mass matrix

简明释义

质量矩阵

英英释义

例句

1.The mass matrix 质量矩阵 plays a crucial role in finite element methods for simulating vibrations.

在有限元法模拟振动中，质量矩阵 mass matrix 起着至关重要的作用。

2.In robotics, the mass matrix 质量矩阵 is essential for calculating the dynamics of robotic arms.

在机器人技术中，质量矩阵 mass matrix 对于计算机器人手臂的动力学至关重要。

3.The diagonal elements of the mass matrix 质量矩阵 represent the mass distribution of the structure.

在质量矩阵 mass matrix 中，对角元素表示结构的质量分布。

4.In structural analysis, the mass matrix 质量矩阵 is used to determine the dynamic response of a building under seismic loads.

在结构分析中，质量矩阵 mass matrix 用于确定建筑在地震荷载下的动态响应。

5.When performing modal analysis, engineers must first assemble the mass matrix 质量矩阵 of the system.

在进行模态分析时，工程师必须首先组装系统的质量矩阵 mass matrix。

作文

In the field of engineering and physics, the concept of a mass matrix is essential for understanding the dynamics of systems. A mass matrix is a mathematical representation that describes the distribution of mass in a system, which can be used to analyze how forces affect the motion of objects. For instance, when considering a multi-body system, each body can have its own mass, and these masses must be considered together to understand the overall behavior of the system. The mass matrix plays a crucial role in this analysis by providing a framework to quantify the inertia of the system. To elaborate further, the mass matrix is typically represented as a square matrix, where each element corresponds to the mass properties of the bodies involved. The diagonal elements represent the individual masses of the bodies, while the off-diagonal elements can represent the coupling between different bodies due to their relative positions and orientations. This matrix is particularly important in finite element analysis, where complex structures are broken down into smaller, manageable pieces. Each piece has its own mass matrix, which contributes to the overall dynamics of the structure. One of the key applications of the mass matrix is in modal analysis, which is used to determine the natural frequencies and mode shapes of a system. By solving the eigenvalue problem associated with the mass matrix and the stiffness matrix, engineers can predict how a structure will respond to various dynamic loads, such as vibrations or impacts. This information is vital in designing safe and effective structures, from bridges to buildings. Moreover, in robotics, the mass matrix is utilized to control robotic movements. Each joint and link in a robot has its own mass, and understanding how these masses interact is crucial for precise movement. The mass matrix helps in calculating the necessary torques required at each joint to achieve desired motions. This application highlights the importance of the mass matrix in real-world scenarios, where precision and accuracy are paramount. In conclusion, the mass matrix is a fundamental concept in various fields of science and engineering. It provides a comprehensive way to analyze the effects of mass distribution on the dynamics of systems. By understanding the mass matrix and its implications, engineers and scientists can design better structures, improve robotic systems, and enhance our overall understanding of physical phenomena. As technology continues to advance, the importance of the mass matrix will only grow, making it an essential topic of study for future generations of engineers and physicists.

在工程和物理学领域，质量矩阵的概念对于理解系统的动态行为至关重要。质量矩阵是描述系统中质量分布的数学表示，可以用于分析力如何影响物体的运动。例如，在考虑多体系统时，每个物体可以具有自己的质量，这些质量必须一起考虑，以理解系统的整体行为。质量矩阵在此分析中发挥着关键作用，提供了一个量化系统惯性的框架。进一步阐述，质量矩阵通常表示为一个方阵，其中每个元素对应于所涉及物体的质量特性。对角线元素表示各个物体的质量，而非对角线元素则可以表示由于相对位置和方向而导致的不同物体之间的耦合。这个矩阵在有限元分析中尤其重要，在这种分析中，复杂结构被分解为较小、可管理的部分。每个部分都有自己的质量矩阵，这对结构的整体动态有贡献。质量矩阵的一个关键应用是在模态分析中，该分析用于确定系统的自然频率和模态形状。通过求解与质量矩阵和刚度矩阵相关的特征值问题，工程师可以预测结构在各种动态载荷（如振动或冲击）下的响应。这些信息对于设计安全有效的结构至关重要，从桥梁到建筑物。此外，在机器人技术中，质量矩阵用于控制机器人运动。机器人的每个关节和连杆都有自己的质量，理解这些质量如何相互作用对于精确运动至关重要。质量矩阵有助于计算每个关节所需的扭矩，以实现所需的运动。这一应用突显了质量矩阵在现实场景中的重要性，在这些场景中，精度和准确性至关重要。总之，质量矩阵是科学和工程各个领域的基本概念。它提供了一种全面分析质量分布对系统动态影响的方法。通过理解质量矩阵及其含义，工程师和科学家可以设计更好的结构、改善机器人系统，并增强我们对物理现象的整体理解。随着技术的不断进步，质量矩阵的重要性只会增加，使其成为未来工程师和物理学家学习的必修课题。