Dynamic characteristic analysis of beam structures with nonlinear elastic foundations and boundaries

The research of structures with elastic foundations has attracted extensive attention and many dynamic modeling and analysis methods for beam structures with elastic foundations have been proposed in current mainstream research. However, the low-dimension and high-accuracy models are more in line with the requirements of engineering practice. Hence, this paper aims to establish a novel nonlinear dynamic model of beam structures with nonlinear elastic foundations and boundaries. The global modes are first obtained by using the global mode method, and the forced vibration response analysis of the beam structures is subsequently carried out by developing a corresponding solving procedure. Thereafter, case studies are conducted on a cantilever beam with nonlinear elastic foundations and boundaries to validate the established nonlinear dynamic model. The consistency of the results obtained by the established model and finite element analysis demonstrates the accuracy of the established model. Finally, the effects of elastic foundations, boundaries, external excitation amplitude and nonlinear coupling terms on the dynamic characteristics of the cantilever beam structure are analyzed through the comparative case studies.