Closed form solutions for the dynamic response of Euler–Bernoulli beams with step changes in cross section

This paper provides an analytical solution for the dynamic response of a discontinuous beam with one step change and an aligned neutral axis. The case of free–free boundary conditions is considered to obtain direct frequency response functions due to harmonic force or couple excitation at either end location. This behavior is confirmed through a series of experimental tests and via comparison to receptance coupling methods.