Harmonic Frequency Response Research Articles

Accurate modal superposition method for harmonic frequency response sensitivity of non-classically damped systems with lower-higher-modal truncation

Frequency response and their sensitivities analysis are of fundamental importance. Due to the fact that the mode truncation errors of frequency response functions (FRFs) are introduced for two times, the errors of frequency response sensitivities may be larger than other dynamic analysis. Many modal correction approaches (such as modal acceleration methods, dynamic correction methods, force derivation methods and accurate modal superposition methods) have been presented to eliminate the modal-truncation error. However, these approaches are just suitable to the case of un-damped or classically damped systems. The state-space equation based approaches can extend these approaches to non-classically damped systems, but it may be not only computationally expensive, but also lack physical insight provided by the superposition of the complex modes of the equation of motion with original space. This paper is aimed at dealing with the lower-higher-modal truncation problem of harmonic frequency response sensitivity of non-classically damped systems. Based on the Neumann expansion and the frequency shifting technique, the contribution of the truncated lower and higher modes to the harmonic frequency response sensitivity is explicitly expressed only by the available middle modes and system matrices. An extended hybrid expansion method (EHEM) is then proposed by expressing harmonic frequency response sensitivity as the explicit expression of the middle modes and system matrices. The EHEM maintains original-space without having to involve the state-space equation of motion such that it is efficient in computational effort and storage capacity. Finally, a rail specimen is used to illustrate the effectiveness of the proposed method.

Affordable headphones for accessible screening audiometry: An evaluation of the Sennheiser HD202 II supra-aural headphone

Objective: Evaluation of the Sennheiser HD 202 II supra-aural headphones as an alternative headphone to enable more affordable hearing screening. Design: Study 1 measured the equivalent threshold sound pressure levels (ETSPL) of the Sennheiser HD 202 II. Study 2 evaluated the attenuation of the headphones. Study 3 determined headphone characteristics by analyzing the total harmonic distortion (THD), frequency response and force of the headband. Study sample: Twenty-five participants were included in study 1 and 15 in study 2 with ages ranging between 18 and 25. No participants were involved in study 3. Results: The Sennheiser HD 202 II ETSPLs (250–16000 Hz) showed no significant effects on ETSPL for ear laterality, gender or age. Attenuation was not significantly different (p > 0.01) to TDH 39 except at 8000 Hz (p < 0.01). Maximum permissible ambient noise levels (MPANL) were specified accordingly. The force of the headband was 3.1N. THD measurements showed that between 500 and 8000 Hz intensities of 90 dB HL and higher can be reached without THD >3%. Conclusion: Sennheiser HD 202 II supra-aural headphones can be used as an affordable headphone for screening audiometry provided reported MPANLs, maximum intensities and ETSPL values are employed.

Ultralow frequency acoustic bandgap and vibration energy recovery in tetragonal folding beam phononic crystal

This paper investigates ultralow frequency acoustic properties and energy recovery of tetragonal folding beam phononic crystal (TFBPC) and its complementary structure. The dispersion curve relationships, transmission spectra and displacement fields of the eigenmodes are studied with FEA in detail. Compared with the traditional three layer phononic crystal (PC) structure, this structure proposed in this paper not only unfold bandgaps (BGs) in lower frequency range (below 300 Hz), but also has lighter weight because of beam structural cracks. We analyze the relevant physical mechanism behind this phenomenon, and discuss the effects of the tetragonal folding beam geometric parameters on band structure maps. FEM proves that the multi-cell structures with different arrangements have different acoustic BGs when compared with single cell structure. Harmonic frequency response and piezoelectric properties of TFBPC are specifically analyzed. The results confirm that this structure does have the recovery ability for low frequency vibration energy in environment. These conclusions in this paper could be indispensable to PC practical applications such as BG tuning and could be applied in portable devices, wireless sensor, micro-electro mechanical systems which can recycle energy from vibration environment as its own energy supply.

