Purpose

This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties.

Design/methodology/approach

Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM.

Findings

CCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method.

Originality/value

The proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.

中文翻译：

---

Chebyshev凸方法用于大不确定凸面结构的中频分析

目的

本文旨在开发一种有效的数值方法，用于大凸度不确定性的组合结构的中频分析。

设计/方法/方法

基于切比雪夫多项式逼近技术，提出一种结合有限元/统计能量分析（FE-SEA）框架的切比雪夫凸方法（CCM）来达到目的。在CCM中，通过使用凸参数的边际间隔，在不确定域上构造用于近似组合结构响应函数的Chebyshev多项式。通过将凸蒙特卡罗模拟应用于近似函数来计算响应函数的边界。介绍了一种相对改进的方法来评估CCM的截断顺序。

发现

当考虑的顺序相同时，CCM在准确性上优于CPM。此外，很容易考虑使用具有Chebyshev多项式的高阶项的CCM来处理较大的凸参数不确定性，并且可以通过相对改进方法有效地评估截断的阶数。

创意/价值

拟议中的CCM与FE-SEA相结合是在建筑物结构的中频振动声波分析中有效处理大凸不确定性的第一项努力。当涉及到大的凸不确定性时，它也有可能成为其他类型系统分析的有力工具。