Expansion of Nonlinear System Response Using Linear Transformation Matrices from Reduced Component Model Representations

2013 ◽  
pp. 743-769 ◽  
Author(s):  
Tim Marinone ◽  
Louis Thibault ◽  
Peter Avitabile
Keyword(s):  
Nonlinear System ◽  
Linear Transformation ◽  
Component Model ◽  
System Response ◽  
Transformation Matrices

Spectrographic Analysis for the Modal Testing of Nonlinear Aeroelastic Systems

2006 ◽  
Author(s):  
Catharine C. Marsden ◽  
Stuart J. Price
Keyword(s):  
Nonlinear System ◽  
Time History ◽  
Modal Testing ◽  
System Response ◽  
Spectrographic Analysis ◽  
Input Frequency ◽  
Frequency Content ◽  
Aeroelastic System ◽  
Time Histories ◽  
Sine Sweep

The spectrograph is a signal processing tool often used for the frequency domain analysis of time-varying signals. When the signal to be analyzed is a function of time, the spectrograph represents the frequency content of the signal as a sequence of power spectra that change with time. In this paper, the usefulness of the technique is demonstrated in its application to the analysis of the time history response of a nonlinear aeroelastic system. The aeroelastic system is modeled analytically as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap is used to provide the forcing input to the system. The nonlinear system is obtained by introducing a freeplay type of nonlinearity in the pitch degree-of-freedom restoring moment. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. Time-histories are obtained for the nonlinear responses of the linear and nonlinear aeroelastic systems to a sine-sweep input. The time-histories are analyzed using the spectrographic technique, and the frequency content of the response is plotted directly as a function of the input frequency. Results show that the combination of the sine-sweep input with the spectrographic analysis permits a unique insight into the behaviour of the nonlinear system with a minimum of testing. It is shown that the frequency of the nonlinear system response is a function of the input frequency and one other characteristic frequency that can be associated with the limit cycle oscillations of the same nonlinear system subject to a transient input.

scholarly journals AUTOMATION OF EVALUATION OF FACTOR RELATIONS AND STRATEGIES OF PRODUCTION AND TECHNOLOGICAL RELATIONS BY THE OPERATOR OF TRANSFORMATION OF THE BASIS OF LINEAR INFORMATION STRUCTURES

2019 ◽  
Vol 7 (4) ◽  
pp. 85-91
Author(s):  
Vladimir Kulikov ◽  
Elena Serova ◽  
Olga Stafeeva ◽  
Anastasia Pestrikova
Keyword(s):  
Linear Transformation ◽  
Structured Data ◽  
Equivalent Transformation ◽  
Information Structures ◽  
Transformation Matrices ◽  
Fixed Price ◽  
Linear Information ◽  
Organization Of Production

In this paper, an attempt is made to equivalent transformation of structured data by tabular forms by means of their adequate transformation into vector similarity forms, which significantly improve the conditions for formalization of computing processes and processing of information structures and data arrays. The solution of the problem is obtained by such a linear transformation of vector structures of information in the corresponding analytical dependencies using transformation matrices. The method of estimation of achievement of balance between expenses on the organization of production and, the income received from sale of production at the fixed price is offered.

scholarly journals Nonlinear Controller Design via Inferenced-Augmentation of Equivalent Linearized System

2019 ◽  
Vol 8 (1) ◽  
pp. 28
Author(s):  
Ovie EseOghene ◽  
Chizea F. D. ◽  
Akachukwu C. M.
Keyword(s):  
Nonlinear System ◽  
Controller Design ◽  
Nonlinear Models ◽  
Design Method ◽  
System Response ◽  
Nonlinear Controller ◽  
Primary Parameter ◽  
Benchmark System ◽  
Linearized System ◽  
Linear Effects

Output compensation of nonlinear system response is studied in this work with an inference-based design method used to control the nonlinear dynamics in the presence of non-linear effects. This design which is driven by practical considerations is informed by the comparisons made between nonlinear models and their linearized derivatives. While a detailed mathematical route has not been followed here, the results seem to show the workability of the proposed method and at its core, the design is driven by its intuitiveness. The proposed technique utilizes as primary parameter for comparison, the steady state error term which is derived from the behavior of the linear dynamics. Possible application areas for this design is in reduced energy control of nonlinear systems. The method was tested in simulation on a generic nonlinear system and a cart-driven inverted pendulum benchmark system.

scholarly journals Consistency of nonlinear system response to complex drive signals

2007 ◽  
Vol 35 (Supplement) ◽  
pp. 17-20
Author(s):  
Atsushi Uchida ◽  
Shigeru Yoshimori ◽  
Ryan McAllister ◽  
Rajarshi Roy
Keyword(s):  
Nonlinear System ◽  
System Response ◽  
Drive Signals

Modeling and Identification of a Nonlinear SDOF Moored Structure, Part 1—Hydrodynamic Models and Algorithms

2004 ◽  
Vol 126 (2) ◽  
pp. 175-182 ◽  
Author(s):  
S. Narayanan ◽  
S. C. S. Yim
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Small Body ◽  
Nonlinear System Identification ◽  
Ocean Waves ◽  
System Response ◽  
Restoring Force ◽  
Nonlinear Structure ◽  
Submerged Sphere ◽  
Highly Nonlinear

The highly nonlinear responses of compliant ocean structures characterized by a large-geometry restoring force and coupled fluid-structure interaction excitation are of great interest to ocean and coastal engineers. Practical modeling, parameter identification, and incorporation of the inherent nonlinear dynamics in the design of these systems are essential and challenging. The general approach of a nonlinear system technique using very simple models has been presented in the literature by Bendat. In Part 1 of this two-part study, two specific nonlinear small-body hydrodynamic Morison type formulations: (A) with a relative-velocity (RV) model, and (B) with an independent flow-field (IFF) model, are formulated. Their associated nonlinear system-identification algorithms based on the reverse multiple-input/single-output (R-MI/SO) system-identification technique: (A.1) nonlinear-structure linearly damped, and (A.2) nonlinear-structure coupled hydrodynamically damped for the RV model, and (B.1) nonlinear-structure nonlinearly damped for the IFF model, are developed for a specific experimental submerged-sphere mooring system under ocean waves exhibiting such highly nonlinear response behaviors. In Part 2, using the measured input wave and output system response data, the algorithms derived based on the MI/SO linear analysis of the reverse dynamic systems are applied to identify the properties of the highly nonlinear system. Practical issues on the application of the R-MI/SO technique based on limited available experimental data are addressed.

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