VIBRATIONS OF A FINITE-LENGTH BEAM WITH AN AXIALLY MOVABLE LOAD

In-plane motion of an elastic rod with an axially movable load is anal yzed. The constitutive equations which take into account compressibili ty and shear stresses are used. The effect of rotary inertia is also c onsidered. The complete system of nonlinear differential equations whi ch describe the motion of the rod is formulated. Equations of motion a re derived for the case when deformations are not small. A special cas e when two continual loads are moving along the rod in opposite direct ions is considered. After linearization the eigenvalues of the vibrati ons of the rod are obtained. The corresponding critical value of the v elocity is estimated analytically. The vibration properties of the non linear and linearized system are compared.