摘要
基于Adomian修正分解法研究悬臂裂纹梁的稳定性,悬臂梁的自由端具有弹簧支承和轴向随从力。将梁的裂纹模拟为无质量的等效扭转弹簧。通过Adomian修正分解法可以把裂纹梁的特征微分方程转换成递归代数公式,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的量纲一固有频率及相应的振形函数解析表达式。通过与前人的计算结果比较,验证了所提方法的有效性。讨论裂纹位置和深度对颤振或屈服失稳的临界随从力的影响。讨论不同失稳形式时裂纹梁支承的临界弹簧刚度。数值计算结果表明,当裂纹位于悬臂梁固定端附近时,对梁的固有频率影响最大。研究还表明裂纹的存在有可能提高梁的稳定性。
A stability analysis of a cracked cantilever beam subjected to a follower compressive load is presented by using Adomian modified decomposition method （AMDM）. The free end of the cantilever beam is restrained by a translational spring and subjected to a follower force. The crack is modeled as an equivalent massless rotational spring. Based on the AMDM the governing differential equation for this cracked beam becomes a recursive algebraic equation. By using boundary conditions and continuity/jump condition equations at crack location, the dimensionless natural frequencies and corresponding closed-form series solution of mode shapes can be obtained simultaneously. The accurate and effective of the proposed method are verified by comparing the results using the AMDM to those given in the literature. The effect of the location and depth of the crack on the critical compressive load for flutter or buckling instability of the beam is studied. Furthermore, the critical spring stiffness is calculated to determine the different type of instability of the beam under the follower compression. The numerical calculations results show that the maximum changes of the natural frequencies are observed when the crack is located near clamped end. It is also found that the stability of beam may be improved due to crack.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2014年第1期24-30,共7页
Journal of Mechanical Engineering
基金
国家自然科学基金(51265037)
江西省高等学校科技落地计划(KJLD12075)
教育部留学回国人员科研启动基金
江西省教育厅科技(GJJ13524)资助项目
关键词
裂纹梁
Adomian修正分解法
随从力
屈服
颤振
cracked beam
adomian modified decomposition method
follower force
buckling
flutter
