The nano/microelectromechanical system (N/MEMS) has triggered worldwide concern, and its applications have revolutionized technologies in various advanced fields from wearable sensors, 5 G communication technology, to energy harvesting, to aerospace. However, when the applied force is sufficiently large, the pull-in instability arises, and reliable operation is forbidden. Therefore, it is extremely important to insight fast and accurately into the periodic motion of the system to prevent the system from its pull-in motion. The basic aim of this study is to demonstrate the applicability of the well-known variational iteration method (VIM) for predicting the dynamic behavior of N/MEMS. For this, a nanobeam-based microstructure with van der Waals force for actuation is used as an example to reveal its periodic properties. The governing equation for the oscillation of the microsystem is obtained from the Euler-Bernoulli beam principle, considering the midplane stretching effect. We then employ the Galerkin technique to transform the governing partial differential equation into an ordinary differential equation, which is highly nonlinear, making it extremely difficult to solve by some traditional analytical methods, however, the VIM shows its ability to elucidate accurately the basic properties of the N/MEMS by simple calculation. This paper offers a new road for fast and accurate prediction of the microsystem's properties, and the result can be used for optimizing the N/MEMS.•A nanobeam-based N/MEMS system with van der Waals force is considered.•A strongly governing equation without a linear term is obtained.•The variational iteration method is applied to figure out the basic properties of the system.
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