Analytical Volterra-based models for nonlinear low order flight dynamics approximation systems

2012 ◽  
Vol 116 (1185) ◽  
pp. 1123-1153 ◽  
Author(s):  
A. Omran ◽  
B. Newman
Keyword(s):  
Nonlinear Response ◽  
Volterra Series ◽  
Design Tool ◽  
Analytical Methodology ◽  
Single Degree Of Freedom ◽  
Response Characteristics ◽  
Nonlinear Responses ◽  
Volterra Theory ◽  
Dynamics Approximation ◽  
Low Order

AbstractAnalytical methodology is presented to conduct dynamical assembly of simple low order nonlinear responses for system synthesis and prediction using Volterra theory. The procedure is set forth generically and then applied to several atmospheric flight examples. A two-term truncated Volterra series, which is enough to capture the quadratic and bilinear nonlinearities, is developed for first and second order generalised nonlinear single degree of freedom systems. The resultant models are given in the form of first and second kernels. A parametric study of the influence of each linear and nonlinear term on kernel structures is investigated. A step input is then employed to quantify and qualify the nonlinear response characteristics. Uniaxial surge and pitch motions are presented as examples of the low order flight dynamic systems. These examples show the ability of the proposed analytical Volterra-based models to predict, understand, and analyse the nonlinear aircraft behaviour beyond that attainable by linear-based models. The proposed analytical Volterra-based model offers an efficient nonlinear preliminary design tool in qualifying the aircraft responses before computer simulation is available or invoked.

Low Order Vibration Models for Tracked Vehicles

1999 ◽  
Author(s):  
C. Scholar ◽  
N. C. Perkins ◽  
Z.-D. Ma
Keyword(s):  
Large Degree ◽  
Element Model ◽  
Forced Response ◽  
Minimum Size ◽  
Order System ◽  
Continuum Approximation ◽  
Translation Speed ◽  
Response Characteristics ◽  
Multi Body ◽  
Low Order

Abstract A vehicle track model is developed with the objective of providing new capabilities in modeling track vibration response. Understanding track vibration is essential to evaluating the durability of track components, the vibration energy transmitted to the vehicle, and the acoustic emission from the vehicle. A new element model is derived herein that represents a track span as a continuous elastic member with distributed inertia. This model captures the effects of static track sag. static and dynamic track tension, track translation speed, and the coupling of longitudinal and transverse track vibration. Results from a companion experimental study on a section of track support the use of this continuum approximation. The track element model is extended to describe an entire track circuit for an example military vehicle. An eigenanalysis of this circuit model leads to the system vibration modes that are subsequently employed in a low-order model for forced response. The forced response characteristics resulting from two major excitation sources, roadarm motion and polygonal action, are described. The modal content of the track response is then examined to determine the minimum size model required to describe track vibration. It is concluded that low-order system models may be developed as efficient alternatives to established large degree-of-freedom multi-body track models.

Shooting With Deflation Algorithm-Based Nonlinear Response and Neimark-Sacker Bifurcation and Chaos in Floating Ring Bearing Systems

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Sitae Kim ◽  
Alan B. Palazzolo
Keyword(s):  
Nonlinear Response ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Operating Conditions ◽  
Fluid Film ◽  
Stable Limit ◽  
Bifurcation And Chaos ◽  
Chaotic Motions ◽  
Response Characteristics ◽  
Computation Efficiency

