计算力学学报2016，Vol.33Issue(2)：171-181,11.DOI:10.7511/jslx201602006
初始纵横向荷载效应对薄板自振频率的影响分析
The analysis for the effect of both initial in-plane and transverse loads on the natural frequency of plates
摘要
Abstract
Firstly ,the strain energy expression ,the dynamic equilibrium differential equation and the element stiffness matrix are presented for plates considering the effect of both initial in‐plane and transverse loads via the energy variation principle .Then ,the approximate solutions of fundamental frequencies for four typical plates ,considering the effect of both initial in‐plane and transverse loads ,are derived by the Galerkin method ,based on the dynamic equilibrium differential equation .And the approxi‐mate solutions of the first three frequencies for a simply supported rectangular plate ,considering the effect of both initial in‐plane and transverse loads ,are solved by the Rayleigh method .The frequencies obtained by the finite plate element agree well with the approximate solutions ,the reliability and efficiency of the presented finite plate element and those frequency approximate solutions are verified . Finally ,the frequencies of plates influenced by the effect of both initial in‐plane and transverse loads and related factors are analyzed by numerical examples ,result show s that the key physical factors governing the effect of initial loads on the frequencies of plates are the initial loads (both in‐plane and transverse) , thickness and boundary condition etc .The effect of both initial in‐plane and transverse loads on funda‐mental frequency is more remarkable than that on high‐order frequencies .The frequencies influenced by initial in‐plane loads and initial transverse loads respectively follow the linear pattern and the parabolic pattern .关键词
初始纵向/横向荷载效应/薄板/自振频率/有限板单元/近似解Key words
the effect of both initial in-plane and transverse loads/plate/natural frequency/finite plate element/approximate solution分类
建筑与水利引用本文复制引用
刘德贵,周世军,王宁,张春涛..初始纵横向荷载效应对薄板自振频率的影响分析[J].计算力学学报,2016,33(2):171-181,11.基金项目
四川省教育厅项目（15ZB0122）；西南科技大学博士基金（14zx7138）资助项目． （）