InGaZnO Thin-Film-Transistor-Based Four-Quadrant High-Gain Analog Multiplier on Glass

This letter presents a novel high-gain four-quadrant analog multiplier using only n-type enhancement indium-gallium-zinc-oxide thin-film-transistors. The proposed circuit improves the gain by using an active load with positive feedback. A Gilbert cell with a diode-connected load is also presented for comparison purposes. Both circuits were fabricated on glass at low temperature (200°C) and were successfully characterized at room temperature under normal ambient conditions, with a power supply of 15 V and 4-pF capacitive load. The novel circuit has shown a gain improvement of 7.2 dB over the Gilbert cell with the diode-connected load. Static linearity response, total harmonic distortion, frequency response, and power consumption are reported. This circuit is an important signal processing building block in large-area sensing and readout systems, specially if data communication is involved.

On frequency responses of period-1 motions to chaos in a periodically forced, time-delayed quadratic nonlinear system

In this paper, frequency responses of periodic motions to chaos in a periodically forced, damped, quadratic nonlinear oscillator are investigated through the finite Fourier series analysis of discrete solutions of periodic motions. The discrete solutions of periodic motions are obtained from mapping structures of discrete nodes, and the corresponding stability and bifurcation analysis of periodic motions are completed by the eigenvalue analysis of fixed points in discrete nonlinear dynamical systems. The frequency–amplitude characteristics for bifurcation trees of periodic motions to chaos are discussed, and the quantity levels of harmonic amplitudes for different harmonic orders are illustrated clearly. Numerical results of periodic motions are illustrated to show harmonic frequency responses effects on periodic motions.

Equivalent Dynamic Stiffness Mapping technique for identifying nonlinear structural elements from frequency response functions

A simple and general Equivalent Dynamic Stiffness Mapping technique is proposed for identifying the parameters or the mathematical model of a nonlinear structural element with steady-state primary harmonic frequency response functions (FRFs). The Equivalent Dynamic Stiffness is defined as the complex ratio between the internal force and the displacement response of unknown element. Obtained with the test data of responses׳ frequencies and amplitudes, the real and imaginary part of Equivalent Dynamic Stiffness are plotted as discrete points in a three dimensional space over the displacement amplitude and the frequency, which are called the real and the imaginary Equivalent Dynamic Stiffness map, respectively. These points will form a repeatable surface as the Equivalent Dynamic stiffness is only a function of the corresponding data as derived in the paper. The mathematical model of the unknown element can then be obtained by surface-fitting these points with special functions selected by priori knowledge of the nonlinear type or with ordinary polynomials if the type of nonlinearity is not pre-known. An important merit of this technique is its capability of dealing with strong nonlinearities owning complicated frequency response behaviors such as jumps and breaks in resonance curves. In addition, this technique could also greatly simplify the test procedure. Besides there is no need to pre-identify the underlying linear parameters, the method uses the measured data of excitation forces and responses without requiring a strict control of the excitation force during the test. The proposed technique is demonstrated and validated with four classical single-degree-of-freedom (SDOF) numerical examples and one experimental example. An application of this technique for identification of nonlinearity from multiple-degree-of-freedom (MDOF) systems is also illustrated.

Electro-acoustic performance of the new bone vibrator Radioear B81: A comparison with the conventional Radioear B71

Objective: The objective is to evaluate the electro-acoustic performance of a new audiometric bone vibrator, the B81 from Radioear Corporation, USA. Comparison will be made with the widely used B71 which has well-known limitations at low frequencies. Design: The B81 is based on the balanced electromagnetic separation transducer (BEST) principle where static forces are counterbalanced so that nonlinear distortion forces are reduced and maximum hearing levels can be increased. Study sample: Maximum hearing level, total harmonic distortion (THD), frequency response, and electrical impedance were measured for six devices of each bone vibrator type on an artificial mastoid. Results: It was found that B81 reaches 10.7–22.0 dB higher maximum (@ THD = 6% or Vin = 6 VRMS) hearing levels than B71 for frequencies below 1500 Hz, and had significantly lower THD up to 1000 Hz. There was no statistically significant difference between their frequency response, except a deviation at the mid frequencies (α = 0.01) where B81 was more efficient and the electrical impedances were practically the same. Conclusions: In general, B81 had an improved electro-acoustic performance compared to B71 and is compatible with same audiometers. In particular, B81 allows for sensorineural hearing loss to be measured at considerably higher hearing levels than with B71 below 1500 Hz.

