求解饱和多孔介质圆柱壳动力学问题的一种半解析方法

PDF(886 KB)

振动与冲击 ›› 2018, Vol. 37 ›› Issue (1) : 208-215.

论文

向宇1,2，孙润1,2，陆静1,2，袁丽芸1,2

作者信息 +

Semi-analytical method for solving the dynamic behaviors of a fluid-saturated porous cylindrical shell

XIANG Yu1,2,SUN Run1,2,LU Jing1,2,YUAN Li-yun1,2

Author information +

文章历史 +

摘要

基于弹性薄壳理论，结合Biot理论中流体和固体骨架的运动方程及本构关系，得到饱和多孔介质圆柱薄壳在谐激励作用下的一阶矩阵常微分控制方程。结合齐次扩容精细积分法和精细元法，建立了分析该类结构振动问题的半解析方法。该方法充分考虑了多孔介质圆柱薄壳骨架与流体的耦合作用，具有广泛的适应性，弥补了现有计算模型和等效媒质法的不足。基于该方法，还讨论了孔隙率对饱和多孔介质圆柱薄壳的频响特性的影响。

Abstract

Based on the elastic theory of thin shells, and by applying the motion equations of the solid frame and fluid part and the constitutive equation for a porous media proposed by Biot, the first order differential governing equations of a thin fluid-saturated porous cylindrical shell under harmonic excitation were established. Employing the extended homogeneous capacity precision integration method and precise element method, a new semi-analytical method for analysing the vibration performance of this kind of structures was developed. Considering thoughtfully the coupling effect between the solid frame and the fluid, the present model is reasonable and adaptable, which could make up the insufficiency of the existed calculated models and the effective medium method. Based on the new method, the effect of porosity on the frequency response of a fluid-saturated porous cylindrical shell was discussed.

导出引用

向宇1,2，孙润1,2，陆静1,2，袁丽芸1,2. 求解饱和多孔介质圆柱壳动力学问题的一种半解析方法[J]. 振动与冲击, 2018, 37(1): 208-215

XIANG Yu1,2,SUN Run1,2,LU Jing1,2,YUAN Li-yun1,2. Semi-analytical method for solving the dynamic behaviors of a fluid-saturated porous cylindrical shell[J]. Journal of Vibration and Shock, 2018, 37(1): 208-215

参考文献

[1] Boit M A. Theory of Propagation of elastic waves in a fluid-saturated porous solid.Ⅰ.low-frequency range[J]. J. Acoust. Soc. Am., 1956, 28(2):168-178.
[2]   Boit M A. Theory of Propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.Higher-frequency range[J]. J. Acoust. Soc. Am., 1956, 28(2):179-191
[3] 刘志军,夏唐代,黄睿等. Biot理论与修正的Biot理论比较及讨论[J].振动与冲击.2015,34(4):148-152.
Liu Z J, Xia T D, Huang R, et al. Compare and discussion for Biot theory and modified Biot one[J]. Journal of Vibration and Shock. 2015, 34(4):148-152.
[4] 敬霖, 王志华, 赵隆茂. 多孔金属及其夹芯结构力学性能的研究进展[J]. 力学与实践, 2015, 37(1):1-24.
Jing Lin, Wang Zhihua, Zhao Longmao. Advances in studies of the mechanical performance of cellular metals and related sandwich structures[J]. Mechanics in Engineering, 2015, 37(1): 1-24
[5] Shah S A. Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells[J]. Journal of Sound and Vibration, 2008, 318(1-2):389–405.
[6] Zhou J, Bhaskar A and Zhang X. Sound transmission through double cylindrical shells lined with porous material under turbulent boundary layer excitation[J]. Journal of Sound and Vibration. 2015, 357:253-268
[7] Daneshjou K, Ramezani H, Talebitooti R. Wave transmission through laminated composite double-walled cylindrical shell lined with porous materials[J]. Applied Mathematics & Mechanics, 2011, 32(6):701-718
[8]   Allard J F and Atalla N. Propagation of sound in porous media: Modelling sound absorbing materials[M]. John Wiley &Sons, Ltd, 2009.
[9] Boily S, Charron F. The vibroacoustic response of a cylindrical shell structure with viscoelastic and poroelasticmaterials[J]. Applied Acoustics, 1999, 58(2): 131-152.
[10] Liu X, Tian X, Lu T J, et al. Blast resistance of sandwich-walled hollow cylinders with graded metallic foam cores[J]. Composite Structures, 2012, 94(8):2485–2493.
[11] Gaunaurd G C, Wertman W. Comparison of effective medium theories for inhomogeneous continua[J]. Journal of the Acoustical Society of America, 1989, 85(2):541-554
[12] 秦波, 梁彬, 朱哲民,等. 含气泡弱可压缩弹性材料的等效媒质法[J]. 声学学报, 2007, 32(02):110-115.
     Qin Bo, Liang Bin, Zhu Zhemin, et al. Effective medium method of slightly compressible elastic media permeated with air-filled bubbles [J]. ACTA ACUSTICA, 2007, 32(02):110-115
[13] 曹志远.板壳振动理论[M].中国铁道出版社,1989.
Cao Zhiyuan. Vibration theory of plates and shells[M].China Railway press,1989.
[14] 吴望一.流体力学(上册)[M].北京大学出版社, 1983.
Wu Wangyi. Fluid Mechanics (Book one)[M].Peking University press,1983.
[15] Ni Q, Xiang Y, Huang Y, et al. MODELING AND DYNAMICS ANALYSIS OF SHELLS OF REVOLUTION BY PARTIALLY ACTIVE CONSTRAINED LAYER DAMPING TREATMENT[J].Journal of solid Mechanics (English Edition), 2013, 05 (5):468–479.
.