Improved Fourier series method for the vibration analysis of a&nbsp; two-parameter foundation system

PDF(825 KB)

Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (14) : 85-91.

Improved Fourier series method for the vibration analysis of a two-parameter foundation system

WANG Ji1，GAO Fangqing1,2

Author information +

History +

Abstract

In a two-parameter foundation system, the bending deflection of the rectangle thin plate is not equal to zero at the free or elastic boundary, which will lead to the transfer and diffusion of the foundation pressure to other parts of the foundation beyond plate edges.Due to the limitation in the simplification of boundary conditions, in existing researches the settlement of the foundation outside the plate is usually ignored, which leads to a large error in the calculation results.Based on an improved Fourier series method and the Vlazov hypothesis, a vibration analysis method, bing able to consider the settlement of the foundation outside the plate under arbitrary boundary conditions, was proposed for studying the bending vibration of rectangular thin plates on the two-parameter foundation.Through parametric analysis and comparison with the results in literatures and by finite element analysis, it is verified that the method had a fast convergence speed and a high computational accuracy.On this basis, the effects of the combination of different number of free boundaries and the foundation settlement under elastic boundaries on vibration characteristics were studied.

Key words

two-parameter foundation / settlement of the foundation outside the plate / improved Fourier series / Vlazov hypothesis / arbitrary boundary condition

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WANG Ji，GAO Fangqing. Improved Fourier series method for the vibration analysis of a two-parameter foundation system[J]. Journal of Vibration and Shock, 2021, 40(14): 85-91

References

［1］黄义.弹性地基上的梁、板、壳［M］.北京：科学出版社, 2005.

［2］HACIYEV V C, SOFIYEV A H, KURUOGLU N.Free bending vibration analysis of thin bidirectionally exponentially graded orthotropic rectangular plates resting on two-parameter elastic foundations［J］.Composite Structures, 2018,184: 372-377.

［3］LU Z, YAO H L, ZHAN Y X, et al.Vibrations of a plate on a two-parameter foundation subjected to moving rectangular loads of varying velocities［J］.Journal of Vibroengineering, 2014,16(3): 1543-1554.

［4］KIM S M.Influence of horizontal resistance at plate bottom on vibration of plates on elastic foundation under moving loads ［J］.Engineering Structures, 2004,26(4): 519-529.

［5］杨端生, 黄炎, 潘军.双参数弹性地基上板的自由振动［J］.动力学与控制学报, 2004,2(1): 92-96.
YANG Duansheng, HUANG Yan, PAN Jun.Free vibration of plates on the bi-parameter elastic foundation［J］.Journal of Dynamics and Control, 2004,2(1): 92-96.

［6］彭立生, 董军.双参数地基上四边自由矩形厚板计算［J］.武汉水利电力学院学报, 1992,25(4): 339-352.
PENG Lisheng, DONG Jun.Thick rectangular plates with four free edges on the two-parameter foundations［J］.Journal of Wuhan University of Hydraulic & Electric Engineering, 1992,25(4): 339-352.

［7］刘艳, 刘洪兵, 刘红艳,等.双参数粘弹性地基矩形板的振动分析［J］.公路工程, 2008,33(2): 94-96.
LIU Yan, LIU Hongbing, LIU Hongyan, et al.Dynamic analysis of plates on two-parameter viscoelastic foundation under impact load［J］.Highway Engineering, 2008,33(2): 94-96.

［8］YANG T Y.A finite element analysis of plates on a two parameter foundation model［J］.Computers & Structures, 1972,2(4): 593-614.

［9］竹学叶, 寿楠椿.双参数弹性地基上自由矩形薄板解析［J］.华北水利水电学院学报, 1995,16(2): 45-49.
ZHU Xueye, SHOU Nanchun.Analysis rectangular thin plates on two-parameter foundation［J］.Journal of North China Institute of Water Conservancy and Hydroelectric Power, 1995,16(2): 45-49.

［10］LAM K Y, WANG C M, HE X Q.Canonical exact solutions for Levy-plates on two-parameter foundation using Green’s functions［J］.Engineering Structures, 2000,22(4): 364-378.

［11］TRONG H N.Analysis of rectangular plates on resting Winkler and two-parameter elastic foundation models by finite difference method［J］.Engineering Technology and Applied Science Research, 2019,9(4): 4490-4494.

［12］杨端生, 黄炎.双参数弹性地基上的正交异性矩形板的弯曲［J］.工程力学, 2009,26(3): 26-30.
YANG Duansheng, HUANG Yan.Bending of orthotropic rectangular plates on double-parameter elastic foundation［J］.Engineering Mechanics, 2009,26(3): 26-30.

［13］LI W L.Vibration analysis of rectangular plates with general elastic boundary supports［J］.Journal of Sound and Vibration, 2004,273(3): 619-635.

［14］LI W L, ZHANG X, DU J, et al.An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports ［J］.Journal of Sound and Vibration, 2009,321(1/2): 254-269.

［15］SELVADURAI A P S, GLADWELL G M L.Elastic analysis of soil-foundation interaction［J］.Journal of Applied Mechanics, 1980,47(1): 219.

［16］张载.双参数地基模型基床系数的获取及应用［D］.长沙：湖南大学, 2014.