Simulation of Dissipation in Solids

项目负责人姓名，单位：Adnan Akay，卡内基梅隆大学项目编号：固体耗散模拟项目摘要：该项目涉及固体耗散的建模和模拟。虽然常见的耗散形式，如内部阻尼和接触阻尼在动力学中起着非常重要的作用，但耗散仍然被视为一种经验现象，没有基于第一性原理的描述。固体中的耗散通常描述动能向热能的转换，例如，声波穿过固体时激发其原子并提高其能级。原子振荡增加的动能决定了固体的热容，假设它们处于热平衡状态。固体耗散的模拟涉及到一个振荡子的三维晶格，振荡子代表用弹簧相互连接的原子。弹簧表示由原子之间的非线性势产生的位移相关力。实现这一目标的具体研究任务从一维非线性连接振荡器阵列开始，以数值方式研究不可逆性和均分性的条件。然后将模拟扩展到包含杂质的非理想晶格，以描述实际固体，以研究它们在波数（和频率）转换中的作用。这项工作的一个重要方面将是确定模拟规模的下限，以正确描述固体中的耗散，并确定量化固体耗散特性的方法。拟议的调查还将有助于澄清模糊阻尼固有的理论要求，将它们置于关于能量均分和能量不可逆吸收的更基本的基础上。

PI's Name, Institution : Adnan Akay, Carnegie Mellon UniversityProposal NumberProposal Title: Simulation of Dissipation in SolidsProject Abstract This project concerns modeling and simulating dissipation in solids. Although common forms of dissipation such as internal damping and contact damping have a very important role in dynamics, dissipation is still treated as an empiricalphenomenon without a description based on first principles. Dissipation in solids often describes conversion of kinetic energy to heat as in, for example, a sound wave passing through a solid exciting its atoms, and raising their energy level. The increased kinetic energy of the oscillations of atoms define the heat capacity of a solid with the assumption that they are inthermal equilibrium. Simulation of dissipation in a solid involves a 3-D lattice of oscillators that represent atoms connected to each other with springs. Springs represent displacement-dependent forces thatresult from the nonlinear potential between the atoms. The specific research tasks to accomplish this goal begin with a one-dimensional array of nonlinearly connected oscillators to investigate numerically the conditions of irreversibility and equipartitioning. The simulations will then be extended to nonideal lattices that include impurities to describe real solids to investigate their role in wavenumber (and frequency)conversion. An important aspect of this effort will be to determine the lower limit of the size of simulations to correctlydescribe dissipation in a solid and determine means to quantify dissipation characteristics of solids. The proposed investigation will also help clarify the theoretical requirements inherent in fuzzy damping by putting them on a more fundamental footing regarding energy equipartition and irreversible absorption of energy.