The main objective of the current paper is to provide a modified thermo-viscoelastic mathematical model based on the Moore-Gibson-Thompson (MGT) equation to study the behavior of fiber-reinforced viscoelastic media. To describe the viscoelastic behavior of the fiber-reinforced material, the Kelvin-Voigt type is used. The relaxation time coefficient is included in the Green and Naghdi type III model (GN-III) to solve the problem of the infinite velocity propagation of heat waves. For an infinite viscosity-reinforced elastic solid with a cylindrical cavity, the proposed model was applied to investigate the effects of thermo-mechanical coupling and thermal relaxation coefficients on the studied fields. The cavity surface is considered to be traction-free and subject to temperature changes that fluctuate harmoniously. The Laplace transform tool was used to find analytical solutions for the distributions of different physical fields. The inverse Laplace transforms were calculated numerically using the Fourier series approximation approach. The effect of viscosity and the frequency of heat pulses on the fields under study are shown graphically. A comparison was made between several related models to confirm the effectiveness of the proposed system by presenting the numerical results in tables.

本论文的主要目的是提供一种基于 Moore-Gibson-Thompson (MGT) 方程的改进的热粘弹性数学模型来研究纤维增强粘弹性介质的行为。为了描述纤维增强材料的粘弹性行为，使用了 Kelvin-Voigt 类型。弛豫时间系数包含在 Green 和 Naghdi 类型 III 模型（GN-III）中，以解决热波的无限速度传播问题。对于具有圆柱腔的无限粘度增强弹性固体，应用所提出的模型来研究热机械耦合和热松弛系数对研究领域的影响。型腔表面被认为是无牵引的，并且会受到和谐波动的温度变化的影响。拉普拉斯变换工具用于寻找不同物理场分布的解析解。使用傅里叶级数近似方法数值计算拉普拉斯逆变换。粘度和热脉冲频率对研究场的影响以图形方式显示。通过在表格中显示数值结果，对几个相关模型进行了比较，以确认所提出系统的有效性。