形状记忆合金纤维正交各向异性层合矩形板的非线性弯曲振动

Large amplitude flexural vibration of the orthotropic composite plate embedded with shape memory alloy fibers

研究了形状记忆合金(SMA)纤维混杂复合材料大挠度层合板的非线性自由与受迫振动特性。基于描述SMA力学行为的Brinson理论以及层合板材料性能预测的混合率,建立了SMA纤维混杂复合材料大挠度层合板的本构方程,基于对称层合各向异性弹性板的非线性理论,建立了以横向挠度和应力函数表示的板的横向振动方程和相容方程。采用Galerkin近似解法将振动方程化为时间变量的含有三次非线性项的Duffing型常微分方程,采用谐波平衡法(HBM)获得系统的固有频率方程和强迫振动稳态频率响应方程。数值计算表明:非线性板自由振动频率比与激励温度的关系具有与线性板相同的特征,马氏体相向奥氏体相转变阶段温度对板的振动频响特性曲线的影响最显著,同时也讨论了SMA纤维含量、板的纵横比以及自由振动幅值对板的非线性频率比的影响。

The free and forced vibration of the large deformation composite plate embedded with shape memory alloy （SMA） fibers was investigated. Based on the thermo-mechanical constitutive equation of SMA proposed by Brinson, the constitutive relationships for evaluation of the properties of a hybrid SMA composite ply were obtained following the rule of mixtures. And based on the nonlinear theory of symmetrically laminated anisotropic plates, the governing equations of flexural vibration in terms of displacement and stress functions were derived. The Galerkin method was used to reduce the original partial differential equation into a nonlinear ordinary differential equation, which was then solved by the harmonic balance method. The numerical results show that the relationship between nonlinear natural frequency ratio and temperature for the composite plate has similar characteristics to those of the linear one, and the effects of temperature on forced response behavior during phase transformation from martensite to austenite are significant. The effects of the volume fraction of the SMA fiber, aspect ratio and free vibration amplitude on the dynamical behavior of the plate were also discussed.