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Influences of material gradient and nonlinearity on the forced vibration of orthotropic shell structures

机译：物质梯度与非线性对正交壳结构强制振动的影响

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摘要

In this study, the influences of material gradient and nonlinearity on the forced vibration of orthotropic shell structures under external excitations are investigated for first time. The mathematical model of inhomogeneous orthotropic double-curved shallow shells is built using the Hamilton principle and von Karman-type nonlinearity. The basic equations are reduced to nonlinear ordinary differential equations using the Galerkin procedure. Using the multiscale method, the frequency-amplitude relations of double-curved shallow shells and the nonlinear frequency response of forced vibrations are obtained for first time. The reliability of the obtained expressions is checked by comparison with the literature data. In numerical analysis, the influence of inhomogeneity, orthotropy, nonlinearity, and the external excitation parameter on the frequency of forced vibrations is investigated in detail by performing unique numerical calculations taking into account various profiles of inhomogeneous orthotropic shallow spherical and hyperbolic paraboloidal (or hypar) shells.
机译：在该研究中，首次研究了物质梯度和非线性对外部激发下的正交壳结构的强制振动的影响。使用Hamilton原理和von Karman型非线性建造了不均匀正性双弯曲浅壳的数学模型。使用Galerkin程序减少到非线性常微分方程的基本方程。使用多尺度方法，首次获得双曲面浅壳的频率幅度关系和强制振动的非线性频率响应。通过与文献数据进行比较来检查所获得的表达式的可靠性。在数值分析中，通过进行独特的数值计算，详细研究了不均匀性，正交分性，非线性和外部激励参数的影响，以考虑非均匀的正性浅球和双曲曲线（或腹部）的各种曲线，详细研究了独特的数值计算贝壳。

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