Study of Forced Transverse Vibrations of Elastic Hinge-Operated Rod Taking Into Account Rotative Movement

Abstract

The forced transverse oscillations of an elastic hinge-supported rod under the action of a normal concentrated time-periodic force are investigated. The problem is solved by the method proposed in [1] using combined conditions, including the dynamic impact on the rod and the rotational motion relative to the bending wave front. In the framework of the linear theory of thin rectilinear inextensible rods the equation of motion and the system of equations of transverse vibrations of an elastic rod are obtained using the Hamilton-Ostrogradsky principle. The solution of the problem is built in the form of a number of own forms of vibrations. Two types of forced transverse oscillations and new resonant frequencies were obtained. Numerical results of calculations are given in the form of tables, graphs; the analysis of the results is provided.