基于二次摄动法的SMA层合梁非线性自由振动分析

Nonlinear Free Vibration Analysis of SMA Laminated Beam Based on Two-step Perturbation Method

为对SMA(形状记忆合金)层合梁的非线性自由振动进行分析,使用Brison一维本构模型描述SMA的力学特性,基于不同剪切函数和Von Karman大变形理论,建立梁质点位移与应变之间的关系,使用Hamilton变分原理,获得在弹性地基上两端简支SMA层合梁的动力学方程并进行无量纲处理。使用二次摄动法获得SMA层合梁的非线性自由振动方程。研究不同SMA体积分数、预应变、SMA铺设角度、温度变化对非线性振动的影响。

The nonlinear free vibration of SMA(shape memory alloy)laminated beams is analyzed.The mechanical properties of the SMA are described by the Brison one-dimensional constitutive model.Based on different shear functions and Von Karman's large deformation theory,the relationship between beam mass displacement and strain is established.Using Hamilton's variational principle,the dynamic equations of the simply supported SMA laminated beams at both ends on elastic foundations are obtained,and dimensionless processing is carried out.The nonlinear free vibration equation of the SMA laminated beam is obtained by the two-step perturbation method.The effects of different SMA volume fraction,pre-strain,SMA laying angle and temperature change on nonlinear vibration are studied.