Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system

M. FEBBO; DIANA V. BAMBILL; RAUL E. ROSSI

STRUCTURAL ENGINEERING AND MECHANICS

TECHNO-PRESS

Año: 2011 vol. 40 p. 637 - 654

1225-4568

The present paper studies the variation of the natural frequencies and mode shapes ofrectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystemchanges (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrangemultipliers as well as a finite element formulation are employed and compared. Numerically reliableresults are presented for the first time, illustrating the convenience of using the present analytical methodwhich requires only the solution of a linear eigenvalue problem. Results obtained through the variation ofthe mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effectivemass concept or Rayleigh’s statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on eachparticular mode of vibration. When the 3-DOF system is placed in the center of the plate, “new” modesare found to be a combination of the subsystem’s modes (two rotations, traslation) and the bare plate’smodes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves awayfrom the center of the plate, since different bare plate’s modes enable distinct motions of the 3-DOFsystem contributing differently to the “new’ modes as its location is modified. Also the natural frequenciesof the compound system when the plate and the subsystem are nearly uncoupled have been calculated bymeans of a first order eigenvalue perturbation analysis.