Application of nonlinear dynamics approaches to the numerical study of PDE

1995 ◽  
Author(s):  
Itaru Hataue
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Study

Dynamic Characteristic Analysis of Rotating Blade with Transverse Crack - Part II: A Comparison Study of Different Crack Models

2020 ◽  
pp. 1-32
Author(s):  
Laihao Yang ◽  
Zheshuai Yang ◽  
Zhu Mao ◽  
Shuming Wu ◽  
Xuefeng Chen ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Comparative Analysis ◽  
Nonlinear Effect ◽  
Numerical Study ◽  
Crack Depth ◽  
Harmonic Component ◽  
Characteristic Analysis ◽  
Load Amplitude ◽  
Rotating Blade ◽  
Comparative Results

Abstract This study aims at the comparative analysis and improvement of different analytical crack models for rotating blade. Part II of this study focuses on the comparative analysis of dynamic characteristics based on modified models mentioned in Part I. A nonlinear damage indicator (NDI) and an equivalent energy indicator (EEI) are introduced to characterize the nonlinear effect of crack from different perspectives. EEI offers a physical mechanism explanation of crack closing behavior, which is invisible. Meanwhile, NDI offers an observable indicator to quantify the nonlinearity of crack. It is demonstrated through the numerical study that the variation of NDI and EEI varies the same with each other, which cross-verified the validity of NDI and EEI for quantifying the nonlinear effect of crack. Comparative investigations are performed to analyze the effects of load amplitude, crack depth, and crack location on the nonlinear dynamics of cracked blade, and both NDI and EEI are utilized to quantify the nonlinear effects of crack. The comparative results suggest that NDI of the second order super-harmonic component increase with the increasing crack depth and excitation load amplitude and decreases with the increasing crack locations, while the variation of EEI follows the variation of NDI. This phenomenon indicates that the crack which is deeper and closer to blade root under a larger load will be more dangerous. This study's comparative results may provide some guidance for choosing the analytical crack models when analyzing the nonlinear dynamics of rotating cracked-blade and blade health monitoring.

scholarly journals Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study

2018 ◽  
Vol 26 (4) ◽  
pp. 4751 ◽  
Author(s):  
Nianqiang Li ◽  
H. Susanto ◽  
B. R. Cemlyn ◽  
I. D. Henning ◽  
M. J. Adams
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Study ◽  
Laser Arrays

Nonlinear Dynamics and Control of the Scan Process in Noncontacting Atomic Force Microscopy

2005 ◽  
Author(s):  
S. Hornstein ◽  
O. Gottlieb ◽  
L. Ioffe
Keyword(s):  
Nonlinear Dynamics ◽  
Atomic Force Microscopy ◽  
Numerical Study ◽  
Initial Boundary ◽  
Atomic Interaction ◽  
Force Microscopy ◽  
Atomic Force ◽  
Dynamics And Control ◽  
And Control ◽  
Nonlinear Dynamics And Control

The focus of this paper is on the nonlinear dynamics and control of the scan process in noncontacting atomic force microscopy. An initial-boundary-value problem is consistently formulated to include both nonlinear dynamics of a microcantilever with a localized atomic interaction force for the surface it is mapping, and a horizontal boundary condition for a constant scan speed and its control. The model considered is obtained using the extended Hamilton’s principle which yields two partial differential equations for the combined horizontal and vertical motions. Isolation of a Lagrange multiplier describing the microbeam fixed length enables construction of a modified equation of motion which is reduced to a single mode dynamical system via Galerkin’s method. The analysis includes a numerical study of the strongly nonlinear system leading to a stability map describing an escape bifurcation threshold where the tip, at the free end of the microbeam, ‘jumps-to-contact’ with the sample. Results include periodic ultrasubharmonic and quasiperiodic solutions corresponding to primary and secondary resonances.

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