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。
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.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2013年第11期76-80,共5页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金资助项目(11172222)
关键词
能量有限元
梁结构
方差
energy finite element analysis
beam
variance
