O 343  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Cite this article:

ZHOU Feng xi, ZHANG Jia qi, CAO Xiao lin. Analysis of cut off frequencies for functionally graded fluid saturated materials. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2016, 50(4): 744-749.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2016.04.020     OR     http://www.zjujournals.com/eng/Y2016/V50/I4/744


梯度饱和多孔材料中弹性波的截止频率

基于Biot多孔介质理论,应用WKB（Wentzel Kramers Brillouin）法,推导得到SH波和Lamb波在梯度非均匀含液饱和材料中截止频率的解析表达式.求解过程中应用波数趋于零的极限条件,通过简化控制方程,获得平面SH波和P SV波的截止频率.问题的解答揭示了截止频率与材料的物理力学性质以及非均匀性密切相关.考虑材料参数沿板厚按指数形式变化的饱和多孔板,通过数值算例分析弹性平面波在该类非均质饱和多孔材料中的截止频率变化规律.数值结果表明,截止频率随着板的厚度、孔隙率和非均匀参数及渗透系数的不同均有显著的变化,验证了计算结果满足精确性要求.

［1］ BIOT M A. Theory of elastic waves in a fluid saturated porous solid, I. low frequency range ［J］. The Journal of Acoustical Society of America, 1956, 28(2)： 168-178.
［2］ BIOT M A. Theory of elastic waves in a fluid saturated porous solid, II. high frequency range ［J］. The Journal of Acoustical Society of America, 1956, 28(2)： 179-191.
［3］ 柯燎亮, 汪越胜, 章梓茂. 非均匀土中Love波的传播特［J］. 岩土力学, 2004, 25(增刊): 369-374.
KE Liao liang, WANG Yue sheng, ZHANG Zi mao. Properties of love waves in inhomogeneous saturated soil ［J］. Rock and Soil Mechanics, 2004, 25(supplement): 369-374.
［4］ 邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限元解法［J］.地球物理学报, 2000, 43(02): 264-278.
SHAO Xiu min, LAN Zhi ling. Finite element methods for the equations of waves in fluid saturated porous media ［J］. Chinese Journal of Geophysics, 2000,43(02): 264-278.
［5］ 李伟华,赵成刚.平面SV波在饱和土半空间中圆柱形孔洞周边的散射［J］.地震工程与工程振动, 2008, 28(6): 2-7.
LI Wei hua, ZHAO Cheng gang. An analytical solution for the scattering of plane SV waves around cylindrical cavity in a fluid saturated porous media half space ［J］. Journal of Earthquake Engineering Vibration, 2008,28(6): 2-7.
［6］ 周凤玺,赖远明.条形荷载作用下梯度饱和土的动力响应分析［J］.岩土力学, 2013, 34(6): 1724-1730.
ZHOU Feng xi, LAI Yuan ming. Dynamic responseanalysis of graded fluid saturated soil under strip load ［J］. Rock and Soil Mechanics, 2013, 34(6): 1724-1730.
［7］ ZHOU F, LAI Y, SONG R. Propagation of plane wave in non homogeneously saturated soils ［J］. Science China Technological Sciences, 2013, 56(2): 430-440.
［8］ LIANG L, MENG Q, CHEN S, et al. Synthesis of TiB2 TiC Ni/TiAl/Ti functionally gradient materials by FAPAS process ［J］. Rare Metals, 2011, 30(supple.1): 467-471.
［9］ RAJAN T P D, PILLAI R M, PAI B C. Functionally graded Al Al3 Ni in situ intermetallic composites: fabrication and microstructural characterization ［J］. Journal of Alloys and Compounds, 2008, 453(1): L4-L7.
［10］ 曹小杉,金峰,王子昆.功能梯度材料板中Lamb波传播特性研究［J］.固体力学学报, 2009, 30(2): 35-41.
CAO Xiao shan, JIN Feng, WANG Zi kun. Propagation properties of Lamb waves in a functionally graded material plate ［J］. Chinese Journal of Solid Mechanics, 2009, 30(2): 35-41.
［11］ GAO L, JI W, ZHENG Z, et al. An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model ［J］. Science in China Series G: Physics, Mechanics and Astronomy, 2008, 51(2): 165-175.
［12］ GAO L, WANG J, ZHONG Z, et al. An exact analysis of surface acoustic waves in a plate of functionally graded materials ［J］. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2009,56(12): 2693-2700.
［13］ 刘睫,王子昆,张陵.梯度材料层状结构中的love波［J］.固体力学学报, 2004, 25(2): 165-170.
LIU Jie, WANG Zi kun, ZHANG Ling. Love waves in layered structures with graded materials ［J］. Acta Mechanic Solida Sinica, 2004, 25(2): 165-170.
［14］ ALLAHVERDIZADEH A, OFTADEH R, MAHJOOB M J, et al. Homotopy perturbation solution and periodicity analysis of nonlinear vibration of thin rectangular functionally graded plates ［J］. Acta Mechanica Solida Sinica, 2014, 27(2): 210-220.
［15］ CAO X, JIN F, JEON I. Characterization of the variation of the material properties in a freestanding inhomogeneous thin film ［J］. Science Direct Physics Letter, 2010, 375(2): 220-224.
［16］ CAO X, SHI J, JIN F. Wentzel Kramers Brillouinsolution of cut off frequency for horizontal shear (SH) waves in various inhomogeneous thin films ［J］. Philosophical Magazine Letters, 2012, 93(1): 34-41.
［17］ NAGLER L, SCHANZ M. An extendable poroelastic plate formulation in dynamics ［J］.  Archive of Applied Mechanics, 2010, 80(10): 1177-1195.
[1] WANG Si zhao, ZHANG Yi ping. Nearly incompressible linear elasticity using five node tetrahedral element based on smoothed finite element method[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2015, 49(10): 1967-1973.
[2] YANG Xing-wang, TAO Wei-ming. Finite element approach for nonlinear coupling analysis of magnetostrictive materials Terfenol-D[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2014, 48(11): 2094-2100.
[3] YANG Xing-wang, TAO Wei-ming. Finite element approach for nonlinear coupling analysis of magnetostrictive materials Terfenol-D[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 0, (): 2094-2100.
[4] LI Zheng-wei, TAO Wei-ming. Multi-layer encapsulation and stretchability analysis for
noncoplanar film-substrate structure[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2012, 46(6): 1143-1147.
[5] WEI Hao-yan, LI Zhong-xue, ZHONG Zheng. Advanced nine-node co-rotational quadrilateral
elastoplastic shell element[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2012, 46(3): 424-430.
[6] LING Dao-sheng, BU Ling-fang, HUANG Gen-qing, HUANG Bo. h-adaptive enhanced finite element method for plane problems[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2011, 45(12): 2150-2158.
[7] LIU Cheng-bin, BIAN Zu-guang, CHEN Wei-qiu. Three-dimensional pyroelectric analysis of
multilayered piezoelectric spherical shell[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2011, 45(6): 1067-1073.
[8] YANG Xin-Wang, BI Guo-Li, ZHANG Xue, et al. Path iterative method for laser-controlled crack propagation and its convergence[J]. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2009, 43(11): 2043-2047.