ON RANDOM TRANSVERSE VIBRATIONS OF A ROTATING BEAM WITH A TIP MASS: METHOD OF INTEGRAL EQUATIONS

摘要

The integral-equation method is studied to establish analytic lower bounds of the first and second natural frequencies of transverse vibrations of a uniform rotating beam, elastically restrained at one end and carrying a tip mass at its free end. The equivalent mathematical problem consists of a fourth-order differential equation and boundary conditions dependent on the eigenvalue parameter. The random element in the problem is an arbitrary coefficient that is present in the boundary condition for the elastically restrained end. It is proved that the spectrum of this problem consists of an unbounded sequence of positive eigenvalues with no accumulation points in the finite complexλ-plane. Numerical results for the analytic lower bounds of the first eigenvalues are presented