Higher Odd Harmonics Research Articles

Surface stress decomposition in large amplitude oscillatory interfacial dilatation of complex interfaces

HypothesisMultiphase materials are often subjected to large deformations during processing, but the rheological responses of complex interfaces (e.g. stabilized by proteins) in this nonlinear deformation regime are still poorly understood. We expect nonlinearities in the response to be introduce by changes of the interfacial network and surface density of the emulsifier. ExperimentsLarge amplitude oscillatory dilatation (LAOD) experiments were performed on WPI-, pea albumin-, pea globulin- and rapeseed lecithin-stabilized interfaces and analyzed with a general stress decomposition (GSD). With GSD, the stress response was decomposed into the four stress terms (τ1-τ4). Here, τ1 and τ2 represent, the elastic and viscous contribution of the odd Fourier harmonics, and τ3 and τ4 represent the dissipative and recoverable contribution of the even harmonics. FindingsAnalysis of WPI-, pea albumin-, pea globulin- and rapeseed lecithin-stabilized interfaces revealed that higher odd harmonics (k≥3) describe in-plane network responses and that even harmonics describe surface density changes. Analysis of these complex interfaces showed that GSD is a valuable tool for (quantitative) description of interfacial responses in LAOD, providing new insights into the origin of asymmetric nonlinear stress responses.

A Tandem Axial-Piston Unit Based Strategy for the Reduction of Noise Sources in Hydraulic Systems

This article presents a novel passive fluid borne noise source reduction strategy, based on tandem axial-piston unit indexing with the usage of symmetric lines. The strategy consists of setting the phase between the two synchronous units to accomplish destructive interference in targeted unit harmonics. A strategy capable of achieving destructive interference in all odd harmonics is investigated first analytically and then confirmed by a simulation study. Experiments on the proposed strategy confirmed its effectiveness at the first and third pump fundamental harmonics, and pressure ripple reduction was accomplished. The fluid borne noise source reduction in the first and third harmonic is verified to be propagated to pipe vibration and sound power. Regarding the first harmonic, pressure ripple was reduced by up to 18 dB; while for third harmonic, pressure ripple was reduced by up to 11 dB. In the experiment, however, noise cancellation is not achieved for the higher odd harmonics, as is instead found in the simulation. Conversely, transfer functions form pressure ripple to pipe wall acceleration are obtained experimentally, and a critical vibration band from 2000 Hz to 3000 Hz is identified as being crucial for effective overall sound power reduction.

Single-shot phase-sensitive wideband active microrheology of viscoelastic fluids using pulse-scanned optical tweezers

We present a fast phase sensitive active microrheology technique exploring the phase response of a microscopic probe particle trapped in a linear viscoelastic fluid using optical tweezers under an external perturbation. Thus, we experimentally determine the cumulative response of the probe to an entire repertoire of sinusoidal excitations simultaneously by applying a spatial square pulse as an excitation to the trapped probe. The square pulse naturally contains the fundamental sinusoidal frequency component and higher odd harmonics, so that we measure the phase response of the probe over a wide frequency band in a single shot, with the band being tunable over the spectrum by choosing suitable experimental parameters. We then determine the responses to individual harmonics using a lock-in algorithm, and compare the phase shifts to those obtained theoretically by solving the equation of motion of the probe particle confined in a harmonic potential in the fluid in the presence of a sinusoidal perturbation. We go on to relate the phase response of the probe to the complex shear modulus , and proceed to verify our technique in a mixture of polyacrylamide and water, which we compare with known values in literature and obtain very good agreement. Our method increases the robustness of active microrheology in general and ensures that any drifts in time are almost entirely ruled out from the data, with the added advantage of high speed and ease of use.

Thermally and electrically controllable multiple high harmonics generation by harmonically driven quasi-two-dimensional electron gas

In this paper, we consider the activation processes in nonlinear meta-stable system based on a lateral (quasi-two-dimensional) superlattice and study the dynamics of such a system externally driven by a harmonic force. The internal control parameters are the longitudinal applied electric field and the sample temperature. The spontaneous transverse electric field is considered as an order parameter. The forced violations of order parameter are considered as a response of a system to periodic driving. We investigate the cooperative effects of self-organization and high harmonic forcing from the viewpoint of catastrophe theory and show the possibility of generation of third and higher odd harmonics in output signal that lead to distortion of its wave front. A higher harmonics detection strategy is further proposed and explained in detail by exploring the influences of system parameters on the response output of the system that are discussed through numerical simulations.

