Modal damping variations in nonlinear dynamical systems

Perturbation Methods

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Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems

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On the jump-up and jump-down frequencies of the Duffing oscillator

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Homotopy–perturbation method for pure nonlinear differential equation

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Comments on the method of harmonic balance

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Numerical computation of nonlinear normal modes in mechanical engineering

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Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance

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Analytical approximations for the period of a nonlinear pendulum

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Oscillator with fraction order restoring force

Cvetićanin, L. (2008) · Journal of Sound and Vibration · doi:10.1016/j.jsv.2008.08.026 · Cited by 100 · see citing works

Application of the harmonic balance method to a nonlinear oscillator typified by a mass attached to a stretched wire

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Application of He’s homotopy perturbation method to conservative truly nonlinear oscillators

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A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”

Mickens, R. E. (2005) · Journal of Sound and Vibration · doi:10.1016/j.jsv.2005.03.005 · Cited by 77 · see citing works

Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments

Quinn, D. D., Hubbard, S. A., Wierschem, N. E., AL-Shudeifat, M. A., Ott, R. J., Luo, J., Spencer, B. F., McFarland, D. M., Vakakis, A. F., & Bergman, L. A. (2012) · Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics · doi:10.1177/1464419311432671 · Cited by 62 · see citing works

Frequencies of oscillators with fractional-power non-linearities

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Approximate analytical solutions for oscillation of a mass attached to a stretched elastic wire

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Transitions from Strongly to Weakly Nonlinear Motions of Damped Nonlinear Oscillators

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Approximations for motion of the oscillators with a non-negative real-power restoring force

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ANALYTICAL METHODS FOR SOLVING STRONGLY NON-LINEAR DIFFERENTIAL EQUATIONS

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Amplitude decay of damped non-linear oscillators studied with jacobian elliptic functions

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Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

Beléndez, A., Beléndez, T., Neipp, C., Hernández-Sabaté, A., & Álvarez, M. L. (2007) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2007.01.089 · Cited by 26 · see citing works

Amplitudes Decay in Different Kinds of Nonlinear Oscillators

AL-Shudeifat, M. A. (2014) · Journal of vibration and acoustics · doi:10.1115/1.4029288 · Cited by 21 · see citing works

Analytical formulas for the energy, velocity and displacement decays of purely nonlinear damped oscillators

AL-Shudeifat, M. A. (2013) · Journal of Vibration and Control · doi:10.1177/1077546313493817 · Cited by 20 · see citing works

Pure odd-order oscillators with constant excitation

Cvetićanin, L. (2010) · Journal of Sound and Vibration · doi:10.1016/j.jsv.2010.09.011 · Cited by 20 · see citing works

Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire

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Asymptotical behaviour of a system with damping and high power-form non-linearity

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On the amplitude decay of strongly non-linear damped oscillators

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Time-varying stiffness method for extracting the frequency–energy dependence in the nonlinear dynamical systems

AL-Shudeifat, M. A. (2017) · Nonlinear Dynamics · doi:10.1007/s11071-017-3528-8 · Cited by 12 · see citing works

Approximation of the Frequency-Energy Dependence in the Nonlinear Dynamical Systems

AL-Shudeifat, M. A. (2016) · doi:10.1115/detc2016-60163 · Cited by 1 · see citing works

Amplitude-Dependent Stiffness Method for Studying Frequency and Damping Variations in Nonlinear Dynamical Systems

AL-Shudeifat, M. A. (2017) · doi:10.1115/detc2017-67918 · Cited by 1 · see citing works

A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types

Saeed, A. S., Abdul Nasar, R., & AL-Shudeifat, M. A. (2023) · Nonlinear Dynamics · doi:10.1007/s11071-022-08094-y · Cited by 208 · see citing works

Frequency–energy plot and targeted energy transfer analysis of coupled bistable nonlinear energy sink with linear oscillator

AL-Shudeifat, M. A., & Saeed, A. S. (2021) · Nonlinear Dynamics · doi:10.1007/s11071-021-06802-8 · Cited by 67 · see citing works

Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled With Piecewise Nonlinear Energy Sink

Al-Shudeifat, M. A., & Saeed, A. S. (2022) · Journal of Computational and Nonlinear Dynamics · doi:10.1115/1.4053509 · Cited by 31 · see citing works

Joint state and fault estimation for nonlinear systems with missing measurements and random component faults under Round-Robin Protocol

Song, X., Rong, L., Li, B., Wang, Z., & Li, J. (2023) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2023.109437 · Cited by 8 · see citing works

Frequency Energy Plots of Dynamical Systems Attached to Piecewise Nonlinear Energy SinkPreprint

Shudeifat, M. A. A. A., & Saeed, A. S. (2021) · Research Square · doi:10.21203/rs.3.rs-252523/v1

Modal Damping and Frequency Variations in Nonlinearly Coupled Oscillators With Negative Linear Stiffness Components

Alhammadi, F. K., & AL-Shudeifat, M. A. (2018) · doi:10.1115/imece2018-87474

Amplitude-Dependent Stiffness Method for Studying Frequency and Damping Variations in Nonlinear Dynamical Systems

AL-Shudeifat, M. A. (2017) · doi:10.1115/detc2017-67918 · Cited by 1 · see citing works

Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments

Quinn, D. D., Hubbard, S. A., Wierschem, N. E., AL-Shudeifat, M. A., Ott, R. J., Luo, J., Spencer, B. F., McFarland, D. M., Vakakis, A. F., & Bergman, L. A. (2012) · Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics · doi:10.1177/1464419311432671 · Cited by 62 · see citing works

Energy-Neutral Transfer of Vibration Energy Across Modes by Using Active Nonlinear Stiffness Variation of Impulsive Type

Pumhössel, T. (2016) · Journal of Computational and Nonlinear Dynamics · doi:10.1115/1.4034264 · Cited by 1 · see citing works

Identification of Equivalent Modal Damping and Frequencies in Multi Degree-of-Freedom Nonlinear Systems

Quinn, D. D., Ott, R. J., Hubbard, S. A., McFarland, D. M., Bergman, L. A., & Vakakis, A. F. (2011) · doi:10.1115/detc2011-48956