In this contribution, we present a space-time formulation of the Newmark integration scheme for linear damped structures under both harmonic and transient excitations. The incremental set of equations of motion and the Newmark approximations are transformed into their corresponding space-time equivalents. The dynamic system is then represented by one algebraic space-time equation only. This equation is projected into a coupled pair of space-time equations, which is solved via the fixed point algorithm. The solution is iteratively assembled by enrichments, each of which is decomposed by a dyadic product of spatial and temporal enrichment vectors. The evolution of the spatial enrichment vectors is investigated during convergence and interpreted by comparing them to the set of linear modes of vibration. The new method is demonstrated by means of four numerical examples, presenting not only the excellent convergence behavior and the numerical efficiency but also the limits of the proposed approach.

在此贡献中，我们提出了在谐波和瞬态激励下线性阻尼结构的Newmark积分方案的时空公式。增量的运动方程组和Newmark近似值被转换为它们相应的时空等效项。这样，动态系统仅由一个代数时空方程表示。该方程式被投影成一对时空方程式，通过定点算法求解。通过富集来迭代地组合解决方案，每个富集都由空间和时间富集矢量的二元乘积分解。在收敛过程中研究了空间富集矢量的演化，并通过将其与线性振动模式集进行比较来解释它们。