A Nonlinear Oscillator Model to Generate Lateral Walking Force on a Rigid Flat Surface

This study proposes a single degree of freedom nonlinear oscillator to model the lateral movement of the body center of mass of a pedestrian walking on a flat rigid surface. Experimentally recorded ground reaction force of a dozen of pedestrians in the lateral direction is used to develop the model. In detail, the hardening and softening effects are observed in the stiffness curve as well as higher odd harmonics are present in the frequency spectrum of the lateral force signals. The proposed oscillator is a modification of the Rayleigh and the Van der Pol oscillators with additional nonlinear softening and hardening terms. To obtain an approximation of the limit cycle of the oscillator and its stability, two methods are studied: the energy balance method and the Lindstedt–Poincare perturbation technique. The experimental force signals of pedestrians at four different walking speeds are used for the identification of the values of the model parameters. The results obtained from the proposed model show a good agreement with the experimental ones.

Detection of cyclic-fold bifurcation in electrostatic MEMS transducers by motion-induced current

This paper presents a new detection method of cyclic-fold bifurcations in electrostatic MEMS transducers based on a variant of the harmonic detection of resonance method. The electrostatic transducer is driven by an unbiased harmonic signal at half its natural frequency, ωa = 1/2 ωo. The response of the transducer consists of static displacement and a series of harmonics at 2 ωa, 4 ωa, and so on. Its motion-induced current is shifted by the excitation frequency, ωa, to appear at 3 ωa, 5 ωa, and higher odd harmonics, providing higher sensitivity to the measurement of harmonic motions. With this method, we successfully detected the variation in the location of the cyclic-fold bifurcation of an encapsulated electrostatic MEMS transducer. We also detected a regime of tapping mode motions subsequent to the bifurcation.

Behavior of a porous particle in a radiofrequency plasma under pulsed argon ion beam bombardment

The behavior of a single porous particle with a diameter of 250 μm levitating in a radiofrequency (RF) plasma under pulsed argon ion beam bombardment was investigated. The motion of the particle under the action of the ion beam was observed to be an oscillatory motion. The Fourier-analyzed motion is dominated by the excitation frequency of the pulsed ion beam and odd higher harmonics, which peak near the resonance frequency. The appearance of even harmonics is explained by a variation of the particles's charge depending on its position in the plasma sheath. The Fourier analysis also allows a discussion of neutral and ion forces. The particle's charge was derived and compared with theoretical estimates based on the orbital motion-limited (OML) model using also a numerical simulation of the RF discharge. The derived particle's charge is about 7–15 times larger than predicted by the theoretical models. This difference is attributed to the porous structure of the particle.

Leakage Current Waveforms of Outdoor Polymeric Insulators and Possibility of Application for Diagnostics of Insulator Conditions

This paper reports the investigation results on the leakage currents (LC) on polymeric outdoor insulators. The samples used were EPDM (ethylene prophylene diene monomer) insulators used at 20 kV distribution lines. AC voltage was applied and the LC waveforms were measured under various environmental conditions (humidity and pollution). Digital data of the LC was transferred from a digital storage oscilloscope to a computer for further analysis. The LC waveform parameters such as magnitude and harmonic content (as indicated by the total harmonic distortion (THD)) were analyzed. The experimental results showed that 3rd, 5th and 7th harmonics and higher odd harmonics were observed for symmetrical-distorted LC waveforms while for unsymmetrical-distorted LC waveforms, odd and even harmonics were observed. The LC analysis indicated that there are 5 stages of insulator conditions from normal condition up to flashover correlated with different kind of LC waveforms. The results also showed that in general the magnitude of LC was good enough to show the condition of the insulators. However, under discharge condition (for example as a result of dry band arching) the LC magnitude should be combined by the THD to show a better correlation with the insulator condition. The product between THD and LC magnitude may be used as a diagnostic parameter.

Temporal Fourier spectra of stationary and slowly moving breathers in Fermi–Pasta–Ulam anharmonic lattice

The temporal Fourier spectra of stationary and slowly moving self-localized large-amplitude modes (breathers) in translationally invariant chain of coupled classical anharmonic oscillators are studied. The breathers arise naturally in the anharmonic lattice from modulational instability of short-wavelength extended vibrational modes. The frequencies of the resonant spectral peaks of the stationary breather are measured numerically and compared with an exact analytical solution for the stationary extended nonlinear sinusoidal wave in the anharmonic lattice, which is conveniently adapted. Symmetrical satellite peaks of the fundamental frequency and its higher odd harmonics in the temporal Fourier spectrum of the stationary breather are observed. Small admixture of the slowly moving breather solution to the stationary one is discussed in connection with these peaks. It is observed that the temporal Fourier spectrum of slowly moving breather consists of two main frequencies symmetrically shifted upwards and downwards with respect to the fundamental frequency of the stationary breather with the same energy, in perfect agreement with the earlier theoretical prediction of one of the authors. The relation between the group velocity of slowly moving breather and the fundamental frequency of the stationary breather with the same energy is derived.

