功能梯度材料梁在后屈曲构形附近的自由振动  

Free vibration of FGM Euler beam with post-buckling configuration subjected to axial force

作　　者：李清禄[1] 李世荣[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《振动与冲击》2011年第9期76-78,135,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金(10872083);教育部博士点基金(200807310002)

摘　　要：基于轴线可伸长杆的几何非线性理论,建立了由陶瓷和金属两种材料组成的功能梯度(FGM)梁在轴向载荷作用下后屈曲横向自由振动的精确模型,采用打靶法数值求解了一端可移简支一端固定的功能梯度梁在后屈曲附近的小振幅自由振动,获得了线性振动的响应,给出了不同梯度指标下FGM梁前三阶固有频率与载荷之间的特征关系曲线。数值结果表明,屈曲前各阶频率随轴向力的增加而降低,而屈曲后轴向力对各阶频率影响不同。Based on geometrically non-linear theory for axially extensible beams,an exact mathematical model of post-buckling transverse free vibration of FGM beams made of metal and ceramic subjected to axial force was derived.By using shooting method,pre-buckling and post-buckling free vibrations of one end simply supported and other end fixed Euler FGM beam were solved and characteristics curves of the lowst three orders of non-dimensional frequencies versus load parameter of FGM beams under different graded indexes were plotted.The numerical results show that all the frequencies of unbuckled beams decrease continuously with the increment of load.However,when the beams are in post-buckled state,the effect of axial force on each order of natural frequency is variant.

关 键 词：功能梯度梁 轴向力 自由振动 频率 打靶法 

分 类 号：O343[理学—固体力学]