形状记忆合金复合梁的振动特性

Study on the vibration properties of a shape memory alloy composite beam

针对复合梁的振动特性问题,利用已有的形状记忆合金(SMA)细观力学本构模型、复合材料力学和振动理论,推导了嵌入SMA的复合梁内SMA的恢复力公式,建立了描述该复合梁的应力、应变及温度间关系的力学本构方程和其固有频率和温度间关系的频率方程.应用SMA的恢复力公式、复合梁力学本构方程及频率方程研究了嵌入SMA复合梁的固有频率与温度间的关系和SMA体积分数对固有频率的影响.数值结果表明,利用SMA能有效实现对梁振动行为的主动控制,可以为利用SMA实现结构智能控制等方面的研究提供参考和借鉴.

In considering the vibration characteristics of the composite beam,the recovery stress formula of the shape memory alloy（SMA） embedded in an SMA composite beam was derived from the micro-mechanical constitutive model of the SMA.The mechanical constitutive equation,which describes the relationship of the stress,strain,and temperature of the SMA composite beam,and the frequency equation,which expresses the relationship of the natural frequency and temperature of the SMA composite beam,were developed according to knowledge of composite material mechanics and the vibration theorem.The relationship of the temperature and natural frequency of the SMA composite beam and the influence of the volume fraction of the SMA on the natural frequency of the SMA composite beam were investigated using the recovery stress formula of the SMA,mechanical constitutive equation and natural frequency equation of the SMA composite beam.Numerical results show that the active control of the vibration of the beam can be realized by using the SMA effectively;therefore a reference can be achieved for the use of the SMA and other aspects of intelligent control.