Amplitude-dependent Nonlinearities Research Articles

Monitoring-based identification of nonlinear aerodynamic damping in multi-mode vortex-induced vibrations of a stay cable

New issues of wind-induced cable vibration, i.e., multi-mode vibrations, increasingly occur in long-span bridges, which are closely associated with underlying damping features. In this study, an analytical method is proposed to identify nonlinear aerodynamic damping in multi-mode wind-induced cable vibrations in fields, involving the assessment of total and mechanical damping. The method is available to extract a series of mono-component resonances/decays from the measured signals based on the analytical mode decomposition (AMD) and random decrement technique (RDT), and then to determine the damping parameters using the Hilbert transform (HT) combined with the smoothing spline or linear least-square fitting. Furthermore, this method is applied to address the vortex-induced vibrations (VIV) of an ultra-long stay cable on the Sutong Bridge. Firstly, the vibrations are reported in terms of a typical event and one-year statistics. Subsequently, the damping parameters are identified to illustrate the in-situ aeroelasticity. The results show that the cable exhibits high-frequency vibrations primarily in the 41st to 43rd modes, and the aerodynamic damping exhibits significant amplitude-dependent nonlinearity. Finally, the damping identifications are employed to reveal the onset mechanism for the vibrations, and a Scruton number (Sc) criterion, i.e., Sc > 5.4, is suggested for mitigating the vibrations.

Investigation of the Phase of Nonlinear Echoes From Microbubbles During Amplitude Modulation.

Contrast-enhanced ultrasound (CEUS) imaging relies on distinguishing between microbubble and tissue echoes. Amplitude modulation (AM), a nonlinear pulsing scheme, has been developed to take advantage of the amplitude-dependent nonlinearity of microbubble echoes. However, with AM, tissue nonlinear propagation can also degrade the image contrast. Segmentation of CEUS images based on amplitude-dependent phase difference in the echoes, defined in this article as [Formula: see text], has been proposed as an additional method of enhancing contrast-to-tissue ratio as tissue is not expected to create the same degree of [Formula: see text]; however, this has not been robustly investigated. In this work, we evaluate the source of [Formula: see text] through simulations of unshelled versus shelled microbubble oscillation and simulations of nonlinear propagation in tissue. We then validate the simulated [Formula: see text] results with experimental [Formula: see text] measurements during in vitro scattering and imaging in a flow phantom. We show that shelled and unshelled microbubbles resulted in a [Formula: see text] with similar overall magnitude with some differences in trends, and that tissue echoes have a small yet detectable degree of [Formula: see text] due to nonlinear propagation. The results from this work can help inform optimal parameter selection for phase segmentation and implementation on a clinical scanner.

Results on FPGA-Based High-Power Tube Amplifier Linearization at DESY

Vacuum-tube amplifiers are the most widespread type of radio frequency (RF) sources used to produce high-power signals needed for beam acceleration in superconducting cavities. At Deutsches Elektronen-Synchrotron (DESY), megawatt-rated klystrons are used to produce millisecond-long RF shots for pulsed operation in particle accelerators. In contrast, inductive output tubes (IOTs) are used to provide a continuous RF signal for continuous-wave (CW) operation. In both cases, the amplifiers suffer from amplitude-dependent nonlinearity between the driving and generated signals. This nonlinearity complicates the setup operations of the low-level RF (LLRF) system and makes it harder to regulate the accelerating field. Therefore, a way to linearize the amplifier is highly valuable. This article covers the design, implementation, and test of a field-programmable gate array (FPGA)-based predistortion linearization unit. The first results on the performance of this component in linearizing the amplifiers of running CW and pulsed superconducting accelerators are presented. Such a component uses programmable interpolating lookup tables (LUT) that are addressed using the squared value of the requested signal amplitude. This component only adds 64-ns latency to the RF control system without relying on any vendor-dependent FPGA component. Other benefits of using programmable interpolating LUT are low usage of FPGA resources and flexibility in terms of the type of amplifier to be corrected. The benefits of using this linearizer for klystrons and IOTs are presented and quantified.

