Abstract

Transverse vibrations of a double-layered viscoelastic orthotropic graphene sheet system are investigated. The two sheets in the system are coupled by the visco-Pasternak medium. General governing equations for free and forced vibrations of the double-layered graphene sheet system with a high-order surface stress effect are formulated. Theoretical solutions for the damped vibrational frequency, damping ratio, and relative deflection of the two sheets with simply supported boundary conditions are obtained. The effects of the high-order surface stress on the damped frequency and damping ratio of the system for in-phase and out-of-phase free vibrations are discussed. The impacts of the high-order surface stress, structural damping, medium damping, Winkler modulus, and shear modulus of the medium on the relative deflection of the two sheets for forced vibrations are investigated. It is demonstrated that the high-order surface stress effects on the vibrational properties of the system are more significant than those of the conventional surface stress.

中文翻译：

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具有高阶表面应力效应的双层粘弹性正交各向异性石墨板的自由和强迫振动

摘要

研究了双层粘弹性正交各向异性石墨烯片系统的横向振动。系统中的两张纸通过粘胶-帕斯泰纳克介质耦合。提出了具有高阶表面应力效应的双层石墨烯片体系自由振动和强迫振动的一般控制方程。获得了在简单支撑边界条件下两张板的阻尼振动频率，阻尼比和相对挠度的理论解。讨论了高阶表面应力对同相和异相自由振动系统的阻尼频率和阻尼比的影响。高阶表面应力，结构阻尼，中阻尼，Winkler模量，研究了两种介质在强迫振动条件下的相对剪切挠度和介质的剪切模量。结果表明，高阶表面应力对系统振动性能的影响比常规表面应力的影响更大。