A New Approximate Analytical Analysis of the Response of Non-Linear Damped Systems Subjected to Step Function Excitation

El-Asir, B.; Mansour, Awad R.; Abu-Mowis, A.; Kassab, N.

doi:10.1006/jsvi.1994.1264

Cited by 6 publications

(2 citation statements)

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“…In this study, we consider a strongly nonlinear damped system of the form subject to the initial conditions where 2γ is the linear damping parameter, ε is the nonlinearity parameter, K is the frequency of underdamped motion, γ1 is a nonnegative real number and E ( t ) is the external excitation (El-Asir et al., 1994; Jang and Chen, 1997). A differential transformation technique to solve equations (1) and (2) was proposed by Jang and Chen (1997).…”

Section: Introductionmentioning

confidence: 99%

Multistage Bernstein collocation method for solving strongly nonlinear damped systems

Bataineh

Al-Omari

Işık

et al. 2018

Journal of Vibration and Control

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In this paper, we propose an approximate solution method, called multistage Bernstein collocation method (MBCM), to solve strongly nonlinear damped systems. The method is given with an error analysis. The systems investigated include step function external excitation and periodical function external excitation. We found that the MBCM gives more accurate approximate solutions than the standard collocation method. Since MBCM splits the domain of the problem [Formula: see text] into n parts, one can overcome oscillations arising from the standard collocation method by increasing n. The results obtained from MBCM compare favorably with that of the fourth-order Runge–Kutta method (RK4).

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Section: Introductionmentioning

confidence: 99%

Multistage Bernstein collocation method for solving strongly nonlinear damped systems

Bataineh

Al-Omari

Işık

et al. 2018

Journal of Vibration and Control

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“…In Asir et al's work, a developed hybrid analytical-numerical method was mentioned [61]. This is a technique developed by Mansour and Hussein.…”

Section: Damped Systemmentioning

confidence: 99%

Drop-impact analysis of packaged electronic products containing nonlinear cushion buffers and multilayer circuit boards

Wang¹

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On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness

Tang

Brennan

2014

International Journal of Mechanical Sciences

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A New Approximate Analytical Analysis of the Response of Non-Linear Damped Systems Subjected to Step Function Excitation

Cited by 6 publications

References 0 publications

Multistage Bernstein collocation method for solving strongly nonlinear damped systems

Multistage Bernstein collocation method for solving strongly nonlinear damped systems

Drop-impact analysis of packaged electronic products containing nonlinear cushion buffers and multilayer circuit boards

On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness

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