USE OF THE ANALYTICAL-AND-NUMERICAL-COMBINED METHOD IN THE FREE-VIBRATION ANALYSIS OF A RECTANGULAR PLATE WITH ANY NUMBER OF POINT MASSES AND TRANSLATIONAL SPRINGS

By means of the analytical-and-numerical-combined method (ANCM), the n atural frequencies and the corresponding mode shapes of a uniform rect angular flat plate carrying any number of point masses and translation al springs are determined. The boundary (supported) conditions of the plate and the magnitudes and locations of the concentrated elements ar e arbitrary. First, the closed form solution of the natural frequencie s and the normal mode shapes of the ''unconstrained'' plate (without a ny concentrated elements attached) are obtained. Second, based on the closed form solution and using the mode superposition technique, the e igenvalue equation of the ''constrained'' plate (with any number of co ncentrated elements attached) is derived. Finally, the eigenvalue equa tion is solved numerically to give the desired natural frequencies and mode shapes of the ''constrained'' plate. Under the condition that th e accuracies of the sought natural frequencies are approximately the s ame, the order of the eigenvalue equation derived from the ANCM is muc h lower than that derived from the traditional finite element method ( FEM). Thus the CPU time required by the ANCM is much less than that re quired by the FEM. Furthermore, the ANCM is also superior to the pure analytical (closed form solution) method, since the former (ANCM) is a vailable for free vibration analysis of a uniform rectangular flat pla te carrying any number of concentrated elements, but the latter is usu ally practical only for single concentrated elements. (C) 1997 Academi c Press Limited.