distributed parameter

简明释义

分布参数

英英释义

例句

1.Heat transfer in a rod can be modeled as a distributed parameter 分布参数 system to analyze temperature variations along its length.

杆中的热传导可以建模为一个分布参数 distributed parameter 系统，以分析其长度上的温度变化。

2.Engineers often use distributed parameter 分布参数 models to simulate the behavior of structures under dynamic loads.

工程师经常使用分布参数 distributed parameter 模型来模拟结构在动态载荷下的行为。

3.The analysis of the beam was conducted using a model that incorporates distributed parameter 分布参数 systems to account for varying stiffness along its length.

该梁的分析采用了一个模型，该模型结合了分布参数 distributed parameter 系统，以考虑其长度上的刚度变化。

4.The distributed parameter 分布参数 model helps predict the response of the system to external disturbances effectively.

该分布参数 distributed parameter 模型有助于有效预测系统对外部干扰的响应。

5.In control theory, distributed parameter 分布参数 systems are essential for modeling processes that vary over space and time.

在控制理论中，分布参数 distributed parameter 系统对于建模随空间和时间变化的过程至关重要。

作文

In the field of engineering and applied mathematics, the concept of distributed parameter systems plays a crucial role in understanding complex dynamics. Unlike lumped parameter systems, which assume that parameters such as mass, stiffness, and damping are concentrated at discrete points, distributed parameter systems consider these parameters to be spread out over a continuous domain. This distinction is essential when analyzing systems that exhibit spatially varying characteristics, such as beams, plates, and fluids.One of the primary advantages of using distributed parameter models is their ability to provide a more accurate representation of physical phenomena. For instance, in structural engineering, a beam subjected to loading will not only deform at a single point but will experience a distribution of stresses and strains along its length. By employing distributed parameter models, engineers can predict the behavior of the entire structure under various loading conditions, leading to safer and more efficient designs.Moreover, distributed parameter systems are often described by partial differential equations (PDEs), which account for the variation of parameters with respect to both time and space. This mathematical framework allows for the analysis of dynamic systems where the response depends on multiple variables. For example, in heat transfer problems, the temperature distribution within a solid object can be modeled using PDEs, which capture how heat flows through the material over time.The application of distributed parameter systems extends beyond structural analysis. In control theory, distributed parameter models are used to design controllers for systems like temperature regulation in chemical reactors or fluid flow in pipelines. These systems require a sophisticated understanding of how changes in one part of the system affect the whole, necessitating the use of distributed parameter approaches.In addition to engineering, the concept of distributed parameter systems is also prevalent in fields such as physics and biology. For example, in population dynamics, the spread of a species across a geographical area can be modeled as a distributed parameter system, where the population density varies continuously in space and time. This allows researchers to study the effects of environmental changes on species distribution more effectively.Despite the benefits of distributed parameter models, they also present challenges. The complexity of the governing equations often requires advanced numerical methods for solutions, which can be computationally intensive. Additionally, obtaining accurate boundary and initial conditions can be difficult, necessitating careful consideration during the modeling process.In conclusion, the understanding and application of distributed parameter systems are vital in various scientific and engineering disciplines. They provide a powerful framework for analyzing complex systems where parameters are not confined to discrete points but are instead distributed across a continuum. As technology continues to advance, the importance of distributed parameter modeling will only increase, enabling more precise predictions and innovative solutions to real-world problems.

在工程和应用数学领域，distributed parameter 系统的概念在理解复杂动态方面发挥着至关重要的作用。与假设质量、刚度和阻尼等参数集中在离散点上的集中参数系统不同，distributed parameter 系统考虑这些参数在连续域上分布。这一区别在分析表现出空间变化特性的系统（如梁、板和流体）时至关重要。使用 distributed parameter 模型的主要优点之一是它们能够提供对物理现象更准确的表示。例如，在结构工程中，承受载荷的梁不仅会在一个点上变形，而是会沿其长度经历应力和应变的分布。通过采用 distributed parameter 模型，工程师可以预测整个结构在各种载荷条件下的行为，从而设计出更安全、更高效的结构。此外，distributed parameter 系统通常由偏微分方程（PDE）描述，这些方程考虑了参数相对于时间和空间的变化。这种数学框架允许分析动态系统，其响应依赖于多个变量。例如，在热传递问题中，固体物体内部的温度分布可以使用 PDE 建模，这些方程捕捉了热量如何随时间在材料中流动。distributed parameter 系统的应用不仅限于结构分析。在控制理论中，distributed parameter 模型用于设计控制器，以调节化学反应器中的温度或管道中的流体流动。这些系统需要对系统某一部分的变化如何影响整体有深入的理解，因此需要采用 distributed parameter 方法。除了工程领域，distributed parameter 系统的概念在物理学和生物学等领域也很普遍。例如，在种群动态中，物种在地理区域内的扩散可以建模为 distributed parameter 系统，其中种群密度在时间和空间上连续变化。这使研究人员能够更有效地研究环境变化对物种分布的影响。尽管 distributed parameter 模型具有诸多优势，但它们也面临挑战。治理方程的复杂性通常需要先进的数值方法来求解，这可能会消耗大量计算资源。此外，获得准确的边界和初始条件可能很困难，因此在建模过程中需要仔细考虑。总之，理解和应用 distributed parameter 系统在各个科学和工程学科中至关重要。它们提供了一个强大的框架，用于分析参数不是局限于离散点而是分布在连续体上的复杂系统。随着技术的不断进步，distributed parameter 建模的重要性只会增加，使我们能够更精确地预测和创新解决现实问题。