On solitary waves in case of amplitude-dependent nonlinearity

The aim of the present paper is to study soliton emergence, modelled by a Boussinesq-type equation with nonstandard nonlinear terms. Such a model has been proposed to describe mechanical waves in cylindrical biomembranes. While the governing equation is of the Boussinesq-type, the nonlinearity is of the nonstandard f(u)·uxx-type instead of the conventional f(ux)·uxx-type and the dispersion can be either normal or anomalous. It is shown that the ratio between the two nonlinear parameters can have significant impact on the solution behaviour and it is shown how the dispersion related parameters affect the evolution of solutions including the demonstration of cases where smaller amplitude waves travel faster than the larger amplitude waves.

Design and evaluation of a mechanical nanomanufacturing system for nanomilling

Abstract This paper presents design and evaluation of a mechanical nanomanufacturing system for performing the nanomilling process. The nanomilling process uses a nanotool (an atomic force microscope probe tip) that is rotated at high speeds to fabricate three-dimensional (3D) nano-scale features on a sample surface. After explaining the kinematics of the two nanomilling process configurations, the nanomilling system, including the 3D piezoelectric actuator that rotates the nanotool, the nanopositioning stage that provides the feeding and depth motions, and the software program that controls the nanomilling motions are described. A measurement system is then constructed to measure the dynamic nanomilling motions. A compensation algorithm is developed to enable obtaining desired nanotool motions in the presence of frequency and amplitude-dependent nonlinearities of the 3D piezoelectric actuator. The nanomilling system is then evaluated directly by measuring the nanotool motions, and indirectly by assessing the accuracy of the fabricated nanoscale features. It was shown that the nanomilling system facilitates fabrication of complex nano-scale features with high accuracy through the high-stiffness nanotool assembly and high-frequency (compensated) nanotool motions.

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.

Vibration Analysis for Damage Detection in Metal-to-Metal Adhesive Joints

Vibration based non-destructive evaluation shows promise for damage detection in metal-to-metal adhesive joints. This research investigates an experimental technique to diagnose damage in single-lap adhesive joints subject to cyclical tensile loading. Vibration analysis reveals that damage can be correlated with changes in identified modal damping ratios. Constant amplitude forcing functions are employed to eliminate amplitude-dependent nonlinearities in the dynamic response profiles. Damping estimates obtained from time-domain analyses correlate well with damage magnitudes. Finite element modal analysis of the lap joints supports the experimental results.

Modal analysis and materials considerations in Caribbean steelpans

Modal analysis contributes significantly to an understanding of the vibrational patterns and the rich spectral tone color of the Caribbean steelpan sound. This will be illustrated with several examples of computer animations of steelpan normal modes. In addition to showing some of the low-order modes which contribute strongly to the radiated sound, these animations also show direct linear coupling effects between note sections. Since impact excitation modal analysis is fundamentally a linear experimental technique a solenoid driven excitation hammer minimizes amplitude-dependent nonlinearities. PANART artisans have emphasized tonal consistency through material and processing controls. This includes steel production to pan crafters specifications, custom drum manufacture, and a systematic sandwich surface hardening process. A European cultural influence has led to some departure from traditional Caribbean standards. Examples of note spectra and modal analysis computer animations will be shown.

Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance.

Continuous stochastic position perturbations are an attractive alternative to transient perturbations in muscle and reflex studies because they allow efficient characterization of system properties. However, the relevance of the results obtained from stochastic perturbations remains unclear because they may induce a state change in muscle properties. We addressed this concern by comparing the force and stiffness responses of isolated muscles of the decerebrate cat elicited by stochastic perturbations to those evoked by "step" stretches of similar amplitudes. Muscle stiffness during stochastic perturbations was found to be predominantly linear and elastic in nature for a given operating point, showing no evidence of instantaneous amplitude-dependent nonlinearities, even during large movements. In contrast, force responses evoked by step stretches were found to be mainly viscous in nature and nonlinear for larger stretches, with only a small maintained (elastic) component. Stiffness magnitude decreased with displacement amplitude for both stochastic and step perturbations. Our results are largely consistent with the crossbridge theory of muscle contraction, indicating that transient and continuous displacements evoke different, although functionally relevant, aspects of muscle behavior. These differences have several implications for the neural control of posture and movement, and for the design of perturbations appropriate for its study.

