Nonlinear oscillation of nanoelectro-mechanical resonators using energy balance method: considering the size effect and the van der Waals force

Abstract

The energy balance method is utilized to analyze the oscillation of a nonlinear nanoelectro-mechanical system resonator. The resonator comprises an electrode, which is embedded between two substrates. Two types of clamped-clamped and cantilever nano-resonators are studied. The effects of the van der Waals attractions, Casimir force, the small size, the fringing field, the mid-plane stretching, and the axial load are taken into account. The governing partial differential equation of the resonator is reduced using the Galerkin method. The energy method is applied to obtain an analytical solution without considering any linearization or small parameter. The results of the present study are compared with the results available in the literature. In addition, the results of the present analytical solution are compared with the Runge-Kutta numerical results. An excellent agreement between the present analytical solution, numerical solution, and the results available in the literature was found. The influences of the van der Waals force, Casimir force, size effect, and fringing field effect on the oscillation frequency of resonators are studied. The results indicate that the presence of the intermolecular forces (van der Waals), Casimir force, and fringing field effect decreases the oscillation frequency of the resonator.In contrast, the presence of the size effect increases the oscillation frequency of the resonator.

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

“…The nonlinear vibration of an electrostatically-actuated nanobeam with van der Waals, Casimir and fringing effects can be modelled as (Ghalambaz et al, 2016):…”

“…The error analysis of Figure 2b showed that the nanobeam undergoes a linear to weakly nonlinear response for 0 < < 0.35, while a strong nonlinear response was predicted when > 0.475. Equations ( 8) was studied by Ghalambaz et al (2016) using the energy balance method (EBM) while Ismail et al (2019) used the global residue harmonic balance method (GRHBM). The EBM solution was simulated for = 0.01 while the GRHBM was applied for ≤ 0.50.…”

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

“…Moreover, the BVP (1), (2) has been analyzed by meshless method through radial basis functions, though they are often used for high-dimensional problems [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The interested readers are also referred to [36][37][38][39] for other useful techniques, which can be applied for the same problems.…”

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

“…biosensors, micro-resonators, atomic force microscopes (AFMs) and actuators [1][2][3][4]. MEMS/NEMS may be actuated using several sources of energy such as electrostatic [5], electromagnetic [6], piezoelectric [7] and may be made of metals or polymer, silicon-based structures or functionally graded materials (FGM) [8][9][10][11][12][13]. Electrostatic actuation has demonstrated good energy density and efficiency.…”