Nonlinear Response Characteristics Research Articles

On the Characteristics of Bifurcation and Nonlinear Dynamic Response

Spectral analysis has been widely applied to the detection of bifurcation and the determination of the extent to which dynamic instability and chaotic responses develop. However, because spectral analysis employs stationary sinusoids in representing time-varying signals of inherent nonlinearity, the use of Fourier domain methodologies would inexorably risk misinterpreting the true characteristics and obscuring the underlying physics of the nonlinear system being investigated. The fact that the amplitude and frequency of all the individual spectral component of a nonlinear, nonstationary dynamic response are modulated and coupled in time necessarily implies that, if the inception and transition of a bifurcated state of unstable motion is to be fully characterized, amplitude modulation and frequency modulation need to be temporally decoupled. The fundamental notion of instantaneous frequency defines frequency as the temporal gradient of phase and thus provides a powerful mechanism through which amplitude modulation and frequency modulation can be disassociated. Results of applying instantaneous frequency to the characterization of bifurcation and evolution of instability for a cracked rotor also indicate that instantaneous frequency interprets nonlinear rotary responses with sound physical bases.

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.

THERMOACTIVE STABILIZATION OF A COMPOSITE LEIPHOLZ COLUMN

A model of the Leipholz column made of orthotropic layers is analyzed. Apart from reinforcing fibers, the layers contain thermoactive shape memory alloy fibers. A nonlinear equation of motion that takes into account moderate deflections of the column, as well as Brazier's cross-section flattening effect, is examined. The effect of the martensite transformation due to external cooling and heating on the system stability expressed in terms of the critical load is investigated. The temperature change is also shown to affect the characteristics of the column nonlinear response, because it can lead to conversion of subcritical bifurcation into a supercritical one.

Non-linearities in flight control systems

AbstractNon-linear behaviour is usually undesirable for the operation of any system and it needs to be minimised in flight control systems in order to provide the pilot with a predictable and well-behaved aircraft. The non-linear response characteristics exhibited by all aircraft and their flight control systems can be characterised by using nonlinear functions to simulate and analyse their behaviour. This paper explores the types of physical non-linearities that exist in aircraft flight control systems and provides some examples. It describes how the non-linear stability might be analysed and addresses the subject of actuation systems modelling. The final section provides recommendations for minimising non-linear behaviour and gives some general guidelines on how to deal with non-linear characteristics.

Effects of Modal Interactions on Vibration Performance in Ultrasonic Cutting

The effects of modal interactions and nonlinear response characteristics can hamper implementation of high power ultrasonic technologies, due to the resulting modal coupling, increased stress, audible noise levels and poor control of the operating response. These different adverse responses are illustrated by characterising the vibration behaviour of single-blade and multi-blade ultrasonic cutting systems. This paper proposes design strategies to eliminate the effects of modal interactions, by focusing on reducing the number of vibration modes, and to reduce the effects of nonlinear responses, by serial coupling of tuned components with appropriate cubic softening and hardening response characteristics.

Deformation Behavior of Fiber-Reinforced Polymer Reinforced Engineered Cementitious Composite (ECC) Flexural Members under Reversed Cyclic Loading Conditions

Research provided herein studies the response of fiber-reinforced polymer (FRP) reinforced engineered cementitious composite (ECC) members, focusing on flexural load-deformation behavior, residual deflection, damage evolution, and failure mode. Critical aspects of conventional FRP-reinforced concrete members are reviewed and compared to FRP reinforced ECC. The interaction of linear FRP reinforcement and ECC matrix with ductile stress-strain behavior in tension results in nonlinear elastic flexural response characteristics with stable hysteretic behavior, small residual deflection, and ultimately gradual compression failure. Compatible deformations of reinforcement and matrix lead to low interfacial bond stress and prevent composite disintegration by bond splitting and cover spalling. Flexural stiffness and strength as well as crack formation and widths in FRP-reinforced ECC members are found effectively independent of interfacial bond properties due to the tensile deformation characteristics of the cementitious matrix. A model for the load-deflection envelope based on a nonlinear moment-curvature relationship is suggested.

Comparison of Static and Dynamic Neural Networks for Limit Cycle Oscillation Prediction

A dynamic artificial neural network in the form of a multilayer perceptron with a delayed recurrent feedback connection is investigated to determine its ability to predict linear and nonlinear flutter response characteristics. Flight-test results show that limit cycle oscillation (LCO) response characteristics are strongly dependent on Mach number in the transonic flight regime. This effect is also evident in the classical transonic small-disturbance theory governing equations. A dynamic network is considered in order to examine the effects of sequential Mach-number dependence on the network's predictive capability. The architecture of a dynamic network allows for modeling data dependent on a sequentially or linearly increasing parameter (usually time, but in this case Mach number). The predictive capabilities are compared to those of a static artificial neural network. The network is developed and trained using linear flutter analysis and flight-test results from a fighter test. Eleven external store carriage configurations are used as training data, and three configurations are used as test cases. The dynamic network was successful in predicting the aeroelastic oscillation frequency and amplitude responses over a range of Mach numbers for two of the test cases. The dynamic network showed slightly better correlation to flight-test results for the typical LCO test case but slightly worse correlation for the flutter case. Predictions for the nontypical LCO test case were not good for either network.

