### IJMSD | 美国伊利诺伊大学芝加哥分校A.A. Shabana教授：固体和液体名义几何与力的度量

1.        因运动与力的定性、定量名义度量有助于更好地理解系统动力学，本文提出了一种新的基于连续介质的名义度量，用以表征振动与力；

2.        借助物质点法，新名义度量独立于推导动力学方程使用的列式方法和广义坐标；该新名义度量源于偏微分方程描述的连续介质力学平衡方程和Frenet几何标架；

3.        使用数据驱动科学（data-driven-science, DDS）方法定义了：一个具有名义曲率和扭转的名义连续空间曲线；一个包含所有合力（含惯性力）的名义瞬时运动平面（instantaneous motion plane, IMP）；以及一个合力沿其分量为零的名义瞬时零力轴（instantaneous zero-force axis, IZFA）;

4.        虽然使用物质点方法无需引入与姿态相关的转动方程，但IMP和IZFA的概念可用来定义会导致事故（如翻车的情况）的重要力矩分量的瞬轴。

Highlights:

1.        Because qualitative and quantitative nominal measures of the kinematics and forces contribute to better understanding of the system dynamics, this paper proposes developing new continuum-based nominal measures for characterization of oscillations and forces.

2.        By using a material-point approach, these new nominal measures, which have their roots in the continuum-mechanics partial-differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion.

3.        The paper uses a data-driven-science (DDS) approach to define a nominal continuum space-curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP) which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero-force axis (IZFA) along which the resultant of all forces vanishes.

4.        While the use of the material-point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment component, which can lead to accidents such as in the case of vehicle rollovers.

Abstract:

Understanding solid- and fluid-inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents. Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity, having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics. This paper proposes developing new continuum-based nominal measures for the characterization of the oscillations and forces. By using a material-point approach, these new nominal measures, which have their roots in the continuum-mechanics partial-differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion. The paper proposes a data-driven-science approach to define a nominal continuum space-curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP), which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero-force axis (IZFA) along which the resultant of all forces vanishes. While using the material-point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components, which can lead to accidents such as in the case of vehicle rollovers.

《国际机械系统动力学学报（英文）》（International Journal Mechanical System Dynamics, IJMSD ）由来自12个国家的15位院士、14位国际学会主席、13位其他国际期刊主编等53位科学家和国际出版巨头美国Wiley出版社合作创立。IJMSD 旨在为用机械系统动力学科学与技术为提升现代装备设计、制造、试验、评估和使用全生命周期性能提供先进的理论、软件、方法、器件、标准，为全球科学家和工程专家提供广泛的机械系统动力学国际交流平台。IJMSD 强调从“系统”视角及系统级工具理解动力学，所涉及的机械系统不仅包括各种不同尺度的机械系统和结构，还包括具有多物理场/多学科特征的综合机械系统。

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