Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical basis and mostly relies on numerical experiments as the only means of assessment. This contribution thoroughly reviews existing methods and connects them to established linear algebra results to derive rigorous eigenvalue bounds and condition number estimates. Our results cover some of the most successful mass scaling techniques, unraveling for the first time well-known numerical observations.

翻译：质量缩放技术被广泛应用于结构动力学的有限元模型中，以提高显式时间积分方法的临界时间步长。尽管该领域多年来蓬勃发展，但仍缺乏坚实的理论基础，主要依赖数值实验作为唯一的评估手段。本文系统综述了现有方法，并将其与成熟的线性代数理论相结合，推导出严格的特征值边界和条件数估计。我们的研究涵盖了一些最成功的质量缩放技术，首次揭示了若干著名数值观测现象的理论本质。