FREE VIBRATION ANALYSIS OF A RECTANGULAR PLATE CARRYING ANY NUMBER OF POINT 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 elastically mounted) point masses and translational springs with various magnitudes and arbitrary locations are determined by using the modiÞed Analytical and Numerical Combined Method (or modiÞed ANCM) and the quasi-ANCM. Instead of seeking the closed-form solution analytically for the natural frequencies and normal mode shapes of the ÔunconstrainedÕ rectangular plate (without any concentrated elements attached) required for the pure ANCM, the normal mode shapes for the modiÞed ANCM and the natural frequencies together with the normal mode shapes for the quasi-ANCM are obtained numerically, however. Then the characteristic equation of the ÔconstrainedÕ rectangular plate (with any number of concentrated elements attached) is derived basing on the natural frequencies and normal mode shapes of the ÔunconstrainedÕ plate and applying the mode-superposition theory. Finally, the natural frequencies and mode shapes of the ÔconstrainedÕ plate are obtained numerically. The pure ANCMis originally available only for the problems that the Ôclosed-formÕ solution for the natural frequencies and normal mode shapes of the ÔconstrainedÕ system is obtainable. Now, the modiÞed 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.