Abstract We explore the analysis of exact three-dimensional free vibrations of visco-thermoelastic solid cylinder, which has been considered at a uniform temperature and undeformed initially in the framework of generalized thermoelasticity. The formulation has been implemented with two relaxation time parameters, i.e., mechanical and thermal relaxation parameters. The series solution has been implemented to solve the differential equations along with the evaluation of stresses, displacements, and temperature by applying stress-free, rigidly fixed, thermally insulated and isothermal boundary conditions. The relations of frequency equations for the existence of different modes of visco-thermoelastic solid cylinder have been developed in compact form using assumed boundary conditions. Thermoelastic damping and frequency shift are presented graphically from the data generated by computations and simulations of numerical results. Also, the natural frequencies are represented in the form of tables which show that with an increase in the ratio of length to the radius and axial wave-number, the variation of vibrations keeps increasing.

中文翻译：

---

具有两个弛豫时间参数的各向同性粘热弹性圆柱体三维自由振动分析

摘要 我们探讨了粘热弹性固体圆柱体的精确三维自由振动分析，该圆柱体在广义热弹性框架下已被考虑在均匀温度下且最初未变形。该公式已使用两个弛豫时间参数实现，即机械弛豫参数和热弛豫参数。通过应用无应力、刚性固定、绝热和等温边界条件，已实施级联求解以求解微分方程以及应力、位移和温度的评估。已经使用假定的边界条件以紧凑形式开发了存在不同模式的粘热弹性固体圆柱体的频率方程关系。热弹性阻尼和频移通过数值结果的计算和模拟生成的数据以图形方式呈现。此外，固有频率以表格的形式表示，表明随着长径比和轴向波数的增加，振动的变化不断增加。