This study deals with a novel model of forced flexural vibrations in a transversely isotropic thermoelastic thin rectangular plate (TRP) due to time harmonic concentrated load. The mathematical model is prepared for the thin plate in a closed form with the application of Kirchhoff’s love plate theory for nonlocal generalized thermoelasticity with Green–Naghdi (GN)-III theory of thermoelasticity. The nonlocal thin plate has a nonlocal parameter to depict small-scale effect. The double finite Fourier transform technique has been used to find the expressions for lateral deflection, thermal moment and temperature distribution for simply supported (SS) thin rectangular plate in the transformed domain. The effect of classical thermoelasticity (CTE) theory of thermoelasticity and nonlocal parameters has been shown on the computed quantities. Few particular cases have also been deduced.

中文翻译：

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基于基尔霍夫薄板理论的非局部薄矩形板的受迫弯曲振动

本研究处理由于时间谐波集中载荷引起的横向各向同性热弹性薄矩形板 (TRP) 中的受迫弯曲振动的新模型。应用基尔霍夫的爱板理论对非局部广义热弹性和格林-纳格迪 (GN)-III 热弹性理论建立了封闭形式薄板的数学模型。非局部薄板具有描述小尺度效应的非局部参数。双有限傅立叶变换技术已被用于在变换域中找到简支 (SS) 薄矩形板的横向挠度、热力矩和温度分布的表达式。热弹性和非局部参数的经典热弹性 (CTE) 理论对计算量的影响已得到证实。