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Appendix III III  PROGRAM 1: FREE VIBRATION OF ISOTROPIC OR ORTHOTROPIC RECTANGULAR PLATE WITHOUT FREE EDGES Program 1 is used for free vibration analysis of isotropic or orthotropic rectangular plates without free edges by the DQM. MMWC-1 is used for applying the simply supported boundary conditions and MMWC-3 (or MMWC-4) is used for applying the clamped boundary conditions. Since the deflection at all boundary points is zero and the other boundary condition of either wxx = 0 or wx = 0 has been built-in during formulations of the weighting coefficients in the subroutines, thus only DQ equations at all inner grid points are formulated. The program is very simple. Note that the program can be used for any combinations of simply supported and clamped boundary conditions, but cannot be used for anisotropic materials (except for the CCCC rectangular plate). Otherwise inaccurate results would be obtained, since the simply supported boundary condition is only approximately satisfied by MMWC-1 for anisotropic materials. It should be mentioned that subroutine TZZ is the standard eigenvalue solver to find all eigenvalues of the real matrix [GS]. The solver is not included in Program 1. To run “Program 1”, the first 4 FORTRAN subroutines in Section II.2 and a standard eigenvalue solver should be included. To run the converted MATLAB file “Prgram1_Main,” the first 4 functions in Section II.2 should be put in the same directory where “Prgram1_Main” is. Description of some variables in Program 1 X(I): x coordinate of a grid point, xi [0,A] Y(I): y coordinate of a grid point, yi [0,B] Input data N: number of grid points in both directions A: plate length in x direction B: plate length in y direction VV: Poisson’s ratio D11, D12, D22, D66, D16 = D26 = 0 : the flexural stiffness (isotropic or orthotropic materials) Note that all input data have been assigned currently. Output data TT: real part of the eigenvalues CK(I): imaginary part of the eigenvalues DSQRT(TT): frequency parameter

Differential Quadrature and Differential Quadrature Based Element Methods. 978-0-12-803081-3 Copyright © 2015 Elsevier Inc. All rights reserved.

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