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Mechanics of tapered axially functionally graded shallow arches

机译：锥形轴向功能渐变浅拱的力学

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This paper investigates the forced nonlinear mechanics of a tapered shallow arch made of an axially functionally graded (AFG) material. A nonlinear model for a clamped-clamped boundary is developed based on the nonlinear strain-displacement relation in the framework of Hamilton's principle. To this end, first, the exponential distributions along the length of the shallow arch are formulated for the material properties such as the mass density, moduli of elasticity, Poisson's ratio, as well as the geometric characteristics such as the cross-sectional area and the second moment of area of the AFG tapered shallow arch. Second, the expressions for the kinetic and the potential energies of the AFG tapered shallow arch, as well as the work of the external excitation force, are constructed and balanced via Hamilton's principle. Third, the nonlinear non-uniform equations of motion are discretised via the Galerkin method retaining an adequate number of symmetric and asymmetric modes. The asymmetric nature of the system, due to the non-uniform mechanical properties and geometry along the length, is addressed through extensive numerical simulations. The influence of internal resonances and internal energy transfers on the dynamic response of the system is investigated. Moreover, the effect of the gradient index as well as the curvature amplitude on the vibration characteristics of the tapered AFG shallow arch is investigated.
机译：本文研究了由轴向功能梯度（AFG）材料制成的锥形浅拱的受力非线性力学。在汉密尔顿原理的框架下，基于非线性应变-位移关系，建立了一个非线性边界模型。为此，首先，针对材料特性（例如质量密度，弹性模量，泊松比）以及几何特性（例如横截面积和弹性系数），制定沿浅拱形长度的指数分布。 AFG锥形浅拱的面积的第二矩。其次，通过汉密尔顿原理构造和平衡了AFG锥形浅拱的动能和势能的表达式，以及外部激励力的功。第三，通过Galerkin方法离散非线性的非均匀运动方程，并保留了足够数量的对称和非对称模式。由于沿长度方向的不均匀的机械性能和几何形状，系统的不对称特性可以通过大量的数值模拟得到解决。研究了内部共振和内部能量传递对系统动态响应的影响。此外，研究了梯度指数和曲率振幅对锥形AFG浅拱的振动特性的影响。

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