含形状记忆合金(SMA)层柔性梁的振动频响特性

主要研究具有形状记忆合金（shape memory alloy,SMA）层的梁结构的动力响应特性，重点分析了应力诱发马氏体相变的影响。首先采用SMA超弹性分段线性的应力－应变模型表示SMA的超弹性本构特征；其次借助有关粘弹性材料结构动力学分析的复模量方法，推出简谐激励作用下SMA层的面内变形和应力之间的关系，提出具有SMA表层的简支梁横向稳态频率响应求解的数学模型。SMA超弹性非线性的影响使得结构产生复杂的动力学特征，如存在多值稳态解、跳跃性、周期3响应等。上述现象的发生与激振力幅值、温度的变化密切相关。

FREQUENCY RESPONSE CHARACTERISTICS OF VIBRATION OF FLEXIBLE BEAM COVERED WITH SHAPE MEMORY ALLOY(SMA) LAYERS

A analytical study on the dynamics of a flexible beam covered with shape memory alloy(SMA) layers is presented. The effect of stress induced phase transformation on the frequency responses is examined. The piecewise linear model of SMA superelastic hysteresis stress strain is used to predict the superelastic constitutive properties of SMA, and the complex modulus approach which has been widely used in structural dynamic analysis of viscoelastic material is employed in order to derive the stress strain relation of SMA layer in which a sinusoidal force is applied. The mathematical model for the solution of steady state response of simply supported beam covered with SMA layers subjected to transversal sinusoidal force is developed. The numerical results show that nonlinearity associated with superelasticity of SMA gives rise to complicated dynamics, such as, the occurrence of multi valued steady state solutions, jump, period three responses, etc. Furthermore, these effects depend on the forcing amplitude and ambient temperature.