In engineering applications, composite structures supported by elastic foundations are being vastly utilized in various operating environmental conditions. The nonlinear hygrothermal effect on vibration analysis of a magnetostrictive viscoelastic laminated composite sandwich plate rested on two-parameter Pasternak’s foundations is studied in the present article. The material properties of the viscoelastic plate’s layers are considered based on the Kelvin–Voigt model. The governing equation system is derived according to Hamilton’s principle. The analytical solution is obtained to study influences of the hygrothermal change, half wave number, magnitude of the feedback control gain, aspect ratios, thickness ratio, and structural viscoelastic damping coefficients on vibration damping characteristics of the plate including the frequencies, the damping rate, and the deflection. The obtained results indicate that the natural frequency and deflection reduce with increasing the structural viscoelastic damping value. The plate takes a long time for suppressing its vibration due to increasing the hygrothermal factor.

在工程应用中，由弹性地基支撑的复合结构在各种运行环境条件下得到了广泛利用。本文研究了基于两参数Pasternak基础的磁致伸缩粘弹性层合夹层板的非线性湿热效应对振动的影响。基于Kelvin-Voigt模型，考虑了粘弹性板层的材料属性。根据汉密尔顿原理导出控制方程组。获得了解析解，以研究湿热变化，半波数，反馈控制增益的大小，纵横比，厚度比和结构粘弹性阻尼系数对板的振动阻尼特性（包括频率）的影响，阻尼率和挠度。所得结果表明，固有频率和挠度随结构粘弹性阻尼值的增加而减小。由于增加了湿热因子，该板需要很长时间来抑制其振动。