摘要
采用欧拉-伯努利梁理论求解等直梁的固有频率存在一定的误差,而考虑剪切变形及转动惯量影响的铁摩辛柯梁理论求解的固有频率较为精确.结合工程实际,在常用设计参数范围内,以矩形、圆形、薄壁圆管、工字形和箱形等工程常用典型截面的简支混凝土梁或钢梁为研究对象,计算分析了欧拉-伯努利梁理论求解横向振动固有频率的误差.计算结果表明:矩形、圆形截面混凝土梁的第1阶频率误差均在5%以内,可满足工程需要;工字形、箱形、圆管截面钢梁的第1阶频率误差,只有在高跨比较小时方可满足5%的限值;而对于第2阶及更高阶频率,误差通常远远超过5%,即该理论不再适用.
Using the Euler-Bernoulli beam theory to calculate the transverse vibration natural frequency of uniform cross section beam exists certain error.The solution of the Timoshenko beam theory considering the influence of shear deformation and rotational inertia can be sufficiently precise.In combination with the engineering practice,within the common scope of design parameters,the calculation error of natural vibration frequency based on the Euler-Bernoulli beam theory has been computed about the rectangular section,the circular section,the thin circular tube section,the I-shape section and the box section for simply supported concrete or steel beam.The results show that,using the Euler-Bernoulli beam theory,for the rectangular section and the circular section concrete beam,the calculation error of the first natural vibration frequency is usually less than 5%,which can meet the engineering need.For the I-shape section,the box section and the thin circular tube section steel beam,the calculation error of the first natural vibration frequency is not more than 5% only when the beam＇s depth-span ratio is small.And concerning the second or higher frequencies,the calculation errors are often far more than 5%,so Euler-Bernoulli beam theory does not work well.
出处
《郑州大学学报（工学版）》
CAS
北大核心
2010年第5期48-51,共4页
Journal of Zhengzhou University（Engineering Science）
基金
河南省2009年度高等学校青年骨干教师资助计划
关键词
简支梁
横向振动
固有频率
误差分析
simply supported beam
transverse vibration
natural vibration frequency
error analysis
