VIBRATIONS OF ELASTICALLY MOUNTED MASS SUPPORTED ON SYMMETRICALLY CROSSED BEAMS

This study presents a novel method to analyze the vibration of an elastically mounted concentrated mass supported on the joint of symmetrically crossed beams with flexible foundation. Analytical and exact solutions of the free and forced vibration responses of the system are also derived. Herein, the dynamics of the mounted mass and the crossed beams are expressed as two-way state-flow (TWSF) graph models, in which the interactions between the components are considered. Based on the proposed model, the frequency responses of the displacement of the mounted mass and every beam are derived using a topological method. Moreover, the force transmissibility from the vibrating mass to the foundation and the frequency equation are obtained. The derived results are expressed in both analytical and closed forms. Also presented herein are some special cases including identical structure properties for each beam, simply supported boundary for each beam, mass directly mounted on the beams, and their combinations.