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.

本文研究了 Timoshenko 梁-梁或梁-拱耦合机械系统的几何非线性时域动态分析。耦合结构通过弹性层中的可变不连续性进行建模，这代表了技术实践中的真实情况，其中弹性层没有连续分布，或者层的刚度因不同位置的其他影响而改变。针对弹性层不连续的剪切变形耦合梁系统的振动，开发了一种改进的 p 版有限元方法。这项工作的主要贡献是在新建模的耦合机械系统的变化不连续性和变化曲率的同步振动分析中发现了耦合效应和现象。提出了新的一般振型，并使用 Newmark 方法分析了时域中的受迫振动。该研究比较了弹性耦合层中不同位置和类型（尺寸）的不连续性以及下部支撑梁的各种曲率的结果。它解释了在实现稳态振动状态时曲率的影响优先于不连续性的情况，反之亦然。分析结果很有价值，在固体和结构领域有更广泛的应用。