Visual cortex neurons of monkeys and cats: temporal dynamics of the contrast response function.

Cortical neurons display two fundamental nonlinear response characteristics: contrast-set gain control (also termed contrast normalization) and response expansion (also termed half-squaring). These nonlinearities could play an important role in forming and maintaining stimulus selectivity during natural viewing, but only if they operate well within the time frame of a single fixation. To analyze the temporal dynamics of these nonlinearities, we measured the responses of individual neurons, recorded from the primary visual cortex of monkeys and cats, as a function of the contrast of transient stationary gratings that were presented for a brief interval (200 ms). We then examined 1) the temporal response profile (i.e., the post stimulus time histogram) as a function of contrast and 2) the contrast response function throughout the course of the temporal response. We found that the shape and complexity of the temporal response profile varies considerably from cell to cell. However, within a given cell, the shape remains relatively invariant as a function of contrast and appears to be simply scaled and shifted. Stated quantitatively, approximately 95% of the variation in the temporal responses as a function of contrast could be accounted for by scaling and shifting the average poststimulus time histogram. Equivalently, we found that the overall shape of the contrast response function (measured every 2 ms) remains relatively invariant from the onset through the entire temporal response. Further, the contrast-set gain control and the response expansion are fully expressed within the first 10 ms after the onset of the response. Stated quantitatively, the same, scaled Naka-Rushton equation (with the same half-saturation contrast and expansive response exponent) provides a good fit to the contrast response function from the first 10 ms through the last 10 ms of the temporal response. Based upon these measurements, it appears as though the two nonlinear properties, contrast-set gain control and response expansion, are present in full strength, virtually instantaneously, at the onset of the response. This observation suggests that response expansion and contrast-set gain control can influence the performance of visual cortex neurons very early in a single fixation, based on the contrast within that fixation. In the DISCUSSION, we consider the implications of the results within the context of 1) slower types of contrast gain control, 2) discrimination performance, 3) drifting steady-state measurements, 4) functional models that incorporate response expansion and contrast normalization, and 5) structural models of the biochemical and biophysical neural mechanisms.

Two-dimensional characteristics of the second-order nonlinear optical response in dipolar donor–acceptor coordination complexesElectronic supplementary information (ESI) available: optimised Cartesian co-ordinates for structures 2–6. See http://www.rsc.org/suppdata/nj/b1/b108672c/

The two-dimensional (2D) nonlinear optical (NLO) response of a series of dipolar donor–acceptor bis(salicylaldiminato)Ni(II) Schiff base planar coordination complexes was investigated using the INDO/SCI-SOS formalism. The in-plane 2D NLO character of this class of materials can be related to various low-energy charge-transfer (CT) states and is achieved by an accurate design of substitution pattern of the unsubstituted bis(salicylaldiminato) framework. While z-polarised electronic transitions, parallel with respect the molecular dipolar (z) axis, contribute to the diagonal hyperpolarisability tensor component, perpendicularx-polarised transitions contribute to off-diagonal hyperpolarisability tensors. Unlike non-dipolar multidimensional NLO structures, whose nonlinearity within the framework of the sum-over-states formalism is necessarily due only to three-level terms, in this case the 2D nonlinearity is generally dominated by two-level terms. It necessarily requires the existence of a strong, lowest energy, perpendicular CT transition in order to provide a substantial two-level contribution to off-diagonal tensors.

