Transcendental dynamic stability functions for beams carrying rigid bodies

This paper shows how the transcendental dynamic stability functions can be used to determine the natural frequencies of a beam system carrying a rigid body. The dynamic stability functions used here satisfy the partial differential equation governing the flexural motion of Euler–Bernoulli beams exactly. The boundary and continuity conditions are expressed in a convenient matrix form by assembling the dynamic stiffness coefficients. This yields a determinantal frequency equation.