Central concern of this article is presenting the high-exactitude analysis on hygro-thermo-mechanical vibration of three-phase multi-scale hybrid composite angle-ply laminated rectangular plate (MHCALRP) for different couples of boundary conditions within the context of twelve-variable refined higher order shear deformation theory (RHOSDT12). Defining the kinematics of the system according to RHOSDT12 is the essential step toward achieving sufficient accuracy in elucidation of vibrational behavior of moderately thick plates. Mechanical properties of MHCALRP are calculated through two-step Halpin–Tsai homogenization process. Numerical solution to the governing differential motion equations is acquired by implementing generalized Differential quadrature method (GDQM). Accuracy of the employed approach is evaluated by a comparative study with the published studies. As a practical conclusion it is revealed that the orientation angle of the macrofibres can effectively compensate the lack of nano reinforcement as well as the absence of extensional load to overcome negative impacts of hygrothermal environment in an affordable cost. The influence of extensional load along two directions, nano/macro scale reinforcements and hygro-thermal environment on the vibrational response of the MHCALRP is completely elucidated through the parametric investigation.

本文的主要关注点是针对十二变量范围内不同边界条件对的三相多尺度混合复合角铺层矩形板（MHCALRP）的湿热机械振动的高精确度分析完善了高阶剪切变形理论（RHOSDT12）。根据RHOSDT12定义系统的运动学，是在阐明中厚板的振动行为方面达到足够精度的必不可少的步骤。MHCALRP的机械性能通过两步Halpin-Tsai均质化过程计算。通过实施广义差分正交方法（GDQM），获得了控制微分运动方程的数值解。通过比较研究与已发表的研究评估所采用方法的准确性。作为实际结论，揭示了大纤维的取向角可以以可负担的成本有效地弥补了纳米增强材料的缺乏以及拉伸载荷的缺乏，从而克服了湿热环境的负面影响。通过参数研究完全阐明了纳米/宏观尺度增强和湿热环境沿两个方向的拉伸载荷对MHCALRP振动响应的影响。作为实际结论，揭示了大纤维的取向角可以以可负担的成本有效地补偿了纳米增强材料的缺乏以及拉伸载荷的缺乏，从而克服了湿热环境的负面影响。通过参数研究完全阐明了纳米/宏观尺度增强和湿热环境沿两个方向的拉伸载荷对MHCALRP振动响应的影响。作为实际结论，揭示了大纤维的取向角可以以可负担的成本有效地弥补了纳米增强材料的缺乏以及拉伸载荷的缺乏，从而克服了湿热环境的负面影响。通过参数研究完全阐明了纳米/宏观尺度增强和湿热环境沿两个方向的拉伸载荷对MHCALRP振动响应的影响。