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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

DOI: https://doi.org/10.1115/1.4053719

Published Online: March 10, 2022

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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

DOI: https://doi.org/10.1115/1.4051998

Published Online: September 6, 2021

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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

DOI: https://doi.org/10.1115/1.4034460

Published Online: September 14, 2016

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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

DOI: https://doi.org/10.1115/1.4031009

Published Online: July 22, 2015

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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

DOI: https://doi.org/10.1115/1.4026555

Published Online: February 10, 2014

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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

DOI: https://doi.org/10.1115/1.4025150

Published Online: September 23, 2013

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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.

DOI: https://doi.org/10.1115/1.2198546

Published Online: February 9, 2006

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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.

DOI: https://doi.org/10.1115/1.2198253

Published Online: February 6, 2006

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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.

DOI: https://doi.org/10.1115/1.2061947

Published Online: May 12, 2005

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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.

DOI: https://doi.org/10.1115/1.1607355

Published Online: October 10, 2003

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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.

DOI: https://doi.org/10.1115/1.2791942

Published Online: December 1, 1998

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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.

DOI: https://doi.org/10.1115/1.2789108

Published Online: September 1, 1998

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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.

DOI: https://doi.org/10.1115/1.2788940

Published Online: September 1, 1997

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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.

DOI: https://doi.org/10.1115/1.2788887

Published Online: June 1, 1996

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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.

DOI: https://doi.org/10.1115/1.2899502

Published Online: June 1, 1992

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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.

DOI: https://doi.org/10.1115/1.3173740

Published Online: December 1, 1988

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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.

DOI: https://doi.org/10.1115/1.3167156

Published Online: December 1, 1983

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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.

DOI: https://doi.org/10.1115/1.3167103

Published Online: September 1, 1983

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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.

DOI: https://doi.org/10.1115/1.3162650

Published Online: December 1, 1982

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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.

DOI: https://doi.org/10.1115/1.3153761

Published Online: September 1, 1980

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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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