热环境中多孔功能梯度材料转动Timoshenko梁的自由振动特性分析

Free vibration characteristics analysis of a porous functionally graded material rotating Timoshenko beam in thermal environment

对于孔隙均匀分布的多孔功能梯度材料梁模型,考虑材料的温度依赖性质并确定梁的物理中面,利用Hamilton原理导出多孔功能梯度材料Timoshenko梁在热环境中转动时横向自由振动的控制微分方程并进行无量纲化处理.应用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,得到包含无量纲固有频率的等价代数特征方程.计算出热环境中多孔功能梯度材料转动Timoshenko梁在固支-固支(C-C)、固支-简支(C-S)、简支-简支(S-S)和固支-自由(C-F)四种边界条件下横向自由振动的固有频率.将其退化所得无量纲固有频率与已有文献的计算结果进行对照,验证了有效性和正确性.分析了边界条件、孔隙率、转速、温度、细长比和梯度指数对转动多孔功能梯度材料Timoshenko梁自振频率的影响.

For the porous functionally graded materials beam model with uniform pore distribution,the temperature dependence of material properties is considered and the physical neutral surface of the beam is determined firstly,then the governing differential equation of the transverse free vibration of porous functionally graded material Timoshenko beam is derived by using Hamilton principle when it rotates in thermal environment,and the dimensionless form of the governing differential equation is also obtained.Secondly,differential transformation method(DTM)is used to transform the dimensionless governing differential equations and its boundary conditions,and the equivalent algebraic characteristic equations including the dimensionless natural frequencies are obtained.The dimensionless natural frequencies of transverse free vibration of a porous functionally graded material rotating Timoshenko beam under four boundary conditions of clamped-clamped(C-C),clamped-simply supported(C-S),simply supported-simply supported(S-S)and clamped-free(C-F)in thermal environment are calculated.After degrading it the dimensionless natural frequencies obtained are compared with the calculated results in existing literatures,the validity and correctness of which are verified.Finally,the effects of boundary conditions,porosity,rotating speed,temperature,elongation ratio and gradient index on the natural frequencies of rotating porous functionally graded material Timoshenko beams are analyzed.