Flying qualities assessment using nonlinear frequency response analysis

A novel approach for the dynamic analysis of Lithium-ion batteries is the investigation of higher harmonic voltage responses with Nonlinear Frequency Response Analysis (NFRA). This is commonly applied in the field of acoustics [1], material science [2], for fuel cells [3] and as a state of charge estimator for Lead-Acid batteries [4]. NFRA is an adaption and advancement of Electrochemical Impedance Spectroscopy (EIS). In contrast to EIS, NFRA allows to study nonlinear processes in Lithium-ion batteries, such as electrode reactions and solid diffusion in spherical particles, without linearization. By analyzing the NFRA spectrum and correlating the dynamic responses with the corresponding EIS spectrum, a novel and deeper insight into battery processes can be provided. We will show the application of NFRA on Lithium-ion batteries with a model-based study for optimal identification and quantification of the individual processes. A state-of-the-art Single Particle Doyle-Newman model [5] is extended with a SEI and double layers at each interface and adapted to simulate NFRA of Lithium-ion batteries. In contrary to EIS, the system is excited with a high amplitude guaranteeing nonlinear behavior. The model output in the time domain is transferred via Fast-Fourier-Transformation (FFT) to the frequency domain, thereby accessing the amplitudes of the individual harmonics Y n as well as their sum in dependency of the frequency. Once a system is excited with a sinusoidal input current, it will reach for a dynamic-steady-state. We will show how state variables, e.g. solid concentration and double-layer potentials, contribute to this behavior at characteristic frequencies defined for the NFRA spectrum in Figure 1. Thereby investigating the number of oscillations needed for dynamic-steady-state analysis. With decreasing frequency, ranging from 1131 Hz to 5.3 Hz to 0.3 Hz, the influence of the anode solid concentration csurf,a increases until it becomes dominant in the low frequency region at 0.3 Hz. Further, only the double-layer potentials Δϕ a and Δϕ SEI at the anode side are influenced, indicating the anode as limiting electrode. We further focus on the investigation of the dynamic-steady-state for process identification by parameter and amplitude variations. The impact of the variation of diffusion coefficient, reaction rates and double-layer capacitances is demonstrated. Changes in SEI processes influence the overall excited frequency range, whereas changes in reaction and diffusion processes affect only certain frequency regions. Thus, frequency ranges can be assigned to processes, therefore enabling process identification. Additionally, with a variation of processes, the amplitude dependency changes. Further, individual harmonics show different characteristic progressions within the overall frequency range. Process identification on Lithium-ion batteries in general can highly benefit from these findings. Besides NFRA, we provide EIS spectra, simulated with small excitation amplitudes for linear excitation of the system, for comparison to NFRA simulation results. With NFRA, a powerful new dynamic analysis tool is created, accessing a new dimension to the electrochemical characterization of Lithium-ion batteries. Literature: [1] Everest, F. A., et al., Master Handbook of Acoustics, The McGraw-Hill Companies, 2009. [2] Wilson, J. R., et al., Electrochimica Acta, 51, p. 1389–1402, 2006. [3] Mao, Qing, et al., Electrochemistry Communications, 12, p. 1517-1519, 2010. [4] S. Okazaki, J. Electrochemical Society 132, p. 1516, 1985. [5] Doyle, Marc, et al., J. Electrochem. Soc., 143, (6), p. 1890-1903, 1996. Figure 1

Determination of residual capacity, or ‘state of health’ (SOH), is important for the management of battery assets in service and when assessing batteries for re-use at the end of service. Nonlinear frequency response analysis (NFRA) has recently been demonstrated as a means to determine SOH, but the effects of temperature and state-of-charge (SOC) on battery NFRA measurements are not yet well understood. In this work, we investigate the effects of SOC on NFRA measurements performed on commercial 21700 cylindrical cells aged under different temperatures to various SOHs. Total harmonic distortion (THD%) is proposed as a capacity fade indicator. THD% in the range of 10 Hz–150 Hz are found to correlate well with SOH at all SOCs. For frequency < 1 Hz, the effect of aging on THD% is SOC dependent, with larger THDs for the new cell at low open-circuit voltages (OCVs) (2.75 V–3.2 V), and larger THDs for aged cells at higher OCVs (3.5 V–4.1 V). This work also demonstrates the feasibility of NFRA to distinguish between cells that have been aged differently based on temperature.

