Surprisingly complicated dynamics of a SDOF linear oscillator coupled to a nonlinear attachment

in ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, 2005 (2005, September)

We study the dynamics of a two-degree-of-freedom nonlinear system consisting of a linear oscillator with an essentially nonlinear attachment. For the undamped system, we perform a numerical study based on ... [more ▼]

We study the dynamics of a two-degree-of-freedom nonlinear system consisting of a linear oscillator with an essentially nonlinear attachment. For the undamped system, we perform a numerical study based on non-smooth temporal transformations to determine its periodic solutions in a frequency–energy plot. It turns out that there is a sequence of periodic solutions bifurcating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using the complexification / averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. [less ▲]

Multi-frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments

in Journal of Sound & Vibration (2005), 285(1-2), 483-490

We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multi-degree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous ... [more ▼]

We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multi-degree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes (NNMs) of the attachment, and is studied utilizing numerical wavelet transforms. The multi-frequency nonlinear energy transfer discussed herein differs from multi-frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single-dof nonlinear attachments takes place. (c) 2004 Elsevier Ltd. All rights reserved. [less ▲]

Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment

in Physica D: Nonlinear Phenomena (2005), 204(1-2), 41-69

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness ... [more ▼]

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness. We consider first the undamped system and perform a numerical study based on non-smooth transformations to determine its periodic solutions in a frequency-energy plot. It is found that there is a sequence of periodic solutions bifurcating or emanating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using a complexification/averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer (energy pumping) from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. (c) 2005 Elsevier B.V. All rights reserved. [less ▲]