The double-sided fluid film force on the inner and outer ring surfaces of a floating ring bearing (FRB) creates strong nonlinear response characteristics such as coexistence of multiple orbits, Hopf bifurcation, Neimark-Sacker (N-S) bifurcation, and chaos in operations. An improved autonomous shooting with deflation algorithm is applied to a rigid rotor supported by FRBs for numerically analyzing its nonlinear behavior. The method enhances computation efficiency by avoiding previously found solutions in the numerical-based search. The solution manifold for phase state and period is obtained using arc-length continuation. It was determined that the FRB-rotor system has multiple response states near Hopf and N-S bifurcation points, and the bifurcation scenario depends on the ratio of floating ring length and diameter (L/D). Since multiple responses coexist under the same operating conditions, simulation of jumps between two stable limit cycles from potential disturbance such as sudden base excitation is demonstrated. In addition, this paper investigates chaotic motions in the FRB-rotor system, utilizing four different approaches, strange attractor, Lyapunov exponent, frequency spectrum, and bifurcation diagram. A numerical case study for quenching the large amplitude motion by adding unbalance force is provided and the result shows synchronization, i.e., subsynchronous frequency components are suppressed. In this research, the fluid film forces on the FRB are determined by applying the finite element method while prior work has utilized a short bearing approximation. Simulation response comparisons between the short bearing and finite bearing models are discussed.

Theoretical and Experimental Analysis of Nonlinear Dynamics in a Linear Compressor

2001 ◽  
Vol 124 (1) ◽  
pp. 152-154 ◽  
Author(s):  
Gyu-Sang Choe ◽  
Kwang-Joon Kim
Keyword(s):  
Steady State ◽  
Nonlinear Response ◽  
Dynamic Models ◽  
Steady State Response ◽  
Describing Function ◽  
Linear Compressor ◽  
Response Characteristics ◽  
State Response ◽  
Jump Phenomena ◽  
Method Effects

Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically and experimentally. In the theoretical approach, motions of not only piston but also cylinder are considered and dynamic models for steady-state response predictions are formulated by applying the describing function method. Effects of piston mass on the jump phenomena are predicted by the derived models as an example of design parameter variation and compared with actual experimental results.

scholarly journals Nonlinear response characteristics of neural networks and single neurons undergoing optogenetic excitation

2020 ◽  
Vol 4 (3) ◽  
pp. 852-870
Author(s):  
Jannik Luboeinski ◽  
Tatjana Tchumatchenko
Keyword(s):  
Neural Networks ◽  
Nonlinear Response ◽  
Pulse Frequency ◽  
Simulation Code ◽  
Response Characteristics ◽  
Optogenetic Stimulation ◽  
Spatial Response ◽  
Temporal And Spatial ◽  
Light Beams ◽  
Indirect Stimulation

Optogenetic stimulation has become the method of choice for investigating neural computation in populations of neurons. Optogenetic experiments often aim to elicit a network response by stimulating specific groups of neurons. However, this is complicated by the fact that optogenetic stimulation is nonlinear, more light does not always equal to more spikes, and neurons that are not directly but indirectly stimulated could have a major impact on how networks respond to optogenetic stimulation. To clarify how optogenetic excitation of some neurons alters the network dynamics, we studied the temporal and spatial response of individual neurons and recurrent neural networks. In individual neurons, we find that neurons show a monotonic, saturating rate response to increasing light intensity and a nonmonotonic rate response to increasing pulse frequency. At the network level, we find that Gaussian light beams elicit spatial firing rate responses that are substantially broader than the stimulus profile. In summary, our analysis and our network simulation code allow us to predict the outcome of an optogenetic experiment and to assess whether the observed effects can be attributed to direct or indirect stimulation of neurons.

Nonlinear Response Characteristics of a Cracked Rotor in Maneuvering Aircraft

2003 ◽  
Author(s):  
Fu-Sheng Lin ◽  
Guang Meng ◽  
Eric Hahn
Keyword(s):  
Fault Diagnosis ◽  
Constant Velocity ◽  
Nonlinear Response ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Parameter Range ◽  
Cracked Rotor ◽  
Periodic Response ◽  
Response Characteristics ◽  
Cracked Rotor System

This paper investigates numerically the nonlinear response of a simple cracked rotor in moving supports, as may occur in aircraft rotors when the aircraft is maneuvering with constant velocity or acceleration. Of particular interest is the influence of the aircraft climb angle. Results show that the climb angle can markedly affect the parameter range for which the system is stable; and over which there results bifurcation, quasi-periodic response or chaotic response. It is shown that aircraft acceleration can also significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for online rotor crack fault diagnosis.

