Oscillation of an elastic bar rigidly linked to a kinematically excited pendulum

Abstract

The oscillation of a mechanical system consisting of an elastic bar rigidly linked at the middle to a kinematically excited pendulum is studied. A system of integro-differential equations with appropriate boundary and initial conditions for the deflections of the bar axis and the rotation angle of the pendulum is derived using the Hamilton-Ostrogradsky principle. Given kinematic excitation conditions, the rotation angle is found as a solution to an inhomogeneous Hill equation in the form of a double power series in the amplitude of kinematic excitation. It is shown that the oscillation of the bar is the linear superposition of three oscillations