热载荷下嵌入SMA丝复合材料梁的固有频率

The Eigenfrequencies of a Composite Beam with Embedded SMA Wires and Subjected to Thermal Load

基于形状记忆合金Brinson一维热力学本构方程,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.利用横向微幅自由振动的特征方程,求解了两端固定约束条件下梁在均匀升降温过程中的线性振动响应,获得了嵌入SMA丝复合材料弹性梁的前四阶固有频率随温度变化的特征关系曲线.结果表明,形状记忆合金丝相变过程中的回复应力和弹性模量的变化对梁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, the one-dimensional thermomechanical constitutive relations of composite beams with embedded shape memory alloy wires and subjected to thermal load are established. By using characteristic equation for transverse linear free vibration, the linear vibration responses of a fixed at both ends beam subjected to a uniform temperature rise and fall are solved. The characteristic curves of the first to fourth-order frequencies versus temperature rise of the composite elastic beam with embedded SMA wires are obtained. Results show that the recovery stress and the variation of modulus of elasticity all have influence on the eigenfrequencies of the beam, which is an effective method that can realize active control of the eigenfrequencies of the beam.