PLANAR VIBRATIONS OF A THIN ELASTIC ROD WITH CIRCULAR CROSS SECTION

Based on the Kirchhoff's theory the planar vibrations of a thinelastic rod with circular cross section are studied. The dynamical equationsof the rod are established in the Frenet coordinates of the centerline asthe reference frame. In the case of planar motion the torsional vibration isdecoupled from the flexural vibration. The torsional vibration of a rod witharbitrary planar shape and the flexural vibration of a straight rod withouttorsion under axial compression are discussed. It is proved that conditionsof Lyapunov's and Euler's stability of equilibrium of a straight rod instatic analysis are necessary conditions of its dynamic stability. Theinfluence of the axial force and the inertial effect of the cross section onthe natural frequency of flexural vibration is considered.