Abstract In this article, the constitutive relations and the governing equations are derived for nonlocal thermoelastic solid in the presence of diffusion. The free vibration of a thermoelastic diffusive cylinder is investigated within the framework of the above newly derived model. Time-harmonic vibration is used to transform the governing equations into a system of ordinary differential equations. The frequency equation is taken under investigation for the survival of a range of possible modes in compact form for traction-free thermal boundary conditions: thermally insulated and isothermal boundary conditions. To explore the vibration analysis from frequency equations, we apply a numerical iteration technique for generating numerical data by taking assistance of the Matlab software. The numerically computed and simulated results for the frequency shift, natural frequency, and the thermoelastic damping are presented graphically. The effect of nonlocality on the above quantities is observed and shown graphically.

中文翻译：

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带扩散的非局部热弹性空心圆柱体的自由振动分析

摘要 本文推导了存在扩散的非局部热弹性固体的本构关系和控制方程。在上述新推导模型的框架内研究了热弹性扩散圆柱体的自由振动。时谐振动用于将控制方程转换为常微分方程组。频率方程正在研究中，用于无牵引热边界条件的紧凑形式的一系列可能模式的生存：绝热和等温边界条件。为了从频率方程探索振动分析，我们在 Matlab 软件的帮助下应用了一种数值迭代技术来生成数值数据。以图形方式显示了频移、固有频率和热弹性阻尼的数值计算和模拟结果。观察并以图形方式显示非定域性对上述数量的影响。