Download Vibration of Mindlin Plates. Programming the p-Version Ritz by K.M. Liew, C.M. Wang, Y. Xiang and S. Kitipornchai (Auth.) PDF

By K.M. Liew, C.M. Wang, Y. Xiang and S. Kitipornchai (Auth.)

During the last numerous years, the 4 authors have together performed study into the research of vibrating Mindlin plates as a collaborative venture among Nanyang Technological college, The nationwide college of Singapore, and The college of Queensland. The study was once caused through the truth that there's a dearth of vibration effects for Mindlin plates compared to classical skinny plate ideas. To generate the vibration effects, the authors have effectively hired the Ritz strategy for basic plate shapes and boundary stipulations. The Ritz process, as soon as considered awkward for normal plate research, might be computerized via compatible trial services (for displacements) that fulfill the geometric plate boundary stipulations a priori. This paintings has been well-received through teachers and researchers, as indicated by means of the continuous requests for the authors' papers and the Ritz software program codes. This monograph is written with the view to proportion this so-called p-Ritz procedure for the vibration research of Mindlin plates and its software program codes with the examine group. To the authors' wisdom, the monograph includes the 1st released Ritz plate software program codes of its kind.

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Extra resources for Vibration of Mindlin Plates. Programming the p-Version Ritz Method

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El . 26) where the elements of the stiffness submatrices [K] are: k~ - 6(1-v)K2 I i { aZ S18~bwc3~b7 1 - a r~ (1 - a) 0~ 0~ aX 2. . . , N 1; j = 1,2 ..... 27d) 37 Chap. , N 3 and the elements of the mass submatrices [M] are: i = 1,2,.. N,; j = 1,2 ..... , N 1, j = 1,2,. 28c) cc ~~ a ( 1 - a ) Z S l ~ ; ~ ; m,j = 4 d4; ce . " r . , . i = 1,2,... , N 3 ee r2 i ' a ( l - a ) Z S z r 1 7 6 1 6 2 1 7 6 m#. = -~ 4 i =1,2,.. N 3;j=1,2,.. 26) may be solved using any standard eigenvalue solver for the natural frequencies (eigenvalues) and mode shapes (eigenvectors) for circular and annular plates.

1974). The source code of this subroutine is not given herein as it is readily available. The analyst may use any other standard eigenvalue solver if desired. 1 SOFTWARE CODE: VPRITZP1 ************************************************************ * * * p-VERSION RITZ METHOD FOR VIBRATION OF CIRCULAR AND ANNULAR MINDLIN PLATES BASED ON POLAR COORDINATES SYSTEM * * * *:,g********* ***** :'g******* ********* $************** :0*** ******** MAIN VPRITZP 1 IMPLICIT DOUBLE PRECISION (A-H,O-Z) PARAMETER (NTERM=40,NTOTAL=3*NTERM,N 1=NTERM, $ N2=NTOTAL,NTAB=25) DIMENSION S(18,N 1,N 1),COEF(NTAB) DOUBLE PRECISION $ K(NZ,NZ),K 1(NZ,NZ),W(NZ),Z(NZ,NZ),FV 1(N2), $ FV2(N2) DOUBLE PRECISION E,LX,LY,H,NU,KAPPA,RHO INTEGER P0,P 1,P2 Chap.

EQ. EQ. EQ. EQ. EQ. 18) THEN CALL DIFXY(FXYSII,IRSII,IS SII,N 1,1,0,N3) CALL SIMPLE(FXYSJJ,IRSJJ,IS SJJ,N2,N4) CALL MULTI(FXYSII,IRSII,IS SII,N3,FXYSJJ,IRSJJ,IS SJJ,N4,N5) CALL CALCU(FXYSII,IRSII,IS SII,N5,SUM,II,0,NTAB,COEF) GOTO 10 ENDIF 10 RETURN END SUBROUTINE CALCU(F,IR,IS,N,SUM,II,IND,NTAB,COEF) * This subroutine CALCU calculates the integrated values of * a polynomial function. EQ. 2) FAC=COEF(IR(I)+ 1) Chap. LE. ) GOTO 10 SUM=SUM+F(I)*FAC CONTINUE RETURN END SUBROUTINE POLYCOMP1D * This subroutine POLYCOMP1D forms the polynomial terms * in symbolic form.

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