摘要
基于单集中力作用下半无限平面的应力分布公式,利用外载荷叠加原理,得到自平衡面内集中力系作用下薄圆盘的应力分布公式,通过积分计算进一步获得自平衡面内分布力系作用下薄圆盘的应力分布表达式。取切比雪夫多项式与边界函数的乘积作为容许函数,应用里兹法分别导出薄圆盘在任意面内静力荷载作用下的横向自由振动与屈曲的特征值方程,数值求解特征值方程得固有频率和屈曲荷载。与取幂级数和傅里叶级数乘积作为容许函数以及有限元结果对比验证了方法的快速收敛性和高精度。
Based on the stress distribution formulae of a semi-infinite plane under a single concentrated force,the in-plane stress distribution formulae of a thin disk under a self-balanced in-plane concentrated force system is obtained by using the principle of superposition of external loads.The stress distribution of the thin disk under the self-balanced in-plane distributed force system is further obtained by the integral calculation.Taking the product of the Chebyshev polynomial and the boundary functions as the admissible functions,the eigenvalue equations of transverse free vibration and buckling of a thin disk under arbitrary in-plane static loads are derived by means of the Ritz method.The eigenvalue equations are numerically solved to obtain the natural frequencies and buckling loads.The fast convergence and the high accuracy of the method are verified by comparison with the results the product of power series and Fourier series as admissible functions and finite element method.
作者
李国荣
周叮
李雪红
霍瑞丽
LI Guo-rong;ZHOU Ding;LI Xue-hong;HUO Rui-li(College of Civil Engineering,Nanjing Tech University,Nanjing 211816,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2021年第5期1001-1008,共8页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(51778285,51778289)
江苏省交通运输科技项目(2014Y01)。
关键词
横向振动
屈曲
薄圆盘
面内荷载
里兹法
transverse vibration
buckling
thin disk
in-plane load
Ritz method
