摘要
根据弹性支承点处的协调条件,基于转换矩阵法,给出了两端简支、两端固定、悬臂梁、两端自由边界条件下欧拉连续梁的特征方程,并认为连续梁各跨段跨度不同、弯曲刚度不同、单位长度质量不同,且中间带弹性支承。通过理论和数值分析,将采用转换矩阵法分析得到的结果与三力矩方程法分析得到的结果进行对比,验证了方法的正确性,最后分析了中间弹性支承刚度和边界条件对连续梁模态的影响。
This paper deals with the modal analysis of a multi-span beam with intermediate flexible constraints and different boundary conditions. Each span of the continuous beam has a different span, a different stiffness and the mass per unit length, which is assumed to obey Euler beam theory. Considering the compatibility requirement on each constraint point, characteristic equations for a simply supported beam, a cantilever beam, a fixed-fixed beam, a free-free beam are presented. Based on the theoretical and numerical analysis, the comparison between the current method （transfer matrix method） and a conventional method （equation of three moments method） is conducted for the validity. Finally, some numerical results are shown to present the influence of intermediate support stiffness and boundary conditions on the mode of multi-span beams.
出处
《工程力学》
EI
CSCD
北大核心
2010年第9期80-85,共6页
Engineering Mechanics
基金
国家自然科学基金项目(50578046
90715025)
广东省自然科学基金项目(07005930)
广州市科技计划项目(08B72070029)
关键词
工程力学
模态分析
转换矩阵法
连续梁
弹性支承
engineering mechanics
modal analysis
transfer matrix method
continuous beam
elastic support
