50 research outputs found
A principle of similarity for nonlinear vibration absorbers
This paper develops a principle of similarity for the design of a nonlinear
absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a
nonlinear primary system. Specifically, for effective vibration mitigation, we
show that the NLTVA should feature a nonlinearity possessing the same
mathematical form as that of the primary system. A compact analytical formula
for the nonlinear coefficient of the absorber is then derived. The formula,
valid for any polynomial nonlinearity in the primary system, is found to depend
only on the mass ratio and on the nonlinear coefficient of the primary system.
When the primary system comprises several polynomial nonlinearities, we
demonstrate that the NLTVA obeys a principle of additivity, i.e., each
nonlinear coefficient can be calculated independently of the other nonlinear
coefficients using the proposed formula
optimization of multiple tuned mass dampers for multimodal vibration control
In this paper, a new computational method for the purpose of multimodal
vibration mitigation using multiple tuned mass dampers is proposed.
Classically, the minimization of the maximum amplitude is carried out using
direct optimization. However, as shall be shown in the paper, this
approach is prone to being trapped in local minima, in view of the nonsmooth
character of the problem at hand. This is why this paper presents an original
alternative to this approach through norm-homotopy optimization. This approach,
combined with an efficient technique to compute the structural response, is
shown to outperform direct optimization in terms of speed and
performance. Essentially, the outcome of the algorithm leads to the concept of
all-equal-peak design for which all the controlled peaks are equal in
amplitude. This unique design is new with respect to the existing body of
knowledge.Comment: This is a new version of a preprint previously named "All-equal-peak
design of multiple tuned mass dampers using norm-homotopy optimization
Suppression of Limit Cycle Oscillations using the Nonlinear Tuned Vibration Absorber
The objective of the present study is to mitigate, or even completely
eliminate, the limit cycle oscillations in mechanical systems using a passive
nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An
unconventional aspect of the NLTVA is that the mathematical form of its
restoring force is not imposed a priori, as it is the case for most existing
nonlinear absorbers. The NLTVA parameters are determined analytically using
stability and bifurcation analyses, and the resulting design is validated using
numerical continuation. The proposed developments are illustrated using a Van
der Pol-Duffing primary system
Broadband passive targeted energy pumping from a linear dispersive rod to a lightweight essentially non-linear end attachment
We examine non-linear resonant interactions between a damped and forced dispersive linear finite rod and a lightweight essentially nonlinear end attachment. We show that these interactions may lead to passive, broadband and on-way targeted energy flow from the rod to the attachment, which acts, in essence, as non-linear energy sink (NES). The transient dynamics of this system subject to shock excitation is examined numerically using a finite element (FE) formulation. Parametric studies are performed to examine the regions in parameter space where optimal (maximal) efficiency of targeted energy pumping from the rod to the NES occurs. Signal processing of the transient time series is then performed, employing energy transfer and/or exchange measures, wavelet transforms, empirical mode decomposition and Hilbert transforms.
By computing intrinsic mode functions (IMFs) of the transient responses of the NES and the edge of the rod, and examining resonance captures that occur between them, we are able to identify the non-linear resonance mechanisms that govern the (strong or weak) one-way energy transfers from the rod to the NES. The present study demonstrates the efficacy of using local lightweight non-linear attachments (NESs) as passive broadband energy absorbers of unwanted disturbances in continuous elastic structures, and investigates the dynamical mechanisms that govern the resonance interactions influencing this passive non-linear energy absorption
Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
The nonlinear tuned vibration absorber (NLTVA) is a recently-developed
nonlinear absorber which generalizes Den Hartog's equal peak method to
nonlinear systems. If the purposeful introduction of nonlinearity can enhance
system performance, it can also give rise to adverse dynamical phenomena,
including detached resonance curves and quasiperiodic regimes of motion.
Through the combination of numerical continuation of periodic solutions,
bifurcation detection and tracking, and global analysis, the present study
identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and
unacceptable operations. The sensitivity of these boundaries to uncertainty in
the NLTVA parameters is also investigated.Comment: Journal pape
Nonlinear Generalization of Den Hartog's Equal-Peak Method
This study addresses the mitigation of a nonlinear resonance of a mechanical
system. In view of the narrow bandwidth of the classical linear tuned vibration
absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber
(NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is
that the mathematical form of its restoring force is tailored according to the
nonlinear restoring force of the primary system. The NLTVA parameters are then
determined using a nonlinear generalization of Den Hartog's equal-peak method.
The mitigation of the resonant vibrations of a Duffing oscillator is considered
to illustrate the proposed developments
MEMS-EYE: A M/NEMS platform for the investigation of multi-physical and complex nonlinear systems
The ultimate goal of this research proposal is the creation of a
micro-optomechanical intelligence. The proposal centers on the development and
investigation of very large-scale integrated (VLSI) arrays of coupled M/NEMS
devices as platforms for the experimental study of nonlinear dynamics of
high-dimensional systems. The potential of VLSI M/NEMS arrays to function as
advanced sensors will be demonstrated through the novel idea of a MEMS EYE, an
electronics-free platform that combines imaging and pattern recognition
functionality
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