Application of Matrix Iteration for Determining the Fundamental Frequency of Vibration of a Continuous Beam

-In the previous paper, the use of matrix iteration to determine the natural frequencies of vibration of continuous beam system using the concept of wave propagation in a prismatic bar is reported. The natural frequencies of vibration obtained from the formulated model were compared with the values obtained from literature and those of the exact solution. An error of 28% and 30% was observed when the fundamental frequency of vibration obtained from the previous model was compared with that obtained from literature and the exact solution. In the present study, an improved mathematical model is formulated to determine the fundamental frequency of vibration of a continuous beam as a structural system with distributed mass using mode shape concept. In the course of the system’s oscillation, the displacements produced by the force of inertia is assumed to have the shape of a particular vibration mode and in harmonic with the particular modal frequency. A numerical example was given to demonstrate the applicability of the present model. The fundamental frequency value obtained from the present model was found to improve by 27.4% and almost identical to the exact fundamental frequency value and that obtained literature.