Nonlinear Frequency Response Analysis Research Articles

Nonlinear Frequency Response Analysis of the Ferrocyanide Oxidation Kinetics. Part II. Measurement Routine and Experimental Validation

Kinetics of ferrocyanide electrooxidation was investigated by nonlinear frequency response analysis (NLFRA) of current output to the sinusoidal large-amplitude potential perturbation input. The aim was to establish a measurement routine and to validate experimentally the NLFRA method on an example of a simple electrochemical reaction comprising charge and mass transfer. The first-order frequency response function (FRF) contains quasi-linear information on the reaction kinetics and corresponds to electrochemical admittance. The nonlinear fingerprint of the system is contained in the second-order FRF. The first- and second-order FRFs are determined from experimental first and second harmonics. Their intensities depend on the input signal amplitude, which has to be chosen carefully to avoid the contributions of higher order harmonics. The influence of the potential and electrode rotation speed on the first- and second-order FRFs has been studied. The experimentally obtained FRFs are compared with the theoret...

Nonlinear Frequency Response Analysis of the Ferrocyanide Oxidation Kinetics. Part I. A Theoretical Analysis

In this work, a nonlinear frequency response (NLFR) analysis was used for a first time in a theoretical study of nonlinear behavior of electrochemical (EC) ferrocyanide oxidation as a simple model reaction. Analytical expressions of the first- and second-order frequency response functions (FRFs) are derived. The first-order FRF is equivalent to the EC admittance and contains information about the linear behavior of the system, whereas the second-order FRF contains additional nonlinear information. The influence of different parameters, such as the heterogeneous rate constant, solution resistance, double-layer capacitance, diffusion coefficients of the reacting species, and electrode rotation rate on the characteristics of the first- and second-order FRFs was checked and discussed. It was found that the second-order FRF is more sensitive to the changes of the studied parameters than the first-order FRF. Experimental verification of the NLFR analysis of EC ferrocyanide oxidation is presented in Part II of this work.

Discrimination of Performance Limiting Processes in PEMFC Using Nonlinear Frequency Response Analysis

not Available.

Nonlinear Vibrations and Frequency Response Analysis of a Cantilever Beam Under Periodically Varying Magnetic Field

In this paper, nonlinear vibration of a cantilever beam with tip mass subjected to periodically varying axial load and magnetic field has been studied. The temporal equation of motion of the system containing linear and nonlinear parametric excitation terms along with nonlinear damping, geometric and inertial types of nonlinear terms has been derived and solved using method of multiple scales. The stability and bifurcation analysis for three different resonance conditions were investigated. The numerical results demonstrate that while in simple resonance case with increase in magnetic field strength, the system becomes unstable, in principal parametric or simultaneous resonance cases, the vibration can be reduced significantly by increasing the magnetic field strength. The present work will be very useful for feed forward vibration control of magnetoelastic beams which are used nowadays in many industrial applications.

Nonlinear frequency response analysis for the diagnosis of carbon monoxide poisoning in PEM fuel cell anodes

Anodic CO poisoning of a PEMFC was analysed by nonlinear frequency response analysis (NFRA) in a differential H2/H2 cell. This special experimental setup excluded potential masking effects, emphasised the main mechanism of CO poisoning and made a simplified modelling approach possible. The main features of CO poisoning were investigated by means of steady state polarisation, EIS and NFRA. The main characteristics of CO poisoning in the NFRA spectra can be used as a “fingerprint” for diagnostic purposes.

Investigation of gas transport through porous membranes based on nonlinear frequency response analysis

Theoretical development of a new experimental method for investigation of mass transport in porous membranes, based on the principle of the modified Wicke-Kallenbach diffusion cell and the nonlinear frequency response analysis is presented. The method is developed to analyze the transport of a binary gas mixture in a porous membrane. The mixture is assumed to consist of one adsorbable and one inert component. Complex mass transfer mechanism in the membrane, where bulk or transition diffusion in the pore volume and surface diffusion take place in parallel, is assumed. Starting from the basic mathematical model equations and following a rather standardized procedure, the frequency response functions (FRFs) up to the second order are derived. Based on the derived FRFs, correlations between some characteristic features of these functions on one side, and the whole set of equilibrium and transport parameters of the system, on the other, are established. As the FRFs can be estimated directly from different harmonics of the measured outputs, these correlations give a complete theoretical basis for the proposed experimental method. The method is illustrated by quantifying the transport of helium (inert gas) and C3H8 and CO2 (adsorbable gases) through a porous Vycor glass membrane.

