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Proceedings Papers

Bifurcations in a Mathieu Equation With Cubic Nonlinearities

Leslie Ng, Richard Rand

Proc. ASME. IMECE2000, Nonlinear Dynamics and Stochastic Mechanics, 1-12, November 5–10, 2000

Paper No: IMECE2000-1746

DOI: https://doi.org/10.1115/IMECE2000-1746

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Topics: Bifurcation, Computer software, Flow (Dynamics), Nonlinear dynamics, Resonance

Proceedings Papers

A Quasiperiodic Mathieu Equation

Richard Rand, Rachel Hastings

Proc. ASME. DETC95, Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems, 747-758, September 17–20, 1995

Paper No: DETC1995-0315

DOI: https://doi.org/10.1115/DETC1995-0315

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Topics: Approximation, Computation, Stability

Proceedings Papers

Impact Dynamics of a Supercavitating Underwater Projectile

Richard Rand, Rudra Pratap, Deepak Ramani, Jeffery Cipolla, Ivan Kirschner

Proc. ASME. DETC97, Volume 1D: 16th Biennial Conference on Mechanical Vibration and Noise, V01DT19A005, September 14–17, 1997

Paper No: DETC97/VIB-3929

DOI: https://doi.org/10.1115/DETC97/VIB-3929

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Topics: Dynamics (Mechanics), Projectiles, Cavity walls, Touch (physiological), Center of mass, Flight, Fluid mechanics, Fluids, Simulation, Spin (Aerodynamics)

Proceedings Papers

Dynamics of Two Coupled Van der Pol Oscillators With Delay Coupling

Stephen Wirkus, Richard Rand

Proc. ASME. DETC97, Volume 1C: 16th Biennial Conference on Mechanical Vibration and Noise, V01CT12A007, September 14–17, 1997

Paper No: DETC97/VIB-4019

DOI: https://doi.org/10.1115/DETC97/VIB-4019

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Topics: Delays, Dynamics (Mechanics), Stability, Bifurcation, Dimensions, Flow (Dynamics), Lasers

Proceedings Papers

Bifurcations in the Dynamics of Two Coupled van der Pol Oscillators With Delay Coupling

Stephen Wirkus, Richard Rand

Proc. ASME. DETC99, Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise, 2559-2568, September 12–16, 1999

Paper No: DETC99/VIB-8318

DOI: https://doi.org/10.1115/DETC99/VIB-8318

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Topics: Bifurcation, Delays, Dynamics (Mechanics), Flow (Dynamics), Dimensions, Lasers, Stability, Steady state

Proceedings Papers

On the Torus Flow Y′ = A + B cos Y + C cos X and its Relation to the Quasiperiodic Mathieu Equation

Stephanie Mason, Richard Rand

Proc. ASME. DETC99, Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise, 1649-1657, September 12–16, 1999

Paper No: DETC99/VIB-8052

DOI: https://doi.org/10.1115/DETC99/VIB-8052

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Topics: Flow (Dynamics), Stability

Proceedings Papers

Dynamics of Towed Cables During Transient Motions

Leslie Ng, Richard Rand, William Keith

Proc. ASME. IDETC-CIE2001, Volume 6B: 18th Biennial Conference on Mechanical Vibration and Noise, 1151-1160, September 9–12, 2001

Paper No: DETC2001/VIB-21438

DOI: https://doi.org/10.1115/DETC2001/VIB-21438

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Topics: Cables, Dynamics (Mechanics), Transients (Dynamics), Vessels, Differential equations

Journal Articles

Mathieu's Equation and Its Generalizations: Overview of Stability Charts and Their Features

Ivana Kovacic, Richard Rand, Si Mohamed Sah

Appl. Mech. Rev. March 2018, 70(2): 020802.

Paper No: AMR-17-1054

DOI: https://doi.org/10.1115/1.4039144

Published Online: February 14, 2018

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Topics: Damping, Excitation, Stability, Delays, Differential equations

Proceedings Papers

Hopf Bifurcations in Two-Player Delayed Replicator Dynamics

Elizabeth Wesson, Richard Rand

Proc. ASME. IDETC-CIE2014, Volume 8: 26th Conference on Mechanical Vibration and Noise, V008T11A055, August 17–20, 2014

Paper No: DETC2014-35404

DOI: https://doi.org/10.1115/DETC2014-35404

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Topics: Bifurcation, Dynamics (Mechanics), Limit cycles

Proceedings Papers

Dynamics of a System of Two Coupled Oscillators Which are Driven by a Third Oscillator

Lauren Lazarus, Richard Rand

Proc. ASME. IDETC-CIE2014, Volume 8: 26th Conference on Mechanical Vibration and Noise, V008T11A049, August 17–20, 2014

Paper No: DETC2014-34642

DOI: https://doi.org/10.1115/DETC2014-34642

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Topics: Bifurcation, Dynamics (Mechanics), Numerical analysis

Proceedings Papers

Hopf Bifurcation in a Disk-Shaped NEMS

Maxim Zalalutdinov, Jeevak Parpia, Keith Aubin, Harold Craighead, Tuncay Alan, Alan Zehnder, Richard Rand

Proc. ASME. IDETC-CIE2003, Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 1759-1769, September 2–6, 2003

Paper No: DETC2003/VIB-48516

DOI: https://doi.org/10.1115/DETC2003/VIB-48516

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Topics: Bifurcation, Disks, Nanoelectromechanical systems, Lasers, Laser beams, Finite element methods, Finite element model, Limit cycles, Oscillations, Stress