scholarly journals Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Mikhail Guskov ◽  
Fabrice Thouverez
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Response ◽  
Duffing Oscillator ◽  
Point Of View ◽  
Periodic Motions ◽  
Computational Costs ◽  
Nonlinear Responses ◽  
Time Marching ◽  
The Stability ◽  
Good Agreement

Quasi-periodic motions and their stability are addressed from the point of view of different harmonic balance-based approaches. Two numerical methods are used: a generalized multidimensional version of harmonic balance and a modification of a classical solution by harmonic balance. The application to the case of a nonlinear response of a Duffing oscillator under a bi-periodic excitation has allowed a comparison of computational costs and stability evaluation results. The solutions issued from both methods are close to one another and time marching tests showing a good agreement with the harmonic balance results confirm these nonlinear responses. Besides the overall adequacy verification, the observation comparisons would underline the fact that while the 2D approach features better performance in resolution cost, the stability computation turns out to be of more interest to be conducted by the modified 1D approach.

A Low-order Model for the Design of Piezoelectric Energy Harvesting Devices

2008 ◽  
Vol 20 (5) ◽  
pp. 495-504 ◽  
Author(s):  
Jeffrey L. Kauffman ◽  
George A. Lesieutre
Keyword(s):  
Energy Harvesting ◽  
Design Tool ◽  
Mode Shapes ◽  
Piezoelectric Energy Harvesting ◽  
Coupling Coefficients ◽  
Order Model ◽  
Power Sources ◽  
Piezoelectric Energy ◽  
Energy Harvesting Devices ◽  
Low Order

Piezoelectric energy harvesting devices are an attractive approach to providing remote wireless power sources. They operate by converting available vibration energy and storing it as electrical energy. Currently, most devices rely on mechanical excitation near their resonance frequency, so a low-order model which computes a few indicators of device performance is a critical design tool. Such a model, based on the assumed modes method, develops equations of motion to provide rapid computations of key device parameters, such as the natural frequencies, mode shapes, and electro-mechanical coupling coefficients. The model is validated with a comparison of its predictions and experimental data.

scholarly journals Nonlinear tuning of microresonators for dynamic range enhancement

2015 ◽  
Vol 471 (2179) ◽  
pp. 20140969 ◽  
Author(s):  
M. Saghafi ◽  
H. Dankowicz ◽  
W. Lacarbonara
Keyword(s):  
Nonlinear Response ◽  
Dynamic Range ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equations Of Motion ◽  
Path Following ◽  
Critical Amplitude ◽  
Inertia Effects ◽  
Response Characteristics ◽  
The Galerkin Method

This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators.

Nonlinear Response Characteristics of Discus Data Buoy Hull

2008 ◽  
Author(s):  
R. Balaji ◽  
S. A. Sannasiraj ◽  
V. Sundar
Keyword(s):  
Experimental Investigation ◽  
Response Time ◽  
Nonlinear Wave ◽  
Nonlinear Response ◽  
Phase Portraits ◽  
Testing Conditions ◽  
Response Characteristics ◽  
Wave Elevation ◽  
Time Histories ◽  
Spectral Representations

The response characteristics of the discus hull shaped data buoy under the influence of nonlinear wave conditions was studied in an experimental investigation. The measured wave elevation and the buoy response time histories were analyzed by phase-portraits as well as through the spectral representations. The details of the model, instrumentation, testing conditions and the analysis are presented and discussed in this paper.

scholarly journals Nonlinear Response Characteristics of Electrostrictive Material Sensors

2019 ◽  
Vol 31 (5) ◽  
pp. 1769
Author(s):  
Qian-Peng Li ◽  
Jia Xu ◽  
Guo-Song Feng ◽  
Zhi-Wen Zhu
Keyword(s):  
Nonlinear Response ◽  
Response Characteristics ◽  
Electrostrictive Material
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