The primary objective of this study is to investigate the nonlinear free vibrational characteristics of temperature-dependent two-directional functionally graded porous (TDFGP) cylindrical shells resting on elastic substrates in a thermal environment. To accomplish this, the thermomechanical equations are derived based on the Donnell nonlinear shell theory framework in conjunction with the von Kármán assumption. Two-directional functionally graded porous cylindrical shell models have mechanical properties that can change smoothly and continuously across the length and thickness of the shell. Additionally, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The nonlinearity in free vibration assessed via the nonlinear-to-linear frequency ratio concerning the central deflection amplitude can be gained employing the Galerkin discretization approach and modified Poincare–Lindstedt (P-L) method. The accuracy and effectiveness of the present analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear free vibration characteristics of structures under different conditions. The results of this article demonstrate that parameters such as gradient indices, volume fraction, distribution pattern of porosity, geometric parameters, and ambient temperature rise significantly influence the structure’s nonlinear frequency and free vibration response.

中文翻译：

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基于Donnell非线性壳理论的热环境下弹性基底双向功能梯度多孔圆柱壳非线性振动分析

本研究的主要目的是研究热环境中弹性基底上的温度相关双向功能梯度多孔 (TDFGP) 圆柱壳的非线性自由振动特性。为了实现这一目标，基于唐奈非线性壳理论框架并结合冯·卡门假设导出了热机械方程。双向功能梯度多孔圆柱壳模型的机械性能可以在壳的长度和厚度上平滑、连续地变化。此外，假设基体材料中的内部孔隙率可以分散成两种独立的模式，即均匀或不均匀的孔隙率分布。通过与中心偏转幅度相关的非线性与线性频率比来评估自由振动的非线性，可以采用伽辽金离散化方法和改进的庞加莱-林德斯特（PL）方法来获得。通过与现有解决方案的比较表明了当前分析模型的准确性和有效性。最后，进行了一些全面的参数研究，以深入了解不同条件下多个因素对结构非线性自由振动特性的影响。本文的结果表明，梯度指数、体积分数、孔隙率分布模式、几何参数和环境温升等参数显着影响结构的非线性频率和自由振动响应。