Frequency response analysis often provides a great deal of information about the system response over the entire range of operation. This can be computationally expensive if time‐domain methods are used, especially for large structural models. Presence of non‐linearity in the system makes it difficult to employ standard frequency response analysis techniques, which are linear in nature. If the system contains mild‐nonlinearities and the response of the system can be assumed to be periodic, it is possible to obtain nonlinear frequency response of the system using harmonic balance techniques. This paper presents the application of the harmonic balance method for solving nonlinear structural dynamics problems. To improve robustness of the solution and capture unstable branches, the continuation procedure technique is included along with the harmonic balance method. The method developed has been implemented in MSC Nastran SOL 128.

This paper is focused to investigate the effects of nonlinear sources, including viscoelastic foundation and geometrical nonlinearity along with the surface elasticity and residual surface stress effects on the primary frequency response of a harmonically excited nanoscale Bernoulli-Euler beam. Due to large surface-area-to-volume ratio, the theory of surface elasticity as well as residual surface stress effects are taken into account within the beam models. The Galerkin approach accompanied by trigonometric shape functions is utilized to reduce the governing PDEs of the system to ODEs. The multiple scales perturbation method theory is applied to compute the nonlinear frequency response of nanobeam. The effects of linear and nonlinear viscoelastic damping coefficient of the medium, crystallographic directions of [100] and [111] of anodic alumina, geometrical nonlinear term and geometrical property on the nonlinear primary frequency response of nanoscale beam are investigated. The results show that theses parameters have a significant effect on the nonlinear frequency response of nanobeams in the case of primary resonance.

Various impedance-based and nonlinear frequency response-based methods for determining the state-of-health (SOH) of commercial lithium-ion cells are evaluated. Frequency response-based measurements provide a spectral representation of dynamics of underlying physicochemical processes in the cell, giving evidence about its internal physical state. The investigated methods can be carried out more rapidly than controlled full discharge and thus constitute prospectively more efficient measurement procedures to determine the SOH of aged lithium-ion cells. We systematically investigate direct use of electrochemical impedance spectroscopy (EIS) data, equivalent circuit fits to EIS, distribution of relaxation times analysis on EIS, and nonlinear frequency response analysis. SOH prediction models are developed by correlating key parameters of each method with conventional capacity measurement (i.e., current integration). The practical feasibility, reliability and uncertainty of each of the established SOH models are considered: all models show average RMS error in the range 0.75%–1.5% SOH units, attributable principally to cell-to-cell variation. Methods based on processed data (equivalent circuit, distribution of relaxation times) are more experimentally and numerically demanding but show lower average uncertainties and may offer more flexibility for future application.

not Available.

Nonlinear Frequency Response Analysis and Optimization of Vibration Systems with Air Springs and Auxiliary Chambers

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

Nonlinear frequency response functions of a chromatographic column—A critical evaluation of their potential for estimation of single solute adsorption isotherms

The Leaning Tower of Pisa was built between 1173 and 1360 and began to lean at the beginning of its construction. Extensive investigations to reveal the causes of the tilting only began in the early 20th century. Although few earthquakes have been recorded, there is a renewed interest in the seismic behavior of the tower triggered by the availability of new data and technologies. This paper highlights the influence of using new strength-controlled constitutive models in case of 1D nonlinear response analysis. This is an aspect that has been poorly investigated. Most of the computer codes currently available for nonlinear seismic response analysis (SRA) of soil use constitutive models able to capture small-strain behavior, but the large-strain shear strength is left uncontrolled. This can significantly affect the assessment of a 1-D response analysis and the Leaning Tower’s subsoil can be useful for this study as it represents a well-documented and well-characterized site. After a geological and geotechnical description of the subsoil profile and a synthesis of available data, the seismic input is defined. One-dimensional SRAs were carried out by means of a computer code which considers an equivalent-linear soil modelling and two codes which assume nonlinear soil response and permit to use strength-controlled constitutive models. All the parameters were calibrated on the basis of the same soil data, therefore allowing for a direct comparison of the results.