Proceedings Papers

Dynamics of Two Van Der Pol Oscillators Coupled via a Bath

Erika Camacho, Richard Rand, Howard Howland

Proc. ASME. IDETC-CIE2003, Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2407-2414, September 2–6, 2003

Paper No: DETC2003/VIB-48593

DOI: https://doi.org/10.1115/DETC2003/VIB-48593

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Topics: Bifurcation, Chemistry, Computer software, Dynamics (Mechanics), Stability

Proceedings Papers

2:2:1 Resonance in the Quasiperiodic Mathieu Equation

Richard Rand, Kamar Guennoun, Mohamed Belhaq

Proc. ASME. IDETC-CIE2003, Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2155-2162, September 2–6, 2003

Paper No: DETC2003/VIB-48563

DOI: https://doi.org/10.1115/DETC2003/VIB-48563

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Topics: Resonance, Flow (Dynamics), Stability

Proceedings Papers

Dynamics of Three Coupled Van der Pol Oscillators With Application to Circadian Rhythms

Kevin Rompala, Richard Rand, Howard Howland

Proc. ASME. IDETC-CIE2005, Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 1791-1799, September 24–28, 2005

Paper No: DETC2005-84017

DOI: https://doi.org/10.1115/DETC2005-84017

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Topics: Brain, Chemistry, Computer software, Dynamics (Mechanics), Flow (Dynamics)

Proceedings Papers

Parametric Resonance of Hopf Bifurcation

Richard Rand, Albert Barcilon, Tina Morrison

Proc. ASME. IDETC-CIE2005, Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 1557-1564, September 24–28, 2005

Paper No: DETC2005-84016

DOI: https://doi.org/10.1115/DETC2005-84016

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Topics: Bifurcation, Resonance, Damping, Dynamics (Mechanics), Harmonic oscillators, Limit cycles, Steady state

Proceedings Papers

Frequency Locking in a Forced Mathieu-van der Pol System

Manoj Pandey, Richard Rand, Alan Zehnder

Proc. ASME. IDETC-CIE2005, Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 1367-1373, September 24–28, 2005

Paper No: DETC2005-84018

DOI: https://doi.org/10.1115/DETC2005-84018

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Topics: Bifurcation, Computer software, Dynamics (Mechanics), Flow (Dynamics), Microelectromechanical systems, Steady state

Proceedings Papers

2:1:1 Resonance in the Quasiperiodic Mathieu Equation

Richard Rand, Tina Morrison

Proc. ASME. IDETC-CIE2005, Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 711-718, September 24–28, 2005

Paper No: DETC2005-84015

DOI: https://doi.org/10.1115/DETC2005-84015

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Topics: Resonance, Algebra

Proceedings Papers

Coexistence Phenomenon in Autoparametric Excitation of Two Degree of Freedom Systems

Geoffrey Recktenwald, Richard Rand

Proc. ASME. IDETC-CIE2005, Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 1937-1948, September 24–28, 2005

Paper No: DETC2005-84020

DOI: https://doi.org/10.1115/DETC2005-84020

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Topics: Degrees of freedom, Excitation, Stability

Proceedings Papers

Slow Passage Through Resonance in Mathieu’s Equation

Leslie Ng, Richard Rand, Michael O’Neil

Proc. ASME. IMECE2002, Design Engineering, 131-140, November 17–22, 2002

Paper No: IMECE2002-39139

DOI: https://doi.org/10.1115/IMECE2002-39139

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Topics: Resonance, Approximation, Flow (Dynamics)

Proceedings Papers

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

Leslie Ng, Richard Rand

Proc. ASME. IMECE2002, Design Engineering, 425-433, November 17–22, 2002

Paper No: IMECE2002-32406

DOI: https://doi.org/10.1115/IMECE2002-32406

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Topics: Bifurcation, Degrees of freedom, Differential equations, Excitation, Free vibrations, Stability, Vibration

Journal citation

NARROW

Bifurcations in a Mathieu Equation With Cubic Nonlinearities

A Quasiperiodic Mathieu Equation

Impact Dynamics of a Supercavitating Underwater Projectile

Dynamics of Two Coupled Van der Pol Oscillators With Delay Coupling

Bifurcations in the Dynamics of Two Coupled van der Pol Oscillators With Delay Coupling

On the Torus Flow Y′ = A + B cos Y + C cos X and its Relation to the Quasiperiodic Mathieu Equation

Dynamics of Towed Cables During Transient Motions

Mathieu's Equation and Its Generalizations: Overview of Stability Charts and Their Features

Hopf Bifurcations in Two-Player Delayed Replicator Dynamics

Dynamics of a System of Two Coupled Oscillators Which are Driven by a Third Oscillator

Hopf Bifurcation in a Disk-Shaped NEMS

Dynamics of Two Van Der Pol Oscillators Coupled via a Bath

2:2:1 Resonance in the Quasiperiodic Mathieu Equation

Dynamics of Three Coupled Van der Pol Oscillators With Application to Circadian Rhythms

Parametric Resonance of Hopf Bifurcation

Frequency Locking in a Forced Mathieu-van der Pol System

2:1:1 Resonance in the Quasiperiodic Mathieu Equation

Coexistence Phenomenon in Autoparametric Excitation of Two Degree of Freedom Systems

Slow Passage Through Resonance in Mathieu’s Equation

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

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