热载荷作用下嵌入SMA丝复合材料梁的横向自由振动

TRANSVERSE FREE VIBRATIONS OF A COMPOSITE BEAM WITH EMBEDDED SMA WIRES SUBJECTED TO THERMAL

基于形状记忆合金Brinson一维热力学本构方程,采用复合材料细观力学分析方法,建立了热载荷作用下嵌入SMA丝复合材料梁的一维热弹性本构关系。其次利用Euler-Bernoulli梁的轴线可伸长几何非线性理论和自由振动理论,建立了嵌入SMA丝复合材料梁在均匀升温场内自由振动的动力学控制方程,导出了热过屈曲构形附近嵌入SMA丝复合材料梁微幅横向自由振动的模型。最后通过打靶法求解了两端固定约束条件下嵌入形状记忆合金丝复合材料梁在加热过程中的振动响应,获得了梁的前四阶固有频率在不同SMA相对体积含量时随温度变化的特征关系曲线。数值结果表明,SMA丝相变过程中的回复应力和弹性模量变化对梁在过屈曲前后的各阶固有频率均有影响,是实现梁自振频率主动控制的一种有效方法。

Based on Brinson＇s one-dimensional thermomechanical constitutive equations of shape memory alloys （SMA） and micro-mechanical law of composites, the one-dimensional thermomechanical constitutive relations of composite beams with embedded shape memory alloy wires subjected to thermal load are established. Using the geometrically nonlinear theory of axially extensible Euler-Bernoulli beams, the general dynamic governing equations for free vibration of composite beams with embedded shape memory alloy wires subjected to a uniform temperature rise are set up. Small amplitude free vibration model near the thermal post-buckling configuration is presented. The vibration responses of a clamped-clamped composite beam with embedded SMA wires in heating process are studied by shooting method and the characteristic curves of the first to fourth-order frequencies versus temperature rise of the beam with different relative volume fraction of SMA wires are obtained. Numerical results show that the recovery stress and the variation of modulus of elasticity have influence on the natural frequencies of the beam, which is an effective way to realize active control of the natural frequencies of the beam.