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

Abstract

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 modified Analytical and Numerical Combined Method (or modified ANCM) and the quasi-ANCM. Instead of seeking the closed-form solution analytically for the natural frequencies and normal mode shapes of the 'unconstrained' rectangular plate (without any concentrated elements attached) required for the pure ANCM, the normal mode shapes for the modified 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 'constrained' rectangular plate (with any number of concentrated elements attached) is derived basing on the natural frequencies and normal mode shapes of the 'unconstrained' plate and applying the 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-form' 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. © 1997 by John Wiley & Sons, Ltd.