Structures face different types of imperfections and defects during the fabrication process, installation and working environment. In this paper, the imperfection effects in the coupled vibration behaviour of axially functionally graded carbon nanotube (CNT)-strengthened beam structures with different boundary conditions are analysed considering porosity as well as geometric and mass imperfections in the structure. Porosity is modelled using different types of formulations for simple-cell, open-cell and closed-cell porous structures. The porosity is assumed to be either uniform or by varying through the thickness of the hollow beam using different functions. Mass imperfection effect is added to the system by considering a concentrated mass in the system affecting the mass homogeneity of the structure. Geometry imperfection is also considered by having an initial deformation in the structure which could be caused by an improper fabrication process. Coupled axial and transverse equations of motion are obtained using Hamilton’s principle and the von Karman geometrical nonlinearity. Governing equations are solved for different types of boundary conditions using a semi-analytical modal decomposition technique. It is shown that strengthening the base matrix with CNT fibres can improve the vibration behaviour of imperfect structures and the influence of CNT volume fraction and distribution through the length of the beam is discussed. The results provided in this paper may be used as a benchmark to validate future experimental results to prevent imperfection, delamination and stress singularities in the structures.

中文翻译：

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具有不同边界条件的碳纳米管增强梁耦合振动特性中的孔隙率、质量和几何缺陷敏感性

结构在制造过程、安装和工作环境中面临不同类型的缺陷和缺陷。在本文中，考虑到孔隙率以及结构中的几何和质量缺陷，分析了具有不同边界条件的轴向功能梯度碳纳米管 (CNT) 增强梁结构的耦合振动行为中的缺陷效应。孔隙率使用不同类型的公式建模，用于单孔、开孔和闭孔多孔结构。孔隙率被假定为均匀的或通过使用不同函数改变空心梁的厚度。通过考虑影响结构质量均匀性的系统中的集中质量，将质量缺陷效应添加到系统中。几何缺陷也可以通过结构中的初始变形来考虑，这可能是由不正确的制造过程引起的。使用哈密顿原理和冯卡门几何非线性获得耦合的轴向和横向运动方程。使用半解析模态分解技术针对不同类型的边界条件求解控制方程。结果表明，用 CNT 纤维加强基体可以改善不完美结构的振动行为，并讨论了 CNT 体积分数和整个梁长度分布的影响。本文提供的结果可用作验证未来实验结果的基准，以防止结构中的缺陷、分层和应力奇异性。