Challenges associated with site response analyses for soft soils subjected to high-intensity input ground motions

The computation of the steady-stateresponse of large finite element discretized systems subject to periodic excitations is unfeasible because of excessive run time and memory requirements. One could in principle resort to reduced order models stemming from the high fidelity counterparts, which typically require a solution time orders of magnitude smaller. However, when many simulations are required, as in the case of parametric studies, the overall effort could be still significant and the analysis process could be severely hindered. In this work, we propose a sensitivity approach to assess the influence of model parameters on the nonlinear dynamic response. As opposed to the costly evaluation of reduced order solutions over a range of excitation frequencies and model parameters, the sensitivities of a nominal response allow one to approximate the dynamic response by a simple evaluation of an expansion in the directions spanning the parameter space. Special care must be taken on the closure equation that needs to be appended to the system of equations stemming from the harmonic balance method. We discuss the limitations of the current constant frequency approach and propose an improvement. We demonstrate the merits of the proposed approach on a micro-electro-mechanical system affected by parameterized manufacturing defects. Leveraging from a previous contribution, the nonlinear response and the sensitivities are obtained from a reduced order model which is analytical in the defect parameters. Our procedure is able to deliver accurate probability density functions of quantities of interest (e.g. nonlinear resonance peaks, triple solution bandwidth, etc) against statistical distributions of manufacturing defects at negligible computational cost.

Ground classification refers to the process of categorizing the ground into different grades based on how soil properties impact ground motion. With the introduction of the National Standard of Seismic Design General (KDS 17 00 00) in South Korea, ground classification is now based on the average shear wave velocity of the soil layer (VSSO) and the depth to bedrock (BRDP). To consider the specific characteristics of the ground classification, this study develops a site amplification model based on a suite of nonlinear ground response analyses that utilize VSSO and BRDP as model variables. We collected borehole data from the National Geotechnical Information DB System and obtained VS profiles through geophysical surveys. In cases where no survey record was available, the N-VS relationship was used to estimate the profiles, or representative shear wave velocity profiles for each soil layer were obtained. The collected 93,486 profiles were then classified into 36 clusters based on VSSO and BRDP. 3,271 shear wave velocity profiles were randomly selected from each group and used for the site response analysis. This study utilized 34 observation records of horizontal components of ground motion from domestic and international earthquakes as input seismic waves. Then, each motion was scaled to 1, 1.5, and 2 times, resulting in 81 seismic waves with PGAs ranging from 0.1g to 1g. Nonlinear site response analyses were then performed using the NLHH(Nonlinear Hybrid Hyperbolic) module using a Python-based site response analysis module, PySeismoSoil. This module requires shear wave velocity profiles and input seismic waves as input parameters. The NLHH module uses the HH model, which employs an empirical dynamic curve (Darendeli, 2001)[1] to estimate the damping ratio. A nonlinear site response analysis of 81 input seismic waves was performed at 3,271 boreholes using the NLHH module, and the response spectrum and site amplification ratio were determined. Based on these, this study develops a nonlinear site amplification model with the ground classification parameters, VSSO, BRDP, and input PGA level at the depth to bedrock as model variables.

This study focuses on the back analysis of a geotechnical laboratory test with nonlinear finite element modeling using the Ramberg-Osgood material model. This model has been used by several authors recently for nonlinear ground response analysis and it has been implemented by Midas into their commercial finite element code Midas GTS NX 2014. The verification of the model for 1D nonlinear site response analysis can be found in the documentation of the software package. In this study, Torsional Simple Shear tests were modeled and a comprehensive study was performed to provide verification of the material model for static torsional loading and axisymmetric conditions.

This paper discusses about comparison of seismic response behaviors, seismic performance and seismic loss function of a conventional special moment frame steel structure (SMF) and a special moment frame steel structure with base isolation (BI-