Numerous applications have been found in various microelectromechanical systems for shape memory alloys. This study analyzes the nonlinear free vibrations of a sandwiched microbeam, consisting of a shape memory alloy core and two elastic layers on either side. The behavior of the shape memory layer is modeled with the one-dimensional Brinson model. The equation of motion is derived from Hamilton’s principle and the modified couple stress theory for the Euler–Bernoulli beam and then truncated into a reduced-order model through Galerkin’s technique. An approximate analytical solution is obtained using the Lindstedt–Poincare method for different temperatures. The effects of temperature, material length scale parameter, aspect ratio, and maximum vibration amplitude on nonlinear normalized frequency have been investigated. The results have been compared with those of some previous studies and can provide a better understanding of the design of sandwiched microbeams, which have a shape memory alloy layer.

在用于形状记忆合金的各种微机电系统中发现了许多应用。这项研究分析了夹层微梁的非线性自由振动，该结构由形状记忆合金芯和两侧的两个弹性层组成。使用一维Brinson模型对形状记忆层的行为进行建模。运动方程式是从汉密尔顿原理和欧拉-伯努利梁的修正耦合应力理论中得出的，然后通过加勒金技术将其截断为降阶模型。使用Lindstedt-Poincare方法获得不同温度的近似分析解决方案。研究了温度，材料长度比例参数，长宽比和最大振动幅度对非线性归一化频率的影响。