The use of flexibility functions with negative domains in the vibration analysis of asymmetrically point-supported rectangular plates

Abstract

A new approach for the simulation of point supports as zeroes of a flexibility function representing a fictitious positive elastic restraint distribution over the boundary was presented in an earlier study, concerned mainly with rectangular plates with symmetric point supports. This paper is concerned with the extension of this flexibility function approach to more general cases of asymmetrically point supported rectangular plates which have simple supports on two opposite edges. First it is shown that sufficiently large negative values of the flexibility of the elastic restraint can simulate the free edge conditions accurately. Based on this, and with use of flexibility functions which cross over from positive to negative values or vice versa over the plate boundary, it is shown that zeroes of the function at arbitrary point-support locations can be easily obtained. Extensive numerical results are obtained for various combinations of boundary conditions, plate aspect ratios and types and locations of point supports. The results show that the flexibility function approach can handle with ease arbitrary locations of point supports by using flexibility functions having both positive and negative domains. A comparative study of this approach with the impulse function approach, based on the representation of the reaction at the point support as a Fourier series expansion of the impulse function, is also presented to bring out the superiority of the flexibility function approach.