Premium
Fundamental frequency analysis of laminated rectangular plates by differential quadrature method
Author(s) -
Farsa Jalaleddin,
Kukreti Anant R.,
Bert Charles W.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361403
Subject(s) - mathematics , antisymmetric relation , mathematical analysis , boundary value problem , quadrature (astronomy) , nyström method , eigenvalues and eigenvectors , discretization , differential equation , numerical partial differential equations , gauss–jacobi quadrature , clenshaw–curtis quadrature , gauss–kronrod quadrature formula , gaussian quadrature , physics , quantum mechanics , optics , mathematical physics
In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.