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《Journal of Vibration and Shock》 2007-01

## ESTIMATING FREE VIBRATION OF RECTANGULAR PLATES WITH GUIDED EDGES BASED ON MODIFIED SPLINE FUNCTIONS

Li Chunxiang~1,Si Weijian~2(1.Department of Civil Engineering,Shanghai University,Shanghai 200072;2.Department of civil Engineering,shanghai Jiaotong university,Shanghai 200030)
The authors present a numerical analysis procedure,referred to as the bidirectional spline discretization procedure,for vibration analysis of an isotropic and orthotropic rectangular plate with possible combinations of the three classical boundary conditions of free(F),simply supported(S), and clamped(C) edges with one guided(G) boundary condition.By discretization through,respectively,dividing the plate into N and M equal subintervals in the x and y directions,the modified B3-spline functions,consisting of the(N+3) and (M+3) local B3-spline functions(The first three and the last three local B3-spline functions have been modified for accommodating to any type of boundary conditions.) with respect to the(N+1) points and two extended additional points in the x direction and the(M+1) points and two extended additional points in the y direction,are employed as the displacement trial functions.Making use of the modified B3spline functions,only one unknown coefficient is required to be determined,respectively,for the deflection(displacement) and the first and the second derivatives of the deflection at a given bound.Characteristic equation of a rectangular plate is derived based on its potential energy functional.In comparison to the finite element method(FEM) and the spline finite strip method(FSM),the present procedure has remarkably fewer numbers of degree of freedom(DOF),and thus it is computatively more efficient.Likewise,the computational program,with minimal preparation of input data,can be developed through the proposed formulation.The numerical results indicate that the proposed method can render a very high accuracy.
【CateGory Index】： TU311
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 【Citations】
 Chinese Journal Full-text Database 3 Hits
 1 Li Xiaojun 1 Chen Liqun 1,2 (1.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072; 2.Department of Mechanics ,Shanghai University, Shanghai 200436);ON TRANSVERSE VIBRATIONS OF AN AXIALLY MOVING BEAM ON FIXED SUPPORTS[J];Journal of Vibration and Shock;2005-01 2 Yu Chunhua Dong Xiaoyun Zhou Ding (Department of Mechanics, Nanjing University of Science & Technology, Nanjing 210094);FREE VIBRATION ANALYSIS OF ARBITRARY SHAPE THICK PLATE WITH CURVED BOUNDARIES BY MEANS OF FOURIER EXPANSION COLLOCATION METHOD[J];Journal of Vibration and Shock;2005-02 3 Li Chunxiang1 Zhang Liqing21.Department of Civil Engineering Shanghai University Shanghai 2000722.Department of Civil Engineering Shanghai Jiaotong University Shanghai 200030;EVALUATION OF THE DUAL-LAYER MULTIPLE TUNED MASS DAMPERS FOR STRUCTURES SUBJECTED TO EARTHQUAKE[J];Journal of Vibration and Shock;2005-05
 【Co-citations】
 Chinese Journal Full-text Database 7 Hits
 1 LI XiaoJun CHEN LiQun (Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics,Shanghai University,Shanghai 200072,China);TRANSVERSE VIBRATION AND STABILITY OF AN AXIALLY MOVING BEAM WITH PINNED AND FIXED ENDS[J];Journal of Mechanical Strength;2006-05 2 Yang Xiaodong~1 Chen Liqun~(2,3)(1.Department of Engineering Mechanics,Shenyang Institute of Aeronautical Engineering,Shenyang 110034;2.Department of Mechanics,Shanghai University,Shanghai 200436;3.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072);VIBRATIONS OF AN AXIALLY TRANSPORTING BEAM WITH TORSIONAL SPRINGS AND SIMPLY SUPPORTED[J];Journal of Vibration and Shock;2006-04 3 Ren Jiusheng Cheng Changjun (Department of Mechanics, Shanghai University, Shanghai 200444);CHAOTIC MOTION ANALYSIS FOR COUPLED LONGITUDINAL AND TRANSVERSE MOTIONS OF PILES OF NONLINEAR VISCOELASTIC MATERIALS[J];Journal of Vibration and Shock;2006-05 4 Lei Yongjun Zhao Xuechuan Zhou Jianping(School of Areospace and Material Engineering,National University of Defense Technology,Changsha 410073);TRANSFER FUNCTION METHOD FOR FINDING NATURAL FREQUENCIES OF A NONLOCAL ELASTIC BAR[J];Journal of Vibration and Shock;2006-06 5 HAN Bing-kang1,LI Chun-xiang2(1.School of Civil Engineering,Tongji University,Shanghai 200092,China;2.Department of Civil Engineering,Shanghai University,Shanghai 200072,China);EVALUATION ON STROKE OF THE SYSTEM PARAMETER COMBINATION BASED MULTIPLE TUNED MASS DAMPERS[J];Journal of Vibration and Shock;2007-02 6 CHEN Jin-ping, WANG Sheng-ze, WU Wen-ying(School of Mechanical Engineering, Donghua University, Shanghai 201620, China);NATURAL FREQUENCIES OF A LONGITUDINALLY MOVING FABRIC[J];Journal of Vibration and Shock;2007-09 7 XU Teng-fei, XIANG Tian-yu, ZHAO Ren-da(Department of Bridge Engineering, Southwest Jiaotong University, Chengdu 610031, China);SERIES SOLUTION OF NATURAL VIBRATION OF THE VARIABLE CROSS-SECTION EULER-BERNOULLI BEAM UNDER AXIAL FORCE[J];Journal of Vibration and Shock;2007-11
 【Secondary Citations】
 Chinese Journal Full-text Database 5 Hits
 1 Li Chunxiang 1, Xiong Xueyu 2(1.School of Civil Engineering and Mechanics, Shanghai Jiaotong University, Shanghai 200030, China;2.Prestress Research Institute of Tongji University, Shanghai 200092, China);Optimum Multiple Tuned Mass Dampers based on ADMF and the combinations available of the system parameters under earthquake[J];Chinese Journal of Computational Mechanics;2002-03 2 Li Chunxiang 1 Xiong Xueyu 2 Si Weijian 1 (1.School of Civil Engineering and Mechanics,Shanghai Jiaotong University,Shanghai 200030; 2.School of Civil Engineering.Tongji University,Shanghai 200092);EVALUATION OF THE EFFECT OF DISPLACEMENT-CONTROL-BASED MTMD ON THE ACCELERATION OF THE STRUCTURE SUBJECTED TO EARTHQUAKE[J];Journal of Vibration and Shock;2003-01 3 Li Chunxiang Du Dong (School of Civil Engineering and Mechanics,Shanghai Jiaotong University,Shanghai 200030);ROBUSTNESS OF MTMD TO PERTURBATION IN STRUCTURAL STIFFNESS AND MASS[J];Journal of Vibration and Shock;2004-01 4 Li Chunxiang Zhou Dai (School of Civil Engineering,Shanghai Jiaotong University,Shanghai 200030);COMPARATIVE STUDY ON PERFORMANCE OF DISPLACEMENT RESPONSE CONTROL BASED MTMD FOR STRUCTURES UNDER VARIOUS EXCITATIONS[J];Journal of Vibration and Shock;2004-02 5 Li Chunxiang (School of Civil Engineering and Mechanics,Shanghai Jiao Tong University,Shanghai 200030);PERFORMANCE ASSESSMENT OF MODELING OF STIFFNESS-DASHPOT BASED ACTIVE MULTIPLE TUNED MASS DAMPERS[J];Journal of Vibration and Shock;2004-04
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