Free vibration analysis of Timoshenko beam

Bernoulli-Euler beam theory that analyses transverse vibration when only inertia force and bending forces are taken into consideration, gives logical results for slender beams but is not preferred for deep and short beams. In this situation, Timoshenko beam theory that take shear impacts; which become important in deep beams and short beams; into consideration, should be used.In this study, the free vibration of Timoshenko beam model, which effects of rotating moment of inertia that is formed from three different zones are also taken into consideration, is analyzed by using dynamic stiffness matrix method and it is aimed to attain to its natural frequencies. The beam is resting on two layered soil that has different specifications. Three different mathematical calculation models are developed for three zones. For the second zone, base specifications are modeled with displaced linear elastic springs and for the third zone, they are modeled with rotational linear elastic springs.Iterative approach is used for the solution of correlation that is developed from mathematical calculation models. Computer program for four different boundary conditions that covers all probabilities is developed in iterative approach and the program flow diagram is presented. By explicating changes in length of the beam, specifications of the base that it rests on, relative rigidity and changes in dynamic parameters in program data, numeric outcomes are presented in graphics.