Rheological properties of peanut butter

The rheological properties of two types of commercial peanut butter have been studied. Both products are concentrated suspensions, and differ by the presence of additives. The first type, referred to as “100% peanuts,” is an unstabilized suspension consisting of solid peanut particles in peanut oil which is a Newtonian fluid. The second type, referred to as “smooth,” consists of the same suspension stabilized with a vegetable oil and contains other ingredients such as salt and sugar in very small quantities. A mean volume particle diameter of 6.6 μm has been determined, the particle diameter distribution was found to be narrow, and the solids volume fraction was estimated to be 0.6. Slip encountered in rheometry was greatly reduced by gluing sandpaper to the parallel plates of the rheometer. Both samples behaved like plastic materials and apparent yield stresses of 24 Pa and 370 Pa have been determined for the unstabilized and the stabilized suspensions, respectively. No linear domain was found for both suspensions and the non-linearity was confirmed by deformed Lissajous curves and higher odd harmonics in the output signal of small amplitude oscillatory shear experiments. The stabilized suspension behaved more like a solid, the elastic modulus being larger than the loss modulus and almost independent of the frequency. This solid-like behavior is supposedly caused by strong repulsive (steric) forces induced by the stabilizing agent.

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 1. Longitudinal vibrations, analytical solution

On the basis of an analysis of the asymptotics of higher approximations to solutions of a differential equation of longitudinal vibrations of a macroelastic body whose nonlinearity is explained by the hysteresis and “breathing” of the damaged material in the process of its cyclic deformation under conditions of tension-compression, we estimate the applicability of the spectral characteristics of strain cycles of the body under conditions of its natural or resonance vibrations to the diagnostics of fatigue damage of structural elements. It is shown that if nonlinearity is explained solely by the hysteresis of the material, then even the most representative first higher odd harmonics revealed in the vibration spectrum have very small amplitudes and the analysis of their variations is, in fact, similar to the analysis of the variations of the logarithmic decrement of vibrations (regarded as an integral characteristic of the dissipative properties of the material of the investigated element) but has lower resolution. At the same time, the discontinuities of the material appearing in the process of strain cycling are characterized by formation of numerous microcracks or a macrocrack and result in more clear detection of the representative constant component and even harmonics (mainly the second and fourth ones) in the spectrum of strain cycles of a vibration-insulated structural element in the process of its natural or resonance vibrations. These characteristics may serve as sensitive and efficient parameters for detection of fatigue damage to the material.

Cycloidal structure of ErY alloys at 4.2 K

Neutron diffraction studies of Er 0.9Y 0.1 and Er 0.8Y 0.2 alloy single crystals have revealed that a spin configuration of both crystals is not conical, but cycloidal in the ac-planeeven at low temperatures. The cycloidal structure has higher odd harmonics up to the fifth order along the c-axis. These magnetic amplitudes and phase angles are determined on reasonable assumptions.

Arcing faults detection on overhead lines from the voltage signals

This paper presents a simple algorithm for arcing faults detection on overhead lines. The algorithm is based on the harmonic analysis of the bus voltage signals. It uses only the sine components of the odd higher harmonics of the bus voltage. Such an approach provides the algorithm with insensitivity to the cosine components of the bus voltage odd higher harmonics which can be generated by current odd cosine higher harmonics. The algorithm can be used for blocking the automatic reclosing of lines with permanent faults. A very simple arc model has been adopted. The algorithm was successfully tested with signals recorded on a real power system and signals obtained through computer simulated and laboratory tests.

Harmonic generation studies in laser ablated YBCO thin film grown on 〈100〉 MgO

The generation of harmonics in a laser ablated YBCO film deposited on a 〈100〉 MgO substrate is reported. Higher odd harmonics appeared when the film was subjected to an ac field. The presence of a dc field induces only the second harmonic with a small value of slope ofV 2−H dc curve (δV 2/δH dc) compared to bulk YBCO. The variation of the amplitude of third harmonic (V 3) withH ac and temperature was studied. These results are explained in terms of a critical state model. The observation of only a small amplitude of second harmonic (V 2) with a smallδV 2/δH dc is explained in terms of a special kind of clean grain boundary present in YBCO laser ablated films on 〈100〉 MgO.

