ABSTRACT
Previous chapters dealt with either buckling or vibration of an inhomogeneous beam. This chapter deals with the vibration of beams in the presence of axial loads. The formula suggesting a linear relationship between the natural frequency squared and the axial load is known to be exact for uniform beams with pinned or guided ends. Its approximate nature for other cases was established by Massonet (1940, 1972) and Galef (1968). In this chapter, we establish, in exact terms, the validity of this linear relationship for a certain class of inhomogeneous beams, under different boundary conditions.