Nonparametric Identification of Nonlinear Systems in Series

In this paper, a method allowing the identification of two nonlinear systems in series is presented. More precisely, the identification of the second nonlinear subsystem under test is achieved by taking into account the effects of the nonlinearities of the first subsystem. The method is based on the estimation of the Higher Harmonic Frequency Responses (HHFRs) from the measurement of distorted input and output signals. The second nonlinear system is then modeled by non-parametric generalized Hammerstein model made up of power series associated with linear filters. The method is experimentally validated in the well-known framework of nonlinear propagation of acoustic waves.

Multiphysics modelling of the separation of suspended particles via frequency ramping of ultrasonic standing waves

A model was developed to determine the local changes of concentration of particles and the formations of bands induced by a standing acoustic wave field subjected to a sawtooth frequency ramping pattern. The mass transport equation was modified to incorporate the effect of acoustic forces on the concentration of particles. This was achieved by balancing the forces acting on particles. The frequency ramping was implemented as a parametric sweep for the time harmonic frequency response in time steps of 0.1s. The physics phenomena of piezoelectricity, acoustic fields and diffusion of particles were coupled and solved in COMSOL Multiphysics™ (COMSOL AB, Stockholm, Sweden) following a three step approach. The first step solves the governing partial differential equations describing the acoustic field by assuming that the pressure field achieves a pseudo steady state. In the second step, the acoustic radiation force is calculated from the pressure field. The final step allows calculating the locally changing concentration of particles as a function of time by solving the modified equation of particle transport. The diffusivity was calculated as function of concentration following the Garg and Ruthven [1] equation which describes the steep increase of diffusivity when the concentration approaches saturation. However, it was found that this steep increase creates numerical instabilities at high voltages (in the piezoelectricity equations) and high initial particle concentration. The model was simplified to a pseudo one-dimensional case due to computation power limitations. The predicted particle distribution calculated with the model is in good agreement with the experimental data as it follows accurately the movement of the bands in the centre of the chamber.

A method for open-loop control of dynamic motions of piezo-stack actuators

Precision control of three-dimensional dynamic motions of piezoelectric actuators is crucial for many applications of nanotechnology and precision engineering. In this paper, an open-loop technique to control the three-dimensional single-frequency motions of multi-axis piezo-stack actuators is presented. In this approach, the dynamic behavior of piezo-stack actuators is represented by the harmonic frequency response functions (hFRFs) that are obtained through an laser Doppler vibrometry (LDV)-based experimental characterization method. To obtain the desired motions at a given frequency, the actuator is excited at both the fundamental (motion) frequency and its harmonics, latter of which aiming to compensate for the unwanted higher-harmonic response components that arise due to non-linear dynamic behavior. The fundamental and the first-order compensatory excitation components are determined analytically using the inverse hFRFs. For the higher-order response terms, a compensation approach based on an iterative experimental technique is proposed. The effectiveness of the presented control method is demonstrated through a set of evaluation tests on two different three-axis piezo-stack actuators, where a set of motion-error metrics were defined and quantified. It was shown that the proposed method can be used to generate single-frequency motions with wide range of nanometric sizes with average errors less than 5% of the targeted motion amplitudes.

A self-assembled, metallo-organic supramolecular frequency doubler

The dimeric self-assembly program of a new, multidentate ligand with cuprous ions overcomes crystal packing forces, which leads to C(i) symmetry in the solid state, to form a no less than partially C(2)-symmetric structure in solution. The resulting tetranitro-substituted dicopper(i) metallocyclophane displays an exceptionally strong second harmonic frequency response (β = (3000 ± 600) × 10(-30) esu for a fundamental at 800 nm).

