For the first time in the present investigation, aiming to improve the performance of mono-gyroscopic systems, the stability and vibrational behavior of flowing fluid coupled functionally graded (FG) porous rectangular plate resting on different foundations subjected to thermal environments are studied. Applying the higher-order shear deformation theory (HSDT) incorporated in nonlocal elasticity theory results in the governing equations of the system. Also, to explain and analyze the effect of various key factors such as nonlocal parameter, power-law index of FG material, the volume fraction of porosity, the height and densities of fluid, structure aspect ratio, boundary conditions, types of substrates, and thermal environments on the dynamic characteristics and critical velocities of the system, a comprehensive parametric study is performed. By utilizing the generalized differential quadrature method (GDQM), the governing size-dependent equations are solved numerically, and the natural frequencies in addition to divergence and flutter corresponding velocities are extracted. To validate the present work, a comparative study is performed between the obtained results and outcomes reported in the engineering literature.

在本研究中，为了提高单陀螺系统的性能，首次研究了在热环境下放置在不同基础上的流动流体耦合功能梯度（FG）多孔矩形板的稳定性和振动行为。应用包含在非局部弹性理论中的高阶剪切变形理论 (HSDT) 可得到系统的控制方程。此外，解释和分析各种关键因素的影响，如非局部参数、FG 材料的幂律指数、孔隙率的体积分数、流体的高度和密度、结构纵横比、边界条件、基底类型和热环境对系统的动态特性和临界速度进行了全面的参数研究。通过利用广义微分求积法 (GDQM)，数值求解控制尺寸相关方程，并提取除发散和颤振对应速度之外的固有频率。为了验证目前的工作，在获得的结果和工程文献中报告的结果之间进行了比较研究。