입체 복합구조물의 하부골조 층수 변화에 따른 비선형 거동특성

상부벽식-하부골조 구조(복합구조)는 일반적으로 전이층을 중심으로 상부는 주거공간의 전단벽식의 고층아파트이고 하부는 상업공간의 보-기등의 골조구조이다. 이러한 구조물은 구조형식의 특성상 강성비정형, 질량비정형, 기하학적 비정형 등 비정형 형태의 특징을 갖고 있다. 본 연구에서는 하부골조 구조물의 층수가 변화할 경우에 대해 복합 구조물의 비선형 거동특성과 내진성능을 파악하였다. 비선형 해석결과로부터 얻은 결론은 다음과 같다. 1) 비선형 정적해석의 최상층변위각과 밑면전 단력계수로부터 하부구조의 층수가 증가할 경우 구조물의 밑면전단력계수는 감소하였으나 최상층변위각은 증가하였다. 2) 하부구조의 층수가 증가할 경우 상부벽식구조의 층간변위각과 소성율은 감소하였으며, 상부벽식은 탄성상태에 가까운 거동을 하였다. 3) 하부구조의 층수가 증가할 경우 하부구조에서 층간변위각이 집중적으로 증가하였다. The upper wall-lower frame structures(mixed building structures) are usually composed of shear wall structure in the upper part of structure which is used as residential space and frame structure in the lower part of structure which is used as commercial space centering around the transfer system in the lower part of structure. These structures are characteristics of stiffness irregularity, mass irregularity, and vertical geometric irregularity. The purpose of this study is to investigate the nonlinear response characteristics and the seismic capacity of mixed building structures when the number of stories in the lower frame is varied. The conclusions of this study are following. 1) As the result of push-over analysis of structure such as roof drift(i.e. roof displacement/structural height) and base shear coefficient, when the stories of lower frame system are increased, base shear coefficient is decreased, but roof drift is increased. 2) According to an increase in stories of the lower fame, story drift and ductility ratio of upper wall system are decreased and behavior of upper wall system is closed to elastic. 3) When the stories of lower frame system are increased, the excessive story drift is concentrated on the lower frame system.

Simulations of non‐stationary frequency content and its importance to seismic assessment of structures

AbstractTo verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 John Wiley & Sons, Ltd.

Monte Carlo based analysis of intermodulation distortion behavior in GaN–AlxGa1−xN high electron mobility transistors for microwave applications

Monte Carlo based calculations of the large-signal nonlinear response characteristics of GaN–AlxGa1−xN high electron mobility transistors with particular emphasis on intermodulation distortion (IMD) have been performed. The nonlinear electrical transport is treated on first principles, all scattering mechanisms included, and both memory and distributed effects built into the model. The results demonstrate an optimal operating point for low IMD at reasonably large output power due to a minima in the IMD curve. Dependence of the nonlinear characteristics on the barrier mole fraction x is also demonstrated and analyzed. Finally, high-temperature predictions of the IMD have been made by carrying out the simulations at 600 K. An increase in dynamic range with temperature is predicted, due to a relative suppression of interface roughness scattering.

Limit Cycle Oscillation Prediction Using Artificial Neural Networks

A static artiŽ cial neural network in the form of a multilayer perceptron is investigated to determine its ability to predict linear and nonlinear  utter response characteristics. The network is developed and trained using linear  utter analysis and  ight-test results from a Ž ghter test. Eleven external store carriage conŽ gurations are used as training data, and three conŽ gurations are used as test cases. The network was successful in predicting the aeroelastic oscillation frequency and amplitude responses over a range of Mach numbers for two of the test cases. Predictions for the third test case were not as good. Several network sizes were investigated, and it was found that small networks tended to overgeneralize the training data and are not capable of accurate prediction beyond the sample space. Conversely, networks that were too large, or trained to error levels that were extreme, tended to memorize the training data, and are also unable to produce adequate predictions beyond the sample space. The results of this study indicate that relatively simple networks using small training sets can be used to predict both linear and nonlinear  utter response characteristics.

Theoretical and Experimental Analysis of Nonlinear Dynamics in a Linear Compressor

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.

A GENERALIZED LOCAL LINEARIZATION PRINCIPLE FOR NON-LINEAR DYNAMICAL SYSTEMS

Tangent spaces in non-linear dynamical systems are state dependent. Hence, it is generally not possible to exactly represent a non-linear dynamical system by a linear one over finite segments of the evolving trajectories in the phase space. It is known from the well-known theorem of Hartman and Grobman that a non-linear oscillator admits a linearization within a neighbourhood of any hyperbolic fixed point in the sense that the linearized flow bears a topological conjugacy to the non-linear flow within the same neighbourhood. This linearization is based on the construction of the tangent space to the non-linear vector field at the hyperbolic fixed point. Even though useful in bifurcation analysis, such a linearization procedure cannot be successfully applied to identically simulate the non-linear flow over the phase space because the functional form of the topological conjugacy is not known. With this in mind, an implicit approach to local linearization is evolved in this paper such that the tangent space of the linearized equation transversally intersects the tangent space to the non-linear dynamical system at that point in the state space where the solution vector is desired. Several numerical schemes for the implementation of this implicit and local linearization procedure are explored and illustrated with several numerical results. It is shown that the locally transversal linearization (LTL) procedure finally reduces the given set of non-linear ordinary differential equations (ODEs) to a set of transcendental algebraic equations with the desired solution vector as the unknown. The variables in the state space appear as unknown quantities in this approach. Finally, one arrives at non-linear Poincare maps for the non-linear oscillator. In this scheme, the characteristic time interval for the map is arbitrarily fixed. The methodology is found to be quite versatile for handling non-linear dynamical systems. In particular, it is verified that these schemes are capable of accurately predicting a wide spectrum of typically non-linear response characteristics, such as limit cycles, multi-periodicity, almost periodicity and chaos. For a limited class of response patterns, the principle proposed has another advantage in that the time step for integrating the non-linear ODEs need not be small. An improved and a more general higher order version of the LTL method is also considered. A distinct advantage of this higher version is in its improved ability for a closer simulation of phase-dependent time histories where a difference in the initial conditions leads to a phase difference in the realized solution history.

