Investigation of the highly complex nonlinear problems via modified energy balance method

In this paper, the modified energy balance method is proposed as an effective analytical approach to achieve more precise approximate results for a non-linear oscillator in a nano-electromechanical system (NEMS). The proposed solution is compared with previous approximate methods, including the Hamiltonian approach, the homotopy perturbation technique, and the numerical solution using Runge–Kutta 4th-order method. The results obtained from the modified energy balance method show excellent agreement with the numerical solutions. This technique is both efficient and precise in solving such nonlinear problems, offering significant advantages. The novelty of this paper lies in demonstrating the utility of the modified energy balance method for studying nano-electromechanical systems, enabling the construction of higher-order analytical solutions. This study allows for a thorough examination of the results obtained through these analytical solutions.