A dynamical model is developed for the tapered composite thin-walled rotating shaft with shape memory alloy (SMA) wires embedded in. The SMA wires are embedded at an interlayer of the shaft and arranged along the conical surface of the tapered composite shaft. Recovery stresses generated during the phase transformation are calculated based on one-dimensional Brinson’s model. The governing equations are obtained based on a refined variational asymptotic method (VAM) and Hamilton’s principle. The partial differential equations of motion are reduced to the ordinary differential governing equations by using the generalized differential quadrature method (GDQM). Numerical results of natural frequencies and critical speeds are obtained. The effects of the fraction of SMA wires, the initial strain of SMA wires, temperature, ply angle, taper ratio, boundary conditions, and rotating speed on the frequency characteristics are investigated.

中文翻译：

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SMA丝嵌入的锥形复合薄壁旋转轴的广义微分求积动力分析。

为锥形复合薄壁旋转轴开发了动力学模型，其中嵌入了形状记忆合金（SMA）线。SMA线嵌入轴的中间层，并沿锥形复合轴的圆锥形表面排列。根据一维布林森模型计算在相变过程中产生的恢复应力。根据改进的变分渐近方法（VAM）和汉密尔顿原理获得控制方程。通过使用广义差分正交方法（GDQM），将运动的偏微分方程简化为普通的微分控制方程。获得了固有频率和临界速度的数值结果。SMA线的比例，SMA线的初始应变，温度，层角，锥度比，