Purpose

In this paper, an analytical investigation of the nonlinear dynamic response and vibrational behavior of stiffened and unstiffened FGM shell panels of different geometries under thermo-mechanical loading is presented.

Methods

The kinematic relations considered for shell panels are in accordance with the first-order shear deformation theory along with von Kármán geometrical nonlinearities, and the contribution of stiffeners is considered based on smeared stiffener technique. The nonlinear governing equations of motion for eccentrically stiffened FGM shell panels are derived using Hamilton’s principle. Navier’s functions are assumed to satisfy the prescribed boundary conditions, whereas Galerkin and fourth-order Runge–Kutta methods are employed to attain nonlinear dynamic responses.

Results

After establishing the accuracy of the present analytical formulation by comparing the results with the existing literature, various numerical studies are conducted to divulge the impact of parameters such as shell geometries, stiffeners, material inhomogeneity, and temperature difference on the nonlinear dynamic response and vibrational behavior of simply-supported FGM shell panels.

Conclusions

It is revealed that among the un-stiffened as well as stiffened FGM shell panels, the spherical shell panel exhibits the highest natural frequency with the lowest vibration amplitude, whereas the lowest natural frequency with the highest amplitude is depicted by the hyperbolic-paraboloidal shell panel. Moreover, the effects of the increase in the temperature difference across the thickness and the power law index are to reduce the natural frequency and to increase the amplitude of dynamic response, irrespective of the geometry of shell panels. Further, the effect of damping on the dynamic behavior of the FGM shell panel is initially indistinguishable; however, after a few time periods the damping is found to have a considerable effect on its dynamic response.

中文翻译：

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热环境下加筋功能梯度壳板的线性和非线性振动行为的分析研究

目的

在本文中，对不同几何形状的加筋和未加筋 FGM 壳板在热机械载荷下的非线性动态响应和振动行为进行了分析研究。

方法

壳板考虑的运动学关系符合一阶剪切变形理论以及 von Kármán 几何非线性，并且基于涂抹加劲肋技术考虑加劲肋的贡献。偏心加筋 FGM 壳板的非线性运动控制方程是使用汉密尔顿原理推导出来的。假设 Navier 函数满足规定的边界条件，而采用 Galerkin 和四阶 Runge-Kutta 方法来获得非线性动态响应。

结果

通过将结果与现有文献进行比较，确定当前分析公式的准确性后，进行了各种数值研究，以揭示壳几何形状、加强筋、材料不均匀性和温差等参数对非线性动力响应和振动行为的影响简单支撑的 FGM 外壳面板。

结论

结果表明，在非加筋和加筋FGM壳板中，球壳板的固有频率最高，振幅最低，而双曲抛物面壳板的固有频率最低，振幅最大。 . 此外，无论壳板的几何形状如何，厚度方向上的温差和幂律指数的增加都会降低固有频率并增加动态响应的幅度。此外，阻尼对 FGM 壳板的动态行为的影响最初是无法区分的。然而，经过几个时间段后，发现阻尼对其动态响应有相当大的影响。