Vibrational analysis of a coupled damaged Timoshenko beam-arch mechanical system with von Kármán nonlinearities and layer discontinuity

The present study investigates vibrations in the nonlinear regime of a partially elastically connected beam with damage and either a curved or straight beam, focusing on the time domain. The mechanical system under consideration consists of two beams with varying discontinuities: one in an elastic layer and the other in a narrow cross-section area of the beam. To analyze the vibrations in this coupled system, a p-version finite element method is employed. This method allows for the examination of shear deformable beam-beam or beam-arch systems with small or large discontinuities in the elastic layer and cross-section area of the beam. The main contribution of this work lies in the dynamic analysis of a novel coupled geometrically nonlinear mechanical system. It has been discovered that in specific cases of combinations of discontinuities in the upper beam and elastic layer, a different energy transmission occurs, caused by geometrically nonlinear couplings of the nonlinearity of the elastic layer, to the lower arch, resulting in multiple cycles of oscillations executed by the system in the steady-state regime of vibrations. The analysis considers various scenarios, including the effects of the discontinuity in the viscoelastic connection layer, beam damage, and the varying curvature of the lower arch. General mode shapes are determined, and forced damped vibrations in the time domain are analyzed using the Newmark method. The findings from this dynamic analysis have broad applications in engineering and technical practice.