Global residue harmonic balance method for a nonlinear oscillator with discontinuity

Ju, Peijun

doi:10.1016/j.apm.2015.02.018

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…26 Simultaneously, Xiao et al 27 studied the fractional order van der Pol oscillator by RHBM. Then, the global RHBM 28,29 was presented by Ju et al and used to solve the approximate solutions of the strongly nonlinear systems. In 2016, Guo and Zhang 30 proposed SRHBM on the basis of RHBM.…”

Section: Introductionmentioning

confidence: 99%

The spreading residue harmonic balance method for studying the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction

Qian

Pan

Qiang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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Since the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction is transformed into a mathematical model through Galerkin method, which is a nonlinear differential equation, the spreading residue harmonic balance method is introduced to solve the approximate solution of the nonlinear problem in this paper. The spreading residue harmonic balance method is developed on the basis of the residue harmonic balance method. The disadvantage of the approach is small parameter assumption is needed. In order to improve the accuracy of the approximate solution, the residual of the former order harmonic approximation is introduced. Besides, we compare the second-order spreading residue harmonic balance method solution with the numerical one by the Runge-Kutta method. This proves the availability and validity of spreading residue harmonic balance method.

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Section: Introductionmentioning

confidence: 99%

The spreading residue harmonic balance method for studying the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction

Qian

Pan

Qiang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

show abstract

“…In what follows, an analytical technique based on the global residue harmonic balance method (GRHBM) is employed to obtain the analytical approximate solutions of the problem discussed before. To obtain higher-order approximate solutions, all the residual errors are considered [33][34][35][36].…”

Section: Application Of the Global Residue Harmonic Balance Methods (...mentioning

confidence: 99%

“…The main aim of this paper is to apply the global residue harmonic balance method introduced by Ju and Xue [34][35][36][37] and recently developed through [38][39][40][41][42], in order to obtain analytical approximate solutions to the large-amplitude vibration of electrostatically actuated micro-beams. The higher-order approximations (mainly second-order approximations) have been obtained for the large-amplitude vibration of electrostatically actuated micro-beams, providing the expected accuracy.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of Electrostatically Actuated Microbeam

et al. 2022

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In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate analytical solutions of an electrostatically actuated micro-beam. To illustrate the applicability and accuracy of the method, a high level of accuracy was established for the analytical solutions by comparing the results of the solutions with the numerical solution as well as the already published literature, such as the variational approach (VA), Hamiltonian approach (HA), energy balance method (EBM), and homotopy analysis method (HAM). It is shown that the GRHB method can be easily applied to nonlinear problems and provides solutions with a higher precision than existing methods. The obtained analytical expressions are employed to study the effects of axial force, initial gape, and electrostatic load on nonlinear frequency.

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“…And, to improve the accuracy, the residual errors are considered in the approximations of each order. us, the GRHBM has found applications in various nonlinear problems [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Global Residue Harmonic Balance Method for a System of Strongly Nonlinear Oscillator

Chen

Liu

2021

Mathematical Problems in Engineering

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In this paper, the global residue harmonic balance method is applied to obtain the approximate periodic solution and frequency for a well-known system of strongly nonlinear oscillator in engineering. This method can improve accuracy by considering all the residual errors in deriving each order approximation. With this procedure, the expressions of the higher-order approximate solution and corresponding frequency for the considered system can be determined easily. The comparison of the obtained results with previously existing and corresponding exact solutions shows the high accuracy and efficiency of the method.

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Global residue harmonic balance method for a nonlinear oscillator with discontinuity

Cited by 6 publications

References 11 publications

The spreading residue harmonic balance method for studying the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction

The spreading residue harmonic balance method for studying the doubly clamped beam-type N/MEMS subjected to the van der Waals attraction

Nonlinear Vibration of Electrostatically Actuated Microbeam

Global Residue Harmonic Balance Method for a System of Strongly Nonlinear Oscillator

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