ANALYSIS OF TRANSVERSE VIBRATION OF RECTANGULAR PLATE WITH DISCRETELY ATTACHED POINT MASSES HAVING ROTARY INERTIA

摘要

In this paper, free vibrations analysis of rectangular plates with attached discrete masses with rotary inertia has been carried by finite element method (FEM). The tool used is Ansys. Simulations are carried out to investigate the changes in natural frequencies and mode shapes. Boundary conditions at the plate edges are those of simply supported plate. The results obtained by FEM are compared with the published results in the literature. It has also examined the results Amabili [8] that a small mass placed on the diagonal of a square thin plate is enough to transform the shape of modes with one nodal line parallel to the edge, into diagonal modes, i.e. modes with diagonal nodal lines. In this paper, the authors have shown that there exists a critical mass which transforms the mode shape with one nodal line parallel to the edge ( Figure 1) into diagonal modes, ie modes with diagonal nodal lines (Figure 2) . If this attached discrete mass is less than 0.3% of the plate, mode shape change does not occur. The ability to alter the mode shape of plates has useful applications in sensing and actuating devices. This critical mass is very important from the point of view of sensors placement, where the mass of the sensor itself may trigger the mode shape change. The placement of sensor is desired in the area of higher deflection region where it can sense the vibration. The authors have also investigated the effect of placement of four symmetrical masses parallel to the edges ( Figure 3) as well as along the diagonals ( Figure 4). The mode shape of the plate without attached masses with two nodal lines parallel to the edges remains unaltered if we place four discrete masses symmetrically along the edges as shown in Figure 3. But when the same four discrete masses are placed symmetrically parallel to the diagonal of the plate, the corresponding mode shape changes to mode shape with two nodal line along the diagonals ( Figure 4). However, it is noteworthy that in both the cases, ( Figures.3,4), the discrete masses location remains in the higher deflection regions. This finding has important bearing on the placement of sensors. It is indicated from the results that instead of placing one sensor at a point on the plate which may trigger the change in mode shape and sensor may fall in the region of lower deflection region, four symmetrical placements of discrete masses may be advisable from sensor point of view.