高频弯曲振动梁的随机参数能量有限元分析

张猛; 陈花玲; 祝丹晖; 张文博; 孔祥杰

doi:10.7652/xjtuxb201311014

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高频弯曲振动梁的随机参数能量有限元分析

更新时间：2025-07-09

- 高频弯曲振动梁的随机参数能量有限元分析
- Stochastic Parameter Energy Finite Element Analysis for High-Frequency Flexural Vibration Beam
- 西安交通大学学报 2013年47卷第11期页码：76-80
- 作者机构：
  
  西安交通大学机械工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2013-04-09。作者简介: 张猛(1989—),男,硕士生;陈花玲(通信作者),女,教授,博士生导师。基金项目: 国家自然科学基金资助项目(11172222)
- DOI：10.7652/xjtuxb201311014
  中图分类号： TB123
- 网络首发：2013-11-10，
  
  纸质出版：2013
- 稿件说明：
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张猛, 陈花玲, 祝丹晖, 等. 高频弯曲振动梁的随机参数能量有限元分析[J]. 西安交通大学学报, 2013,47(11):76-80.

Stochastic Parameter Energy Finite Element Analysis for High-Frequency Flexural Vibration Beam[J]. 2013, 47(11): 76-80.
张猛, 陈花玲, 祝丹晖, 等. 高频弯曲振动梁的随机参数能量有限元分析[J]. 西安交通大学学报, 2013,47(11):76-80. DOI： 10.7652/xjtuxb201311014.

Stochastic Parameter Energy Finite Element Analysis for High-Frequency Flexural Vibration Beam[J]. 2013, 47(11): 76-80. DOI： 10.7652/xjtuxb201311014.

摘要

为了研究单个结构参数值遵循均匀分布规律随机变化时梁的高频振动响应统计特性

提出了随机参数能量有限元方法。该方法利用传统能量有限元方法

得到了确定梁结构能量密度响应的解析解

运用连续型随机变量的期望和方差公式

得到参数随机时系统任意位置处响应的均值和方差

并与能量密度模态解的蒙特卡罗仿真结果进行了比较。梁的截面宽度、高度及密度随机变化的响应统计特性的对比结果表明

响应方差对截面宽度的变化最敏感

对密度最不敏感

能量密度的方差随梁上位置坐标的增大呈先增大后减小的趋势

在激励点处取得最大值。为了保证系统响应值的稳定

在结构设计时尤其要注意保证截面高度的精度。

Abstract

To statistically analyze high-frequency vibration response when a parameter of beam structure is randomly and evenly distributed

a method called stochastic parameter energy finite element analysis(SPEFEA)is proposed. The energy density response of a deterministic beam is acquired by the traditional EFEA. Then adopting the expectation and variance formulas of continuous random variable

the mean and variance values at any position are acquired for uncertain parameter case. Monte Carlo simulations of analytical modal solution are conducted and compared with SPEFEA. The statistic features of energy density response

varying with beam section width

height and density

are investigated. It is found that the response variance gets most sensitive to the section height and least sensitive to the mass density. The energy density variance increases firstly then decreases with the increasing location coordinates

and reaches maximum at the exciting point. Special attention should be paid to the precision of section height in structure design to ensure the system stability.

关键词

Keywords

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