Structures with varying discontinuities and curvatures: A dynamic analysis approach by the p-version finite element method

The present paper investigates the geometrically nonlinear time domain dynamic analysis of a coupled Timoshenko beam-beam or beam-arch mechanical system. The coupled structure is modelled with a variable discontinuity in an elastic layer, which represents a real case from technical practice where there is no continuous distribution of the elastic layer or the stiffness of the layer is changed by other influences at different locations. A modified p-version finite element method is developed for the vibrations of a shear deformable coupled beam system with a discontinuity in an elastic layer. The main contribution of this work is the discovery of coupled effects and phenomena in the simultaneous vibration analysis of varying discontinuity and varying curvature of the newly modelled coupled mechanical system. New general mode shapes are presented, and the forced vibrations in the time domain are analyzed using the Newmark method. The study compares the results for various locations and types (size) of discontinuity in an elastic coupling layer and various curvatures of the lower supported beam. It explains the cases in which the influence of curvature takes precedence over discontinuity and vice versa in achieving a steady-state regime of vibrations. The analysis results are valuable and have broader applications in the field of solids and structures.