插值在求解结构动力响应中的应用
虽然在一般情况下，对结构设计和结构分析而言，静力问题是首先要面对的，而且是问题的主要方面，但有时动力荷载引起的破坏却是致命的，是引起结构毁灭性破坏的主要原因。例如，地震引起的结构倒塌破坏；风振动引起的大桥破坏。因此，在工程结构的研究、设计和安全性评价时，进行结构的动力反应分析是重要的。
结构动力学响应的数值计算一直是力学工作者研究的热点，本文主要考虑求解动力学响应的逐步积分法，通过比较多种不同的直接积分格式，对各自的优缺点有了较直观的了解。首先简要介绍了四种经典插值算法中心差分法、newmark法、Wilson、精细积分法；其次主要考虑了插值在求解结构动力学响应的逐步积分法中的应用，实现了袁晓彬等《基于二阶拉格朗日插值求解动力响应的逐步积分法》和《双参数hermite插值逐步积分求解结构动力响应》两篇文章给出的基于插值求解动力学结构响应的算法，并对结果与解析解进行了比较分析。
毕业论文关键字：拉格朗日插值；hermite插值；动力；振动；逐步积分
Application of Interpolation in Solving Structure Dynamic Response
Abstract：In the nature, in addition to static problems, there are a lot of power . Vibration problems such as building structures under earthquake action; Vibration problems of rotating machine unbalance force caused by the large machine foundation .
Although in general, the structural design and structural analysis, static problem is first of all have to face, but also is a major aspect of the problem, but sometimes the dynamic load caused by failure is fatal, is the main cause of the destruction of structure. For example, collapse earthquake induced structural vibration caused by wind; bridge damage; the plane hit nuclear power plant, building, Therefore, in the study, the engineering structure design and safety evaluation, dynamic response analysis of structure is important.
In view of the above problems, the classical interpolation algorithm and Yuan Xiaobin, " A New Step- by- step Integration Method Based on Quadratic Lagrangian Interpolation for Dynamic Response " and " A New Step- by- step Integration Method Based on 3-order Hermite Interpolation By Double-parameter for Dynamic Response" two articles carried out research and analysis. This paper mainly realizes the interpolation algorithm of Yuan Xiaobin, and analyzed the result
Keywords: Lagrange interpolation ; Hermite interpolation ; Power ; Edge detection
目录
目录 iii
1．绪论 1
1.1 研究背景和研究现状 1
1.2 课题研究的目的和意义 2
1.3 应用领域 3
1.4 研究内容 3
1.5 论文结构 4
2．求解结构动力响应的典型数值方法 5
2.1 中心差分法 5
2.2 Newmark法 6
2.3 Wilson-θ法 7
2.4 精细积分法 8
3．插值在求解结构动力响应方面的应用 10
3.1 基于二阶拉格朗日插值求解动力响应的逐步积分法 10
3.1.1 算法描述 10
3.1.2 算法实现 11
3.1.3 实验结果与分析 12
3.2 双参数hermite插值逐步积分求解结构动力响应 15
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