In this research, we present an approach to identify variable characteristics of an inhomogeneous thermoelectroelastic radially polarized elongated hollow cylinder. The cylinder’s thermomechanical characteristics depend on the radial coordinate. We consider two loading types for the cylinder—the mechanical and the thermal ones. The radial displacement is considered as the additional data collected on the outer cylinder’s surface under the first type load, while the temperature measured over a certain time interval is considered for the second type load. The direct problem after non-dimensioning and applying the Laplace transform is solved by jointly applying the shooting method and the transform inversion based on expanding the actual space in terms of the shifted Legendre polynomials. The effect of the laws of change in variable characteristics on the input data values taken in the experiment is analyzed. A nonlinear inverse problem on the reconstruction of the cylinder’s variable properties is formulated and solved on the basis of an iterative technique. The initial approximation is set in the class of positive bounded linear functions whose coefficients are determined from the condition of minimizing the residual functional. To find the corrections at each stage of the iterative process, the Fredholm integral equations of the first kind are solved by means of the Tikhonov method. A series of computational experiments on recovering one and two variable characteristics is conducted. The effect of coupling parameters and input noise on the reconstruction results is revealed.

在这项研究中，我们提出了一种识别非均匀热电弹性径向极化细长空心圆柱体可变特性的方法。圆柱体的热机械特性取决于径向坐标。我们考虑气缸的两种加载类型——机械加载和热加载。径向位移被认为是在第一类负载下在外圆柱表面上收集的附加数据，而在一定时间间隔内测量的温度被认为是第二类负载。通过联合应用射击法和基于移位勒让德多项式扩展实际空间的变换反演，解决了无量纲化和应用拉普拉斯变换后的直接问题。分析了变量特征变化规律对实验中输入数据值的影响。基于迭代技术制定并解决了圆柱体可变属性重建的非线性反问题。初始近似设置为正有界线性函数类，其系数由最小化残差函数的条件确定。为了找到迭代过程每个阶段的修正，第一类 Fredholm 积分方程通过 Tikhonov 方法求解。进行了一系列恢复一变量和二变量特征的计算实验。揭示了耦合参数和输入噪声对重建结果的影响。