A novel 3-D integrated HFET/RTD frequency multiplier

A merged heterostructure field-effect transistor/resonant tunneling diode (HFET/RTD) combination is proposed to act as a (sub)millimeter wave source via highly efficient frequency multiplication and its functionality is demonstrated at intermediate frequency. On a semi-insulating InP-substrate a HFET followed by a double barrier RTD-layer sequence is grown in a single molecular beam epitaxy (MBE)-run. A novel monolithic frequency multiplier circuitry is developed where the RTD is used as load in contrast to other concepts where the RTD is inserted in the input of a three-terminal device. The resulting output voltage is rectangular type and rich in higher odd harmonics. This approach avoids classical disadvantages of the RTD because biasing in the negative-differential-regime is not required and bistability of the I-V-characteristic is used rather than the negative differential resistance. The small signal parameters of the single devices realized with optical lithography, wet etching, and self-aligned process technology are used as input data for a microwave design software (MDS) and the frequency multiplication is modeled up to submillimeter wave frequencies.

Even-harmonic lasing

Operation of a free-electron laser at harmonics of the fundamental frequency is explored with the numerical simulation code HELEX. This code includes coupling to the harmonics caused by misalignment of the electrons with the optical beam and coupling due to transverse gradients. Albeit weak, the transverse gradient of the electron beam density produces the dominant coupling of the electrons to the even-harmonic light. Even-harmonic lasing occurs in a TEM 0.2m+1 - like mode where the field on-axis is zero. As bunching of the electron beam progresses, radiation at the higher odd harmonics is suppressed owing to the absence of higher-order odd-harmonic Fourier components in the bunch. Growth of the even-harmonic power from small signal requires suppression of competing harmonics (including the fundamental) that have higher gain. Lasing at an even harmonic has yet to be experimentally demonstrated in an open resonator (i.e. optical cavity). Strategies to make possible such an experiment are discussed.

Fiber-optic microbend sensors: sensitivity as a function of distortion wavelength

The attenuation of optical power in multimode fibers with parabolic-index profiles has been analyzed as a function of the distortion wavelength in microbend sensors with sharp ridges. In agreement with the theory, measurements show that attenuation peaks of almost equal strength originate from the fundamental and the odd higher harmonics in the distortion spectrum.

Surface-wave generation in crystals with high dielectric constant

The generation of surface acoustic waves by interdigital transducers in materials with high and strain-dependent dielectric constants, which are not necessarily piezoelectric, was studied theoretically using Lamb’s integral-solution method and the flat-field approximation of Tseng for the solutions of the wave equation. The influence of the dependence of the dielectric constant on the strain was considered in the approximation given by Pekar and Ogg. As a result, a transducer gain proportional to an applied dc field has been obtained. With respect to the frequency responses, an increased output at higher odd harmonics as compared to transducers on piezoelectric crystals was found. The transducers are shown to be tunable because of a stiffening of the surface-wave velocity by the applied field. Thus, amplitude modulation and frequency modulation should be possible in a simple manner.

Effects of Entrance Loss on Harbor Oscillations

By assuming a head loss across the harbor entrance the wave-induced response in a rectangular model harbor is studied theoretically. The loss is assumed to be quadratic in local velocity with a constant friction coefficient. Bottom and side-wall dissipation are not considered. It is shown that odd higher harmonics are present. The resonance characteristics of the fundamental harmonic response in the harbor are significantly influenced by the additional damping due to friction, especially for the lowest peaks. While in the perfect fluid theory these peaks heighten with diminishing entrance width, in the presence of friction the opposite is true for sufficiently narrow mouth.

Nonlinear Properties of Circular Orifices

The results of an experimental study of the nonlinear fluid flow properties of thin, square-edged, circular orifices are described. Liquids were used at low frequencies. The flow conditions considered are a sinusoidal oscillation of the fluid in the orifice and a sinusoidal oscillation with a steady flow component added. For the sinusoidal flow condition the pressure differential developed across the orifice contains higher odd harmonics. The addition of a steady flow component adds second harmonic to the pressure as well as influences the magnitude of the odd harmonics. Further, in this case, the steady pressure component is a function of the magnitude of both the sinusoidal and steady flow components. An equation descriptive of the pressure-flow relation is presented. In this equation the orifice properties are specified by three constants, two of which are the acoustic resistance and acoustic inertance as normally measured at low amplitudes of excitation. The relations derived from this equation are compared with experimental measurements.