An improved HSFR method for natural vibration analysis of an immersed cylinder pile with a tip mass

Immersed cylinder piles are usually modelled as immersed cantilever cylinder columns carrying a tip mass and rotary moment of inertia. In this paper, the equations of motion of an immersed cylinder pile along transversal modes of vibration are developed. Compressibility of water and structural damping are included in the formulation. Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses. The proposed method is applied to numerical examples, and the results obtained are shown satisfactory when compared to other numerical solutions in the literature, or to finite element solutions and experimental data.

A helical ionic polymer–metal composite actuator for radius control of biomedical activestents

Helical ionic polymer–metal composite (IPMC) actuators are newly developed to controlthe radius of biomedical active stents. The helix-shaped IPMC actuator is fabricatedthrough the thermal treatment of an IPMC strip helically coiled on a glass rod. Thehelical IPMC actuator can be used to realize not only bending motion but alsotorsional and longitudinal motion. In particular, the dynamic responses of the helicalIPMC actuators are evaluated according to various structural parameters such asdiameter, pitch and width of the helical configuration. The present experimentalresults for the harmonic responses and frequency response functions show thatdiameter, among the structural parameters, plays an important role in the actuationperformance required to efficiently control the radius of the helical stent. The staticand dynamic responses of the helical IPMC actuators are also investigated withstep and harmonic electrical inputs, a voltage–current diagram and a mechanicalcompression test. This study shows that a helical IPMC actuator can be usedfor biomedical smart systems capable of controlling the radius of active stents.

Investigation on Harmonic Response of Pneumatic Vibration Isolation System with Single and Double-Frequency Excitations

In this paper, a nonlinear model of pneumatic vibration isolator was established, considering the volumetric compressibility of air. Based on this, simulation analyses were done using matlab/simulink software. The response to two different types of disturbances is studied: single-frequency excitation and double-frequency excitation. Single-frequency excitation can induce harmonic frequency response and offset response at the zero frequency. When the frequency is near to the the linearized natural frequency, the harmonic frequency response become stronger. Nonlinear characters have much to do with the drive amplitude. When the drive amplitude become large, the nonlinear characters are more obvious. Double-frequency excitation can induce combination resonance. When the two drive frequencys are close, combination resonance are more strong.

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the nonlinear output frequency response functions (NOFRFs) are one of the solutions obtained using the harmonic balance method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components. Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear.

Harmonic environment and frequency response of vascular cells. Toward a definition of distrubed flow

La survenue d’une encéphalopathie postérieure réversible au cours de l’éclampsie est une éventualité connue mais rare. Nous en rapportons les caractéristiques cliniques, radiologiques et évolutives.Une étude rétrospective a été réalisée de janvier 2005 à avril 2010 incluant tous les cas de posterior reversible encephalopathy syndrome (PRES) survenus sur un terrain d’éclampsie hospitalisés au service d’anesthésie-réanimation obstétrical du CHU de Casablanca.Treize cas de PRES sur éclampsie ont été colligés, l’âge moyen était de 29 ans (18–42). La pression artérielle systolique et la pression artérielle diastolique à l’admission étaient supérieures à 150 et 100 mmHg respectivement dans dix cas. Les signes retrouvés étaient : une cécité régressive dans cinq cas, des signes neurologiques de localisation présents dans quatre cas. Les complications associées étaient une thrombopénie dans dix cas, une cytolyse hépatique dans huit cas, un Hellp syndrome chez neuf patientes, une insuffisance rénale aiguë chez deux patientes. Les régions cérébrales les plus fréquemment touchées étaient les territoires pariétaux et occipitaux (13 cas), suivies par les régions temporales, frontales, et les ganglions de la base (huit cas chacune). Le recours à la ventilation assistée (VA) plus de 24 heures fut nécessaire chez cinq patientes. Le décès a compliqué l’évolution de quatre de nos patientes, aucun n’était directement imputable au PRES lui-même ; toutes les quatre avaient un Hellp syndrome et ont nécessité une VA supérieure à 48 heures. L’évolution a été marquée dans les autres cas par une régression totale des atteintes neurologiques.Ce travail souligne la gravité du syndrome d’encéphalopathie postérieure « réversible » sur terrain d’éclampsie.The occurrence of posterior reversible encephalopathy in eclampsia is a rare but known event. We propose to describe the clinical and radiological features and the outcome.A retrospective study was conducted from January 2005 to April 2010 including all cases of posterior reversible encephalopathy syndrome (PRES) occurring on eclampsia in patients hospitalized in the obstetrical intensive care unit, University Hospital of Casablanca.Thirteen cases of PRES on eclampsia were collected, the average age was 29 years (18–42). Systolic pressure and diastolic blood pressure at admission were higher than 150 mmHg and 100 respectively in 10 cases. The signs found were: a regressive blindness in five patients and focal signs in four. The complications were thrombocytopenia in 10 patients, abnormal liver function in eight, Hellp syndrome in nine, and acute renal failure in two. The brain regions most commonly affected were the parietal and occipital areas (13 patients), followed by temporal regions, frontal, and basal ganglia (eight patients each). Five patients required assisted ventilation (AV) over 24 hours. Death complicated the outcome in four of our patients, but no deaths were directly attributable to PRES itself, and all four patients had Hellp syndrome and required AV greater than 48 hours. In the other patients, total regression of neurological signs was noted.This study emphasizes the severity of the Posterior ‘reversible’ encephalopathy syndrome on eclampsia.

