Importance of satisfaction of point support compatibility conditions in the simulation of point supports by the flexibility function approach

Abstract

A new approach for the representation of point supports in the vibration analysis of plates has been presented previously [1–3]. The application of this approach to a variety of problems concerning rectangular plates with point supports was demonstrated in subsequent studies [4–6]. The approach is based on simulating a point support on free edges as a zero of a flexibility function, representing a fictitious elastic restraint distribution over the free edge, with explicit satisfaction of the compatibility conditions at the point support location. This leads to a situation of having a greater number of equations than of unknowns. In the solution procedure the compatibility conditions are accounted for by ignoring the appropriate number of equilibrium equations (boundary conditions). In this paper the role of point support compatibility conditions in the simulation of a point support by the flexibility function approach is evaluated. A sample problem of free vibration of rectangular plate with simple supports on two opposite edges and a combination of elastic restraint and mid-edge point supports is considered. The numerical results indicate the relevance of the satisfaction of the point support compatibility condittions in relation to the magnitude of the elastic restraint, plate aspect ratio and mode number. The results bring out the fact that for the simulation of point support conditions, both the compatibility as well as the equilibrium at the point support need to be satisfied in an appropriate manner. Some typical results for combinations of elastic restraint and mid-edge point supports are also included.