温度影响下纤维增强FGM梁的自由振动特性

Free vibration characteristics of fiber-reinforced FGM beams considering temperature effect

运用微分求积法(DQM)研究温度影响下纤维增强功能梯度材料(FGM)梁的横向自由振动问题。材料的物性参数由混合率模型给出,并考虑梁内部均匀升温和材料的温度依赖特性。首先基于经典梁理论(CBT)和Hamilton变分原理,建立温度影响下纤维增强FGM梁的运动微分方程,再引入无量纲量对梁自由振动控制微分方程进行无量纲化,然后运用DQM将无量纲自由振动微分方程与边界条件转换为代数特征方程;其次通过编写程序求解特征方程得到无量纲固有频率,并将其退化为FGM梁并与已有文献数据结果对照,验证了文中方法的有效性和正确性;最后研究了不同边界条件下纤维体积分数、温度变化及长细比对纤维增强FGM梁无量纲固有频率的影响。

The transverse free vibration problem of fiber-reinforced functionally graded materials(FGM)beams considering temperature effect is investigated using the differential quadrature method(DQM).The physical parameters of fiber-reinforced FGM beams are given by the mixing rate model,and the uniform temperature rising inside the beam and the temperature-dependent properties of the materials are considered.Firstly,the motion differential equation for fiber-reinforced FGM beams under temperature influence is established based on the classical beam theory(CBT)and Hamilton’s variational principle,and the governing differential equation of free vibration for beams is dimensionless by introducing dimensionless parameters.Then the DQM is applied to convert the dimensionless differential equation of free vibration and boundary conditions into algebraic characteristic equations.By writing a program to solve the characteristic equations,the dimensionless natural frequencies are obtained and degenerated into FGM beams to verify the correctness of the existing literature data results,then the validity and correctness are verified.Finally,the effects of the fiber volume fraction,temperature changes and slenderness ratio on the dimensionless natural frequencies of fiber-reinforced FGM beams with different boundary conditions are discussed.