Vibration of a variable cross-section beam considering rotational inertia and viscous friction

Abstract

The paper describes free vibrations of a beam in the presence of viscous friction taking into account rotational inertia by a homogeneous partial differential equation of hyperbolic type. The equation involves elastic force, axial force, force of rotation, linear viscous friction force and inertial force of linear displacements. The analytical methods in determining eigenvalues and amplitude-frequency characteristics meets serious difficulties therefore finite difference method is used.