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Journal Articles

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Large Initial Displacements

Ke Ding, Arne J. Pearlstein

J. Appl. Mech. June 2022, 89(6): 061001.

Paper No: JAM-21-1490

https://doi.org/10.1115/1.4053719

Published Online: March 10, 2022

View Article titled, Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Large Initial Displacements

Topics: Chaos, Damping, Energy dissipation, Fractals, Harmonic oscillators, Transients (Dynamics), Stability, Oscillations

Includes: Supplementary data

Journal Articles

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Intermediate Initial Displacements

Ke Ding, Arne J. Pearlstein

J. Appl. Mech. December 2021, 88(12): 121009.

Paper No: JAM-21-1193

https://doi.org/10.1115/1.4051998

Published Online: September 6, 2021

View Article titled, Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Intermediate Initial Displacements

Topics: Chaos, Damping, Energy dissipation, Harmonic oscillators, Oscillations, Rotation, Transients (Dynamics), Time series, Displacement, Fractals

Includes: Supplementary data

Journal Articles

Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

Pol D. Spanos, Alberto Di Matteo, Yezeng Cheng, Antonina Pirrotta, Jie Li

J. Appl. Mech. December 2016, 83(12): 121003.

Paper No: JAM-16-1282

https://doi.org/10.1115/1.4034460

Published Online: September 14, 2016

View Article titled, Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

Topics: Harmonic oscillators, Probability

Journal Articles

Responses of Linear and Nonlinear Oscillators to Fractional Gaussian Noise With Hurst Index Between 1/2 and 1

Mao Lin Deng, Wei Qiu Zhu

J. Appl. Mech. October 2015, 82(10): 101008.

Paper No: JAM-15-1180

https://doi.org/10.1115/1.4031009

Published Online: July 22, 2015

View Article titled, Responses of Linear and Nonlinear Oscillators to Fractional Gaussian Noise With Hurst Index Between 1/2 and 1

Topics: Displacement, Harmonic oscillators, Noise (Sound), Damping, Spectral energy distribution, Brownian motion, Kinetic energy

Journal Articles

Energy Harvester Synthesis Via Coupled Linear-Bistable System With Multistable Dynamics

Z. Wu, R. L. Harne, K. W. Wang

J. Appl. Mech. June 2014, 81(6): 061005.

Paper No: JAM-13-1081

https://doi.org/10.1115/1.4026555

Published Online: February 10, 2014

View Article titled, Energy Harvester Synthesis Via Coupled Linear-Bistable System With Multistable Dynamics

Topics: Dynamics (Mechanics), Energy harvesting, Harmonic oscillators, Vibration, Damping, Excitation

Journal Articles

Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Analytical Study

L. I. Manevitch, G. Sigalov, F. Romeo, L. A. Bergman, A. Vakakis

J. Appl. Mech. April 2014, 81(4): 041011.

Paper No: JAM-13-1235

https://doi.org/10.1115/1.4025150

Published Online: September 23, 2013

View Article titled, Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Analytical Study

Topics: Approximation, Dynamics (Mechanics), Energy transformation, Resonance, Harmonic oscillators, Flow (Dynamics), Oscillations

Journal Articles

Quasi-Periodic Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing

O. V. Gendelman, Yu. Starosvetsky

J. Appl. Mech. March 2007, 74(2): 325–331.

https://doi.org/10.1115/1.2198546

Published Online: February 9, 2006

View Article titled, Quasi-Periodic Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing

Topics: Damping, Harmonic oscillators, Manifolds, Oscillations, Stability, Steady state, Simulation, Resonance, Shapes

Journal Articles

Nonstationary Response Envelope Probability Densities of Nonlinear Oscillators

P. D. Spanos, A. Sofi, M. Di Paola

J. Appl. Mech. March 2007, 74(2): 315–324.

https://doi.org/10.1115/1.2198253

Published Online: February 6, 2006

View Article titled, Nonstationary Response Envelope Probability Densities of Nonlinear Oscillators

Topics: Boundary-value problems, Differential equations, Eigenfunctions, Fokker-Planck equation, Probability, White noise, Harmonic oscillators, Computer simulation, Approximation, Density

Journal Articles

Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap

Gang Wang, Xisen Wen, Jihong Wen, Yaozong Liu

J. Appl. Mech. January 2006, 73(1): 167–170.

https://doi.org/10.1115/1.2061947

Published Online: May 12, 2005

View Article titled, Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap

Topics: Elastic waves, Energy gap, Harmonic oscillators, Periodic structures, Resonance, Stiffness, Dynamic light scattering, Phononic crystals

Journal Articles

Approximate Model for a Viscoelastic Oscillator

Y. Ketema

J. Appl. Mech. September 2003, 70(5): 757–761.

https://doi.org/10.1115/1.1607355

Published Online: October 10, 2003

View Article titled, Approximate Model for a Viscoelastic Oscillator

Topics: Damping, Harmonic oscillators, Relaxation (Physics), Temperature effects, Approximation, Vibration, Temperature, Oscillations

Journal Articles

On the Existence of Normal Modes of Damped Discrete-Continuous Systems

H. T. Banks, Zheng-Hua Luo, L. A. Bergman, D. J. Inman

J. Appl. Mech. December 1998, 65(4): 980–989.

https://doi.org/10.1115/1.2791942

Published Online: December 1, 1998

View Article titled, On the Existence of Normal Modes of Damped Discrete-Continuous Systems

