Analytical study of the vibrating double-sided quintic nonlinear nano-torsional actuator using higher-order Hamiltonian approach

Abstract

In this work, we investigate and apply higher-order Hamiltonian approach (HA) as one of the novelty techniques to find out the approximate analytical solution for vibrating double-sided quintic nonlinear nano-torsional actuator. Periodic solutions are analytically verified, and consequently, the relationship between the initial amplitude and the natural frequency are obtained in a novel analytical way. The HA is then extended to the second-order to find more accurate results. To show the accuracy and applicability of the technique, the approximated results are compared with the homotopy perturbation method and numerical solution. According to the numerical results, it is highly remarkable that the second-order approximate solutions produce better than previously existing results and almost similar in comparing with the numerical solutions.

Non-chaos-mediated mixed-mode oscillations in an extended Hindmarsh-Rose neuronal oscillator with time delay

“…The system can be solved analytically by the multiple scales method [10], frequency analysis [11][12][13][14], He-Laplace method [15], the variational principle [16][17][18][19][20], the homotopy perturbation [21,22], Fourier spectral method [23], and direct algebraic method [24]. For numerical simulation, He-Li's neural network computation is recommended for its high simulation efficiency [25].…”

Nonlinear Vibration of Electrostatically Actuated Microbeam

“…In recent years, many efficient analytical methods have been used to solve nonlinear differential equations, such as the variational iteration method [12], spreading residue harmonic balance method [13], energy balance method [14][15][16], frequency-amplitude formulation [17,18], homotopy perturbation method [19][20][21][22][23], modified harmonic balance method [24], differential quadrature method [25], parameter expansion method [26], variational approach [27,28], homotopy analysis method [29,30], higher-order Hamiltonian approach [2,[31][32][33], and so on.…”