A NEW APPROACH FOR THE CONTINUUM REPRESENTATION OF POINT SUPPORTS IN THE VIBRATION ANALYSIS OF BEAMS

The formulation of a new approach for the representation of point supports in the analysis of plates and its application to various problems of point supported plates was presented in earlier studies. The application of this approach to the vibration analysis of beams with intermediate point supports is presented in this paper. This approach is based on the use of a flexibility function, representing the distribution of a fictitious elastic foundation of the beam, which is such that it has a zero value at the point support location but assumes large values resulting in negligible restraint over the rest of the span of the beam. The application of this approach is demonstrated by considering the free vibration of a simply supported beam with point supports. The results obtained by using this approach are compared with those obtained by using the method based on the representation of the concentrated reaction at the point support location by a Fourier series expansion of the impulse function. The fictitious foundation approach for the simulation of intermediate point supports presented in this paper provides a method of absorbing the discrete discontinuities in the force field in the interior of the beam and obtaining a continuum representation in a single domain, namely that of a simply supported beam. © 1990.