Nonlinear Frequency Response of Electrochemical Methanol Oxidation Kinetics: A Theoretical Analysis

In this theoretical contribution, nonlinear frequency response analysis was applied for the investigation of electrochemical methanol oxidation. This technique expresses the input–output behavior of any weakly nonlinear system with the help of the Volterra series expansion and generalized Fourier transform into so-called higher order frequency response functions. These functions contain the system’s nonlinear fingerprint. They can be derived analytically from a nonlinear model. These functions can be obtained experimentally from the measurement of higher harmonics induced by a high amplitude sinusoidal perturbation of the system of interest. Frequency response functions up to the second order have been derived analytically for four different model varieties describing the kinetics of the electrochemical methanol oxidation. The first-order frequency response function corresponds to the reciprocal value of the well-known electrochemical impedance, which represents the linear part of the frequency response. This function does not contain sufficient information for discrimination between the different kinetic models. In contrast, the symmetrical second-order frequency response functions show differences in shape, which substantiate the availability of the theoretical prerequisites for model discrimination. A detailed parametric study for all four model variants has been performed. The results show that the basic features of the shapes of the amplitude spectra corresponding to the four models remain unique. The ubiquitousness of the qualitative differences between the competing models, for the whole set of parameters chosen for our analysis, suggests that the aforementioned amplitude spectra contain sufficient information for an unequivocal model discrimination.

Fast evaluation of periodic operation of a heterogeneous reactor based on nonlinear frequency response analysis

The concept of higher-order frequency response functions (FRFs), which is based on Volterra series representation of nonlinear systems, is used to analyse the time-average performance of a perfectly mixed reactor subject to periodic modulation of the inlet concentration, for a simple n-th order heterogeneous catalytic reaction. The second order frequency response function G 2( ω,− ω), which corresponds to the dominant term of the non-periodic (DC) component, essentially determines the average performance of the periodic process. Thus, in order to evaluate the potential of a periodic operation, it is sufficient to derive and analyse the G 2( ω,− ω) function. The sign of this function defines the sign of the DC component and reveals whether the periodic operation is favourable compared to conventional steady state operation, or not. It will be shown that, for the case investigated, the sign of this function depends both on the reaction order and on the shape of the adsorption isotherm.

Nonlinear dynamic analysis of the whole vehicle on bumpy road

Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found. The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincare maps were used simultaneously to derive strange super chaotic attractor. According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of the nonlinear system was verified. Numerical results by 4-order Runge-Kutta method presented the multiform dynamic behavior of the system.

Nonlinear Frequency Response Analysis for the Diagnosis of PEM Fuel Cells

not Available.

Nonlinear frequency response analysis of PEM fuel cells for diagnosis of dehydration, flooding and CO-poisoning

Membrane dehydration, fuel cell flooding and anode catalyst poisoning by carbon monoxide are diagnosed in a single polymer electrolyte fuel cell (PEMFC) using nonlinear frequency response analysis (NFRA). A sinusoidal perturbation of high amplitude is applied to the fuel cell current and the resulting voltage is analysed using the concept of higher order frequency response functions. It is shown that the linear part of the system response corresponds to classical Electrochemical Impedance Spectra (EIS), which are not sufficient to clearly distinguish between different fuel cell failures. Therefore, the nonlinear behaviour is additionally taken into account in the form of the second order frequency response function. With this, it is possible to distinguish unambiguously between the three analysed PEM fuel cell failures.

An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams

The nonlinear vibration analysis of a directly excited cantilever beam modeled as an inextensible viscoelastic Euler–Bernoulli beam has been studied by the authors and is reported in the literature. The viscoelastic damping was modeled as Kelvin–Voigt damping, and the nonlinearities arisen from the inextensibility assumption. This paper extends our theoretical developments presented in the previous papers and utilizes the method of multiple scales in order to arrive at the modulation equations and the closed-form frequency response function. The analytically derived frequency response is experimentally verified through harmonic force excitation of samples of carbon nanotube-reinforced beams. The beam used in experiment consists of two elastic layers of high-carbon steel sandwiched together through a viscoelastic layer of carbon nanotube–epoxy mixture. The results demonstrate that increasing the excitation amplitude or decreasing damping ratio can cause a minor decrease in the nonlinear resonance frequency despite the significant increase in the amplitude of vibration due to reduced damping.

Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers

Microcantilevers have recently received widespread attentions due to their extreme applicability and versatility in both biological and non-biological applications. Along this line, this paper undertakes the non-linear vibrations of a piezoelectrically driven microcantilever beam as a common configuration in many scanning probe microscopy and nanomechanical cantilever biosensor systems. A part of the microcantilever beam surface is covered by a piezoelectric layer (typically ZnO), which acts both as an actuator and sensor. The bending vibrations of the microcantilever beam are studied considering the inextensibility condition and the coupling between electrical and mechanical properties in the piezoelectric materials. The non-linear terms appear in the form of quadratic expression due to presence of piezoelectric layer, and cubic form due to geometrical non-linearities. The Galerkin approximation is then utilized to discretize the equations of motion. In addition, the method of multiple scales is applied to arrive at the closed form solution for the fundamental natural frequency of the system. An experimental setup consisting of a commercial piezoelectric microcantilever attached on the stand of a state-of-the-art microsystem analyzer for non-contact vibration measurement is utilized to verify the theoretical developments. It is found that the experimental results and theoretical findings are in good agreement, which demonstrates that the non-linear modeling framework could provide a better dynamic representation of the microcantilever than the previous linear models. Due to microscale nature of the system, excitation amplitude plays an important role since even a small change in the amplitude of excitation can lead to significant vibrations and frequency shift.