FREE-VIBRATION ANALYSIS OF A RECTANGULAR PLATE CARRYING ANY NUMBER OFPOINT MASSES AND TRANSLATIONAL SPRINGS BY USING THE MODIFIED AND QUASI-ANALYTICAL AND NUMERICAL COMBINED METHODS

The natural frequencies and the corresponding mode shapes of a uniform rectangular plate carrying any number of rigidly attached (or elastic ally mounted) point masses and translational springs with various magn itudes and arbitrary locations are determined by using the modified An alytical and Numerical Combined Method (or modified ANCM) and the quas i-ANCM. Instead of seeking the closed-form solution analytically for t he natural frequencies and normal,mode shapes of the 'unconstrained' r ectangular plate (without any concentrated elements attached) required for the pure ANCM, the normal mode shapes for the modified ANCM and t he natural frequencies together with the normal mode shapes for the qu asi-ANCM are obtained numerically, however. Then the characteristic eq uation of the 'constrained' rectangular plate (with any number of conc entrated elements attached) is derived basing on the natural frequenci es and normal mode shapes of the 'unconstrained' plate and applying th e mode-superposition theory. Finally, the natural frequencies and mode shapes of the 'constrained' plate are obtained numerically. The pure ANCM is originally available only for the problems that the 'closed-fo rm' solution for the natural frequencies and normal mode shapes of the 'constrained' system is obtainable. Now, the modified ANCM and quasi- ANCM presented in this paper break the limitation of the pure ANCM and extend the area of problems solvable by the ANCM. (C) 1997 by John Wi ley & Sons, Ltd.