摘要
利用汉密尔顿原理推导出了自由阻尼悬臂梁的控制方程,计算了各阶模态自由阻尼悬臂梁的振动频率;然后根据模态叠加的方法构造悬臂梁的挠度函数,再利用虚功原理推导出集中力突然撤去情况下的自由阻尼悬臂梁瞬态响应近似解析解.算例分析表明:推导的公式准确可靠,且该方法简单,便于应用于工程计算.
The vibration equations for unconstrained damped cantilever beam are derived by using Hamilton′s principle,and the natural frequencies for each of modes of cantilever beam are obtained.The deflection of cantilever beam is established by mode superposition.Approximate analytical solutions to the transient response of unconstrained damped cantilever beam when the concentrated force is withdrawn suddenly are obtained.Numerical results show that equations are accurate and reliable.The method is simple,and can be easily used in engineering application.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2009年第11期108-110,共3页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(10572150)
关键词
悬臂梁
自由阻尼
瞬态响应
汉密尔顿原理
模态叠加
cantilever beam
unconstrained damping
transient response
Hamilton′s principle
modes superposition
