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
Js. Wu et Ss. Luo, 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, International journal for numerical methods in engineering, 40(12), 1997, pp. 2171-2193
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.