By K.M. Liew, Y. Xiang, S. Kitipornchai, C.M. Wang
Over the past a number of years, the 4 authors have together performed learn into the research of vibrating Mindlin plates as a collaborative venture among Nanyang Technological college, The nationwide collage of Singapore, and The college of Queensland. The learn was once triggered via the truth that there's a dearth of vibration effects for Mindlin plates in comparison to classical skinny plate suggestions. To generate the vibration effects, the authors have effectively hired the Ritz approach for common plate shapes and boundary stipulations. The Ritz procedure, as soon as considered awkward for common plate research, could be computerized via appropriate trial services (for displacements) that fulfill the geometric plate boundary stipulations a priori . This paintings has been well-received by means of 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 strategy for the vibration research of Mindlin plates and its software program codes with the learn neighborhood. To the authors' wisdom, the monograph comprises the 1st released Ritz plate software program codes of its sort.
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Extra resources for Vibration of Mindlin plates: programming the p-version Ritz Method
12d) C23 = J'. 12f) where i = 1,2. 3 present some values of the natural frequency parameters for circular plates with free, soft simply supported and clamped edges, respectively. Note that the Chap. 3 and the shear correction factor 31 as K "2 =it'2/12. The eigenvalues of thin plates are also given under the column headed by h/R = 0 in the Tables. In the tables, n refers to the number of nodal diameters while s denotes the number of nodal circles, excluding the boundary circle. Axisymmetric vibration solutions of thick circular plates that include the effects of geometric nonlinearity, may be obtained from the paper by Kanaka Raju and Venkateswara Rao (1976) who have used the finite element method to solve the problem.
N 1, j = 1,2,. " 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. 29c) q=0 i=0 P3 q q=0 i=0 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.
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.
Vibration of Mindlin plates: programming the p-version Ritz Method by K.M. Liew, Y. Xiang, S. Kitipornchai, C.M. Wang