In the present study, the viscoelastic free vibration behavior of nano‐scaled plates is studied by employing a finite element method based on the two‐phase nonlocal integral theory. Various boundary conditions, surface effects and cutouts have been assumed. The principle of total potential energy is used for developing the nonlocal finite element method, and the classical plate theory is assumed to derive the formulations. By numerically solving the eigenvalue problem, which has been obtained by the variational principle, the complex eigenvalues of free vibration of the viscoelastic nano‐scaled plates are acquired. The current results are compared with those available in the literature and those obtained by commercial finite element software, and the influences of the nonlocal parameter, viscoelastic parameter, geometrical parameters (e.g. cutout and size), surface effects and different boundary conditions on the complex eigenvalues are studied. It is noted that the current method is able to handle quite versatile boundary conditions and geometries like cutouts, which are rather difficult (or impossible) to be tackled by employing other methods available in most researches.

中文翻译：

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具有矩形切口和表面效应的非局部粘弹性纳米尺度板的自由振动特性

在本研究中，采用基于两相非局部积分理论的有限元方法研究了纳米级板的粘弹性自由振动行为。假定各种边界条件，表面效果和切口。总势能原理用于发展非局部有限元方法，并假设采用经典板理论推导公式。通过数值求解由变分原理获得的特征值问题，获得了粘弹性纳米尺度板的自由振动的复特征值。将当前结果与文献中的结果以及通过商业有限元软件获得的结果进行比较，以及非局部参数，粘弹性参数，几何参数（例如，并研究了复杂特征值的表面效应和不同边界条件。应当指出，当前方法能够处理相当通用的边界条件和几何形状（例如切口），而采用大多数研究中可用的其他方法很难（或不可能）解决这些问题。