Abstract: According to the idea of measuring Young＇ s modulus using dynamic method, we establish the partial differential equation of transverse vibration of the bar. By using variable separation method, the general solution is obtained. On the analysis of boundary conditions of free vibration, we present a transcendental equation and the coefficients of the general solution. Also, by using graphic method in Matlab 7.0 environment, we obtain the approximate solution and high precision numerical solution to the first three order natural frequencies of the transverse vibration of the bar. The first three order vibration modes and nodes location are given by graphic, which consistent with the theoretical values in the textbook.

Key words: transverse vibration, natural frequency, graphic method, vibration modes