Use of hypergraphs and complete structural numbers in the analysis of vibrating beam systems with non-linearly changing cross sections

The authors examine the flexural vibrations of a complex mechanical beam system with a piecewise linear variable cross section. A method of studying continuous vibrations of beam systems with positions of nonlinearly varying cross section is presented which makes use of hypergraphs and structural numbers and is distinguished by the fact that it permits an algebraic algorithmic computation of any dynamic response regardless of the degree of complexity of the system or of the function defining cross-sectional variability.