10,972 research outputs found
Identification of Nonlinear Normal Modes of Engineering Structures under Broadband Forcing
The objective of the present paper is to develop a two-step methodology
integrating system identification and numerical continuation for the
experimental extraction of nonlinear normal modes (NNMs) under broadband
forcing. The first step processes acquired input and output data to derive an
experimental state-space model of the structure. The second step converts this
state-space model into a model in modal space from which NNMs are computed
using shooting and pseudo-arclength continuation. The method is demonstrated
using noisy synthetic data simulated on a cantilever beam with a
hardening-softening nonlinearity at its free end.Comment: Journal pape
Thermal vortex dynamics in thin circular ferromagnetic nanodisks
The dynamics of gyrotropic vortex motion in a thin circular nanodisk of soft
ferromagnetic material is considered. The demagnetization field is calculated
using two-dimensional Green's functions for the thin film problem and fast
Fourier transforms. At zero temperature, the dynamics of the
Landau-Lifshitz-Gilbert equation is simulated using fourth order Runge-Kutta
integration. Pure vortex initial conditions at a desired position are obtained
with a Lagrange multipliers constraint. These methods give accurate estimates
of the vortex restoring force constant and gyrotropic frequency, showing
that the vortex core motion is described by the Thiele equation to very high
precision. At finite temperature, the second order Heun algorithm is applied to
the Langevin dynamical equation with thermal noise and damping. A spontaneous
gyrotropic motion takes place without the application of an external magnetic
field, driven only by thermal fluctuations. The statistics of the vortex radial
position and rotational velocity are described with Boltzmann distributions
determined by and by a vortex gyrotropic mass ,
respectively, where is the vortex gyrovector.Comment: 18 pages, 17 figure
Nonlinear normal modes, modal interactions and isolated resonance curves
The objective of the present study is to explore the connection between the
nonlinear normal modes of an undamped and unforced nonlinear system and the
isolated resonance curves that may appear in the damped response of the forced
system. To this end, an energy balancing technique is used to predict the
amplitude of the harmonic forcing that is necessary to excite a specific
nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip
serves to illustrate the developments. The practical implications of isolated
resonance curves are also discussed by computing the beam response to sine
sweep excitations of increasing amplitudes.Comment: Journal pape
Development of numerical algorithms for practical computation of nonlinear normal modes
When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible
with limited implementation effort, which paves the way to a practical method for determining the NNMs
of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting
procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to
reduce the computational burden of the algorithm. A simplified discrete model of a nonlinear bladed disk is
considered to demonstrate the developments
- …