Effect of Mass Based Imperfections on Behavior of Linear Vibrating Plates Near Degenerate Modes

Abstract

The principal objective in this study is to investigate the special behaviors of linear vibrating plates with special parameters near degenerate modes. Near degenerate modes, plates may lack geometric stability because they exhibit a qualitatively different behavior under an arbitrarily small change in special parameters. The special parameters considered in this study are the location and quantity of an additional mass, which have an effect on removing the system symmetry. To this end, analyses are carried out for three plate systems with each having different boundary conditions. The effect of the location and the quantity of additional mass on degenerate modes are significantly different from those of other mode types. Clearly, these effects are of theoretical importance and should be taken into consideration in practical applications. With the view of the deterministic approach, it can be stated that the study determines some unspecified parts of forced vibration behaviors of mass loaded plates.