An ANN-based smart capacitive pressure sensor in dynamic environment

A multilayer artificial neural network (ANN) is proposed for modeling of a capacitive pressure sensor (CPS). When the ambient temperature changes over a wide range, the nonlinear response characteristics of a CPS change significantly. In many practical conditions, the effect of temperature on the change in the CPS characteristics may be nonlinear. The proposed ANN model can provide correct readout of the applied pressure under such conditions. A novel scheme for estimation of the ambient temperature from the sensor characteristics itself is proposed. A second ANN is utilized to estimate the ambient temperature from the knowledge of the offset capacitance, i.e., the zero-pressure capacitance. A microcontroller unit (MCU)-based implementation scheme for this model is also considered. Simulation results show that this model can estimate the pressure with a maximum error of ±2% over a wide variation of temperature from −50°C to 150°C.

Nonlinear impedance of a microwave-driven Josephson junction with noise

The nonlinear impedance of a point Josephson junction is calculated under various conditions for the resistively shunted junction model in the presence of noise. The calculation proceeds by solving the Langevin equation for the mechanical problem of a Brownian particle in a tilted cosine potential in the presence of a strong ac force ignoring inertial effects. The exact solution of the infinite hierarchy of equations for the moments (expectation values of the Fourier components of the phase angle), which describe the dynamics of the junction, is expressed in terms of a matrix continued fraction. This solution allows one to evaluate the nonlinear response of the junction (nonlinear microwave impedance, for example) to an ac microwave current of arbitrary amplitude. Strong nonlinear effects in the resistance and the reactance are observed for large ac currents as is demonstrated by plotting the nonlinear response characteristics as a function of the model parameters. For weak ac currents and low noise strengths, our results agree closely with previously available linear response and nonlinear response noiseless solutions, respectively. Applications of the model to the interpretation of recent experimental data found in the literature for the nonlinear behavior of microwave impedance of superconducting weak links are discussed.

Auto-calibration and -compensation of a capacitive pressure sensor using multilayer perceptrons

Using multilayer perceptrons (MLPs), a smart model for a capacitive pressure sensor (CPS) is proposed. When the ambient temperature changes, the nonlinear response characteristics of a CPS may vary widely. Under such conditions, calibration of the sensor and compensation of the nonlinear sensor characteristics to obtain correct readout becomes a difficult task. The proposed MLP model can provide automatic nonlinear compensation and calibration of the CPS characteristics. A microcontroller unit (MCU)-based implementation scheme for this model is also considered. Simulation results show that this model can estimate the pressure with a maximum full-scale error of ±1% over a variation of temperature from −50 to 150°C.

ANN-based intelligent pressure sensor in noisy environment

A novel artificial neural network (ANN)-based intelligent capacitive pressure sensor (CPS) in noisy environment is proposed in this paper. A switched capacitor circuit (SCC) is used to convert the change in capacitance of the CPS due to applied pressure into a proportional voltage which is then applied to the ANN model to estimate the pressure. Because of the nonlinear response characteristics of the CPS and its temperature dependence, complex signal processing of the SCC output is required to estimate the applied pressure accurately, especially when the room temperature changes with time, place, or both. The situation becomes further complicated when the CPS encounters random noise, as is the case in many practical situations. To alleviate these difficulties in estimation of unknown applied pressure in a CPS, a multilayer perceptron (MLP) has been utilized to model the CPS characteristics over a wide temperature range with noise. By training the MLP model suitably, a direct digital readout of the applied pressure can be obtained. From the simulation studies it was verified that the performance of this model is quite satisfactory for a wide variation of temperature, starting from −20°C to 70°C, and for a signal-to-noise ratio (SNR) of 40 dB and above. This modeling technique provides greater flexibility and accuracy in a changing and noisy environment.

Nonlinear dc response in composites: A percolative study

The dc response, namely the $I\ensuremath{-}V$ and $G\ensuremath{-}V$ characteristics, of a variety of composite materials are in general found to be nonlinear. We attempt to understand the generic nature of the response characteristics and study the peculiarities associated with them. Our approach is based on a simple and minimal bond percolative network model. We do simulate the resistor network with appropriate linear and nonlinear bonds and obtain macroscopic nonlinear-response characteristics. We discuss the associated physics. An effective-medium approximation of the corresponding resistor network is also given.