THE DYNAMICS OF A BEAM OF CHANGING CROSS SECTION

An investigation has been carried out to determine the response of a cantilever beam having a time-varying cross section, to a prescribed harmonic displacement at its support. The assumption of classical beam theory leads to a set of ordinary differential equations of the Mathieu type. A general solution to these non-homogeneous equations is developed and programmed for the IBM 7040 digital computer. The strong dependence of the lateral motion to the frequency of the support displacement and to the frequency of the changing cross section is investigated for a wide range of ratios of these frequencies. (Author)