Incorporating capacitance into partial-core transformer models to determine first natural resonant frequencies

Capacitive components are added to partial core transformer models to allow resonant analysis at harmonic frequencies (50-5 kHz). The harmonic frequency responses of partial core transformers with relatively low turns ratio are analysed with the model. Capacitive loads of various magnitudes are then connected to the secondary terminals in order to calculate loaded resonant frequencies. The calculated values are validated with test results. The harmonic frequency responses of two high-voltage partial-core transformers with large turns ratio are presented. Calculations of the transformers' first natural resonant frequency were validated with test results. Additionally, a capacitive load was placed across each of the secondary terminals and the loaded resonant frequencies, calculated by the model, are compared to the measured values.

Study of fast diffusion in zeolites using a higher harmonic frequency response method

The high harmonic frequency response (FR) method has been applied for the first time to measure fast diffusion processes in zeolites, e.g. carbon dioxide/silicalite-1, hexane/beta-zeolite and hexane/NaX. The frequency range can be increased to 90 Hz when the ninth harmonic is taken in the Fourier transformation of the squarewave signals. The diffusivities of carbon dioxide in silicalite-1 and hexane in NaX measured by this frequency response method are in a good agreement with the corresponding values determined by PFG NMR. The diffusivities of carbon dioxide in silicalite-1 were found to be one order of magnitude larger than those in theta-1. The difference in diffusivity between these two 10-ring zeolites can be explained by the different diffusion mechanisms involved, i. e. the single-file diffusion for the one-dimensional theta-1 and the random jump model for the three-dimensional silicalite-1. The faster diffusion of n-hexane in NaX (12-ring windows link the supercages) than in beta-zeolite (three mutually intersected 12-ring channels) was also observed by this FR method.

Large-signal modulation response of monolithic active integrated-optic waveguides

A large-signal dynamic travelling optical flux analysis of a GaAs/AlGaAs monolithic active integrated-optic waveguide (AIOW) is presented. The model uses a combination of numerical and analytical techniques to solve the photon flux and carrier density conservation equations in time, the longitudinal dimension and optical wavelength. An analysis of the fundamental and harmonic frequency response of the waveguide is obtained, along with pulse and sinusoidal modulation response. This analysis is compared with a small signal analysis of the guide, and the two models are found to be in extremely close agreement for the limiting case of a small signal input applied to the large signal model.

A parametrically driven harmonic analysis of a non-linear stretched string with time-varying length

This paper is concerned with the first, second and third harmonic lateral vibrations of a string having a forced, periodic, small length variation. Account is taken of the non-linear term arising from the correction to the tension of the string due to local elongation. It is found that increasing the amplitude of the length variation of the string results in a narrowing of the frequency response range of each of the harmonic oscillation components. Both numerical and analytical calculations of the harmonic frequency responses have been carried out The relationships for initial values between the original differential equation and the approximate differential equations for the harmonic responses are discussed in detail.