Visually-induced adaptive plasticity in the human vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR) is under adaptive control which corrects VOR performance when visual-vestibular mismatch arises during head movements. However, the dynamic characteristics of VOR adaptive plasticity remain controversial. In this study, eye movements (coil technique) were recorded from normal human subjects during sinusoidal rotations in darkness before and after 8 h. of adaptation to 2X binocular lenses. The VOR was studied at 7 frequencies between 0.025 and 4.0 Hz at 50 degrees/s peak head velocity (less for 2.5-4 Hz). For 0.025 and 0.25 Hz, the VOR was tested at 4 peak head velocities between 50 and 300 degrees/s. Before 2X lens adaptation, VOR gain was around 0.9 at 2.5-4.0 Hz and dropped gradually with decreasing frequency to under 0.6 at 0.025 Hz. Phase showed a small lead at the highest frequencies which declined to 0 degree as frequency decreased to 0.5-0.25 Hz, but then rose to 14 degrees by 0.025 Hz. VOR gain was independent of head velocity in the range 50-300 degrees/s at both 0.025 and 0.25 Hz. However, Phase lead rose with increasing head velocity, more so at 0.025 than at 0.25 Hz. After 2X lens adaptation, gain rose across the frequency bandwidth. However, the proportional gain enhancement was frequency dependent; it was greatest at 0.025 Hz (44%), and declined with increasing frequency to reach a minimum at 4 Hz (19%). Phase lead increased after 2X lens adaptation at lower frequencies, but decreased at higher frequencies. New velocity-dependent gain nonlinearities also developed which were not present prior to adaptation; gain declined as peak head velocity increased from 50 to 300 degrees/s at both 0.025 (23% drop) and 0.25 Hz (15% drop). This may suggest an amplitude-dependent limitation in VOR adaptive plasticity. Results indicate both frequency and amplitude dependent nonlinearities in human VOR response dynamics before and after adaptive gain recalibration.

Nonlinear dynamic properties of a somatomotor reflex system. A model study.

AbstractThe time course of polysynaptic reflex responses is known to exhibit two prominent non‐linearities, one dependent on the amplitude of the stimulus and the other dependent on the direction of change of the stimulus. Both nonlinearities were demonstrated in the open‐loop responses of the acoustic middle ear reflex and simulated in a piecewise linear model. Their significance for stability of the closed‐loop feed‐back system was investigated. In this model the source of nonlinearity was a pool of “reflex units” with various thresholds and time constants. The mode! responses were studied in the time domain and the frequency domain. The amplitude dependent nonlinearity could be simulated when low threshold reflex units were made slow and tonic and high threshold units fast and tonic or when some of the high threshold units were phasic. A decrease in transport delay at increased input step amplitude was seen under these conditions but also when all units mere made equal. Both types of nonlinearities were found to improve the stability of the model system without decreasing its bandwidth (a measure of the speed of action). The nonlinearities were suggested to be important in systems with high values of transport delay.

Multimodal and transitional behaviour in second-order nonlinear systems

Second-order systems with amplitude-dependent nonlinearities can exhibit multirnodal behaviour. A method of finding the range of parameters for which this behaviour is observed is considered, and the method is then extended to predict the type of transients which occur in the system from a given set of initial conditions. The method is based on the describing function of the nonlinearity. The effect of the shape of the nonlinearity on the number of possible fundamental modes of response is discussed, and attention is given to the possibility of exciting subharmonic modes of response, the purpose being to find the range of parameters for which the analysis of the fundamental modes of response is valid.

Dynamical Characteristics of the Fusional Vergence Eye-Movement System

Experiments have been performed on the fusional vergence eye-movement mechanism in humans to provide a comparison with the established dynamical characteristics of the versional eye-movement system. Transient and frequency response experiments indicate that the fusional vergence system is not characterized by sampled data or refractory operation. When provided with a periodic input, this system may utilize prediction to reduce inherent phase lags. The gain of the system, although apparently unaffected by the predictive mechanism, is subject to input amplitude-dependent nonlinearities. Under conditions of artificially high loop gain, the system breaks into smooth sustained oscillations at a frequency predicted by frequency response data. The absence of a refractory period in the fusional vergence system is demonstrated by the system response to brief pulsatile stimulation. These results are discussed, emphasizing comparison with corresponding results from experiments on the versional system.