Node-Locally-Based Smoothed Point Interpolation Method for Calculating Upper/Lower Bounds of Natural Frequency

doi:10.7652/xjtuxb201705023

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Node-Locally-Based Smoothed Point Interpolation Method for Calculating Upper/Lower Bounds of Natural Frequency

更新时间：2025-07-09

- Node-Locally-Based Smoothed Point Interpolation Method for Calculating Upper/Lower Bounds of Natural Frequency
- Vol. 51, Issue 5, Pages: 165(2017)
- 作者机构：
  
  大连理工大学船舶工程学院辽宁省深海浮动结构工程实验室,辽宁,大连,116024
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201705023
  CLC： O313.7
- Online First：10 May 2017，
  
  Published：2017
- 稿件说明：
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Node-Locally-Based Smoothed Point Interpolation Method for Calculating Upper/Lower Bounds of Natural Frequency[J]. 2017, 51(5): 165.
DOI：

Node-Locally-Based Smoothed Point Interpolation Method for Calculating Upper/Lower Bounds of Natural Frequency[J]. 2017, 51(5): 165. DOI： 10.7652/xjtuxb201705023.

摘要

针对传统有限元方法得到的刚度阵过硬导致所提供的固有频率上限值较为粗糙、点基光滑点插值方法得到的刚度阵过软导致所提供的固有频率下限值较为宽泛且存在时间不稳定性等问题

提出了点基局部光滑点插值法(NLS-PIM)。该方法将有限元和点基光滑点插值法相结合

对背景网格基础上形成的点基光滑域进行局部应变光滑

通过调整二者结合的权重来控制计算模型的整体刚度。研究发现

采用局部梯度光滑方法控制模型刚度而形成的点基局部光滑点插值法

克服了点基光滑点插值方法的时间不稳定性及有限元法的固有缺陷

且能提供更为精细的固有频率上下界区间。所提方法简便、实用、易于实现

可用于复杂问题求解。

Abstract

The traditional finite element method(FEM)gives over-hard stiffness and hence provides rough upper bounds for natural frequencies

but the node-based smoothed point interpolation method(NS-PIM)gives over-soft stiffness hence provides lower bounds with temporal instability for natural frequencies. A node-based locally smoothed point interpolation method(NLS-PIM)is thus proposed. FEM is combined with NS-PIM by conducting locally gradient smoothing operation on the node-based smoothing domains based on background cells. And the stiffness can be adjusted by changing the parameter α

which is the proportion of the locally smoothed domain over each background cell. It is found that the proposed method can successfully overcome the temporal instability of NS-PIM and the inherent shortcomings of FEM and provide much tighter upper and lower bounds for natural frequencies due to the controlled model stiffness by the node-based locally gradient smoothing operation.

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references

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