Analytical approximate solutions to large amplitude vibration of a spring-hinged beam

Large amplitude free vibrations of beams experiencing a severe dynamic environment are often encountered in many practical engineering structures, such as aerospace, automobile and other slender or light weight structures. In practical engineering structures, depending on the end support flexibility, the end of the beam can be treated as elastically restrained against rotation. By assuming elastic rotational springs with specific values of rotational stiffness to represent the type of support, one could make the boundary conditions more realistic. The spring constant, which is a measure of the support rotational flexibility, is an input for the analysis. The classical boundary conditions are obtained as the limiting cases of the spring constant tending to zero for simple supported conditions and tending to infinity for clamped conditions.