GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF CLAMPED THIN PLATES

被引：17
|
作者：
Li, Shanqing [1 ]
Yuan, Hong [1 ]
机构：
[1] Jinan Univ, Inst Appl Mech, MOE Key Lab Disaster Forecast & Control Engn, Guangzhou 510632, Guangdong, Peoples R China
来源：
ACTA MECHANICA SOLIDA SINICA | 2012年 / 25卷 / 01期
关键词：
Green function; integral equation; R-function; clamped thin plates; free vibration; R-FUNCTION METHOD; DISCRETE SINGULAR CONVOLUTION; GENERALIZED DIFFERENTIAL QUADRATURE; ARBITRARILY-SHAPED PLATES; SHALLOW SPHERICAL-SHELL; RECTANGULAR-PLATES; CIRCULAR PLATES; TRANSFORMATION METHOD; FINITE-DIFFERENCE; EDGES;
D O I：
10.1016/S0894-9166(12)60004-4
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula. Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation. Two examples demonstrate the validity of the present method. Comparison with both the series solution and ANSYS finite-element solution shows fine agreement. The present method is a novel and effective mathematical one.
引用
收藏
页码：37 / 45
页数：9
相关论文
共 50 条
  • [1] GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF CLAMPED THIN PLATES
    Shanqing Li Hong Yuan 1 (MOE Key Laboratory of Disaster Forecast and Control in Engineering
    [J]. Acta Mechanica Solida Sinica, 2012, 25 (01) : 37 - 45
  • [2] Green Quasifunction Method for Free Vibration of Clamped Thin Plates
    Shanqing Li
    Hong Yuan
    [J]. Acta Mechanica Solida Sinica, 2012, 25 : 37 - 45
  • [3] Green quasifunction method for bending problem of clamped orthotropic thin plates with trapezoidal boundary shape
    Li, Shanqing
    Yuan, Hong
    [J]. MATERIALS AND COMPUTATIONAL MECHANICS, PTS 1-3, 2012, 117-119 : 456 - 459
  • [4] Green Quasifunction Method for Bending Problem of Clamped Orthotropic Trapezoidal Thin Plates on Winkler Foundation
    Li, Shanqing
    Yuan, Hong
    [J]. APPLIED MECHANICS AND MECHANICAL ENGINEERING II, PTS 1 AND 2, 2012, 138-139 : 705 - 708
  • [5] Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation
    Hong, Yuan
    Shan-Qing, Li
    Ren-Huai, Liu
    [J]. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2007, 28 (07) : 847 - 853
  • [6] Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation
    袁鸿
    李善倾
    刘人怀
    [J]. Applied Mathematics and Mechanics(English Edition), 2007, (07) : 847 - 853
  • [7] Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation
    Hong Yuan
    Shan-qing Li
    Ren-huai Liu
    [J]. Applied Mathematics and Mechanics, 2007, 28 : 847 - 853
  • [8] Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation
    Shan-qing Li
    Hong Yuan
    [J]. Applied Mathematics and Mechanics, 2011, 32 : 265 - 276
  • [9] Quasi-Green's function method for free vibration of clamped thin plates on Winkler foundation
    Li, Shan-qing
    Yuan, Hong
    [J]. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2011, 32 (03) : 265 - 276
  • [10] Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation
    李善倾
    袁鸿
    [J]. Applied Mathematics and Mechanics(English Edition), 2011, 32 (03) : 265 - 276
12345