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

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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. 29c) q=0 i=0 P3 q q=0 i=0 38 Sec. 32) The basic functions ~b~w, r ~o in Eq. 33) where ne is the number of edges of the plate and Ej (~', r/) is the boundary equation of thej-th supporting edge. 35) OCm ' tS~lm ' ~ e m The substitution of Eqs.

2c-e) and by substituting Eqs. 15a,b) into Eqs. 17) Sec. 18c) where n is the number of circumferential nodal diameters. (a) Circular plate a = 0, fl=2rc (b) Annular plate a r 0, fl= 27c SffSS~Sff (c) Sectorial plate a=0, fl~0 (d) Annular sectorial plate a , O , fl~O Fig. 1 Definitions of a and flfor various plate shapes Chap. 3 Formulation in Polar Coordinates 35 As a result of using Eqs. 1 CIRCULAR AND ANNULAR PLATES For axisymmetric plates, the energy functionals in the one-dimensional form given in Eqs.

EQ. EQ. EQ. 4) THEN CALL DIFXY(FXYSII,IRSII,IS SII,N 1,1,0,N3) CALL SIMPLE(FXYSJJ,IRSJJ,IS SJJ,N2,N4) 49 Sec. 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.

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