Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

Wang, Kang‐Jia; Wang, Guodong

doi:10.1177/14613484211032757

Cited by 18 publications

(3 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to these unprecedented advantages, the formulation caught immediate attention after publication due to its extremely simplicity and remarkable reliability. It has been successfully applied to Kundu-Mukherjee-Naskar oscillator [27], nonlinear vibration of embedded carbon nanotube [28], fractal vibration systems [29,30], packaging systems [31] and MEMS oscillators [32]. It has been hailed as an unprecedented success.…”

Section: Introductionmentioning

confidence: 99%

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

2022

FU Mech Eng

View full text Add to dashboard Cite

The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory.

show abstract

Section: Introductionmentioning

confidence: 99%

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

2022

FU Mech Eng

View full text Add to dashboard Cite

show abstract

“…( ) Various nonlinear systems in physics, mechanics and engineering can be modeled as a nonlinear oscillator with an odd restoring force function. The vibration of carbon nanotubes embedded in elastic medium [64], and the nonlinear vibration of bi-directional functionally grade beams [8] are two wellknown examples. Equation (1) can be rewritten in terms of the independent variable t w = t as follows:…”

Section: Solution Proceduresmentioning

confidence: 99%

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Mohammadian,

Ismail

2024

Phys. Scr.

View full text Add to dashboard Cite

The non-linear differential equation governing some mechanical systems, such as the non-linear vibrations of FG beams resting on a nonlinear foundation, behaves similarly to the oscillations of a non-linear oscillator with an asymmetric restoring force function that includes both odd and non-odd non-linear terms. The objective of this research is to obtain higher-order approximate analytical solutions for such problems by introducing an enhanced harmonic balance method. By building upon the original problem, two new symmetric systems with odd non-linear terms are introduced, and their higher-order approximate analytical solutions are derived using a novel approach. In proposed method, the restoring force function is represented by its Fourier series expansion. Unlike previous papers, linearizing the equation or taking the first derivative of the Fourier series in the subsequent iteration is unnecessary. However, to enhance the solution’s accuracy, the remaining error from each iteration is utilized in the next one. Finally, by combining the results from the two introduced systems, the analytical period and corresponding periodic solution of the original problem can be obtained. This method is applied to the governing differential equation of FG beams resting on non-linear foundations, a physical non-natural oscillator, and conservative Toda oscillator. The key advantages of this approach are its simplicity and its ability to provide highly precise solutions for both small and large amplitudes in a single iteration.

show abstract

“…The real train test showed that the vertical vibration of the power pack frame was reduced by 55.77% after the particle damper was added, and the vibration reduction effect under other conditions was 51.83%. Wang Jinchao et al [58] designed particle damping and constrained damping to solve the problem of abnormal vibration of carbon slide of subway pantograph. Through comparison of test results, particle damping has stronger vibration suppression effect under transverse excitation condition.…”

Section: Application Analysis Of Particle Damped Rail Transitmentioning

confidence: 99%

Research progress and analysis of particle damping technology

Liang

2023

International Conference on Optoelectronic Information and Functional Materials (OIFM 2023)

View full text Add to dashboard Cite

Particle damping technology is a passive vibration and noise reduction technology, and its energy dissipation mechanism is complex, which leads to the slow research progress at present. The basic concept of particle damping technology, the energy dissipation mechanism and the factors affecting particle damping were introduced. The experimental research, numerical simulation and engineering application of particle damping technology were summarized. The research status of particle damping technology in the field of rail transit was introduced and some suggestions were put forward according to the actual situation.

show abstract

Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

Cited by 18 publications

References 46 publications

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

Simplified Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Vibration Systems

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Research progress and analysis of particle damping technology

Contact Info

Product

Resources

About