Topics: Damping, Dimensions, Equations of motion, Harmonic oscillators

Journal Articles

Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

M. Wiercigroch, V. W. T. Sin

J. Appl. Mech. September 1998, 65(3): 657–663.

https://doi.org/10.1115/1.2789108

Published Online: September 1, 1998

View Article titled, Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

Topics: Symmetry (Physics), Stiffness, Bifurcation, Calibration, Chaos, Clearances (Engineering), Design, Dynamics (Mechanics), Harmonic oscillators, System dynamics

Journal Articles

Nonseparable Solutions to the Hamilton-Jacobi Equation

C. M. Leech, B. Tabarrok

J. Appl. Mech. September 1997, 64(3): 636–641.

https://doi.org/10.1115/1.2788940

Published Online: September 1, 1997

View Article titled, Nonseparable Solutions to the Hamilton-Jacobi Equation

Topics: Dynamics (Mechanics), Hamilton-Jacobi equations, Harmonic oscillators, Partial differential equations, Potential energy, Transfer functions

Journal Articles

Transition From Soliton to Chaotic Motion Following Sudden Excitation of a Nonlinear Structure

M. A. Davies, F. C. Moon

J. Appl. Mech. June 1996, 63(2): 445–449.

https://doi.org/10.1115/1.2788887

Published Online: June 1, 1996

View Article titled, Transition From Soliton to Chaotic Motion Following Sudden Excitation of a Nonlinear Structure

Topics: Excitation, Solitons, Buckling, Waves, Aircraft, Harmonic oscillators, Periodic structures, Ships, Space frame structures, Stress

Journal Articles

Vibration of Harmonically Excited Oscillators With Asymmetric Constraints

S. Natsiavas, H. Gonzalez

J. Appl. Mech. June 1992, 59(2S): S284–S290.

https://doi.org/10.1115/1.2899502

Published Online: June 1, 1992

View Article titled, Vibration of Harmonically Excited Oscillators With Asymmetric Constraints

Topics: Damping, Displacement, Excitation, Harmonic oscillators, Nonlinear systems, Stability, Steady state, Stiffness, Vibration

Journal Articles

Response of Linear Systems to Polynomials of Gaussian Processes

M. Grigoriu, S. T. Ariaratnam

J. Appl. Mech. December 1988, 55(4): 905–910.

https://doi.org/10.1115/1.3173740

Published Online: December 1, 1988

View Article titled, Response of Linear Systems to Polynomials of Gaussian Processes

Topics: Linear systems, Polynomials, Approximation, Differential equations, Harmonic oscillators

Journal Articles

A Periodically Forced Impact Oscillator With Large Dissipation

S. W. Shaw, P. J. Holmes

J. Appl. Mech. December 1983, 50(4a): 849–857.

https://doi.org/10.1115/1.3167156

Published Online: December 1, 1983

View Article titled, A Periodically Forced Impact Oscillator With Large Dissipation

Topics: Displacement, Energy dissipation, Equilibrium (Physics), Excitation, Harmonic oscillators, Transients (Dynamics)

Journal Articles

An Approach to the First Passage Problem in Random Vibration

A. B. Mason, Jr., W. D. Iwan

J. Appl. Mech. September 1983, 50(3): 641–646.

https://doi.org/10.1115/1.3167103

Published Online: September 1, 1983

View Article titled, An Approach to the First Passage Problem in Random Vibration

Topics: Analytical methods, Computer simulation, Harmonic oscillators, Noise (Sound), Probability, Random excitation, Random vibration, Simulation results, Spectral energy distribution, White noise

Journal Articles

Solution to the Backward-Kolmogorov Equation for a Nonstationary Oscillation Problem

G. P. Solomos, P-T. D. Spanos

J. Appl. Mech. December 1982, 49(4): 923–925.

https://doi.org/10.1115/1.3162650

Published Online: December 1, 1982

View Article titled, Solution to the Backward-Kolmogorov Equation for a Nonstationary Oscillation Problem

Topics: Approximation, Harmonic oscillators, Oscillations, Random excitation

Journal Articles

On the Computation of the Confluent Hypergeometric Function at Densely Spaced Points

P-T. D. Spanos

J. Appl. Mech. September 1980, 47(3): 683–685.

https://doi.org/10.1115/1.3153761

Published Online: September 1, 1980

View Article titled, On the Computation of the Confluent Hypergeometric Function at Densely Spaced Points

Topics: Algorithms, Approximation, Computation, Harmonic oscillators

Journal citation

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Supplemental Material

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Large Initial Displacements

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Intermediate Initial Displacements

Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

Responses of Linear and Nonlinear Oscillators to Fractional Gaussian Noise With Hurst Index Between 1/2 and 1

Energy Harvester Synthesis Via Coupled Linear-Bistable System With Multistable Dynamics

Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Analytical Study

Quasi-Periodic Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing

Nonstationary Response Envelope Probability Densities of Nonlinear Oscillators

Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap

Approximate Model for a Viscoelastic Oscillator

On the Existence of Normal Modes of Damped Discrete-Continuous Systems

Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

Nonseparable Solutions to the Hamilton-Jacobi Equation

Transition From Soliton to Chaotic Motion Following Sudden Excitation of a Nonlinear Structure

Vibration of Harmonically Excited Oscillators With Asymmetric Constraints

Response of Linear Systems to Polynomials of Gaussian Processes

A Periodically Forced Impact Oscillator With Large Dissipation

An Approach to the First Passage Problem in Random Vibration

Solution to the Backward-Kolmogorov Equation for a Nonstationary Oscillation Problem

On the Computation of the Confluent Hypergeometric Function at Densely Spaced Points

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