Abstract Application of the scaled boundary finite element method (SBFEM) in free vibration and transient dynamic problems of the composite magneto-electro-elastic (MEE) cylindrical shell is considered in this paper for the first time. The mathematic model of the composite MEE cylindrical shell is governed by the three-dimensional (3D) theory of magneto-electro-elasticity in the cylindrical coordinate system, and the dynamic equilibrium equations are then derived into a second-order ordinary differential equation by using the SBFEM. In this method, discretizations are confined only to the surfaces or boundaries of the computational domain but no fundamental solutions and singular integrals are required, which reduces the spatial dimension of problem by one and making mesh generation much easier. At the same time, the transverse shear locking can be successfully avoided due to the analyticity of the SBFEM governing equation in the radial direction of the scaled boundary coordinate system. Based on the state space approach, the basic equations of the composite MEE cylindrical shell in the scaled boundary coordinate system are reduced to a system of first-order ordinary differential equation in terms of the independent variable involving the generalized displacement and internal nodal force fields, and then the free vibration and transient dynamic responses of the system are solved by using the generalized eigenvalue technique and Newmark's integration scheme, respectively. Numerical results illustrate that the convergence of the proposed formulations is satisfactory, and excellent agreement can be achieved for limiting cases with the solutions available in published work or that obtained using the commercial software ANSYS. In addition, the influences of the structural parameters (including thickness ratio, aspect ratio and stacking configuration), material properties and boundary conditions on the vibration and dynamic behaviors of the composite MEE cylindrical shells are discussed.

中文翻译：

---

复合圆柱壳结构自由振动和瞬态动力响应的磁电弹性半解析模型

摘要 本文首次探讨了尺度边界有限元法(SBFEM)在复合磁电弹性(MEE)圆柱壳自由振动和瞬态动力学问题中的应用。复合MEE圆柱壳的数学模型由圆柱坐标系中的磁电弹性三维（3D）理论控制，然后通过使用以下公式将动态平衡方程导出为二阶常微分方程SBFEM。在这种方法中，离散化仅限于计算域的表面或边界，不需要基本解和奇异积分，这将问题的空间维数减少了一个，使网格生成更加容易。同时，由于 SBFEM 控制方程在缩放边界坐标系的径向方向上的解析性，可以成功避免横向剪切锁定。基于状态空间方法，将复合MEE圆柱壳在缩放边界坐标系中的基本方程化为一阶常微分方程组，自变量涉及广义位移和节点内力场，然后分别使用广义特征值技术和Newmark积分方案求解系统的自由振动和瞬态动态响应。数值结果表明，所提出的公式的收敛性是令人满意的，并且可以通过已发表的工作中可用的解决方案或使用商业软件 ANSYS 获得的解决方案在极限情况下实现极好的一致性。此外，还讨论了结构参数（包括厚度比、纵横比和堆叠配置）、材料特性和边界条件对复合材料 MEE 圆柱壳振动和动力学行为的影响。