论文标题
结构保存算法，用于模拟线性抑制声系统
Structure preserving algorithms for simulation of linearly damped acoustic systems
论文作者
论文摘要
用于构建时间稳定算法的能量方法对非线性问题的应用有更多的兴趣，因为可以从系统能量的保护中推断出数值稳定性。另外，可以构建符号积分器，以保留系统的符号形式。该方法已为哈密顿系统建立，并在工程问题中应用了许多应用。在本文中，提出了这种方法向非保守的声学系统的扩展。离散的保护定律（相当于能源持续方案）是针对线性阻尼的系统得出的，并结合了外力的作用。此外，在连续和离散的情况下分析了互合结构的演变。检查现有方法，并使用集总振荡器作为元素模型设计新方法。所提出的方法扩展到分布式系统的情况，并通过案例研究的案例研究，该案例研究振动弦弹性弹跳刚性障碍物。
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic integrators may be constructed that preserve the symplectic form of the system. This methodology has been established for Hamiltonian systems, with numerous applications in engineering problems. In this paper an extension of such methods to non-conservative acoustic systems is presented. Discrete conservation laws, equivalent to that of energy-conserving schemes, are derived for systems with linear damping, incorporating the action of external forces. Furthermore the evolution of the symplectic structure is analysed in the continuous and the discrete case. Existing methods are examined and novel methods are designed using a lumped oscillator as an elemental model. The proposed methodology is extended to the case of distributed systems and exemplified through a case study of a vibrating string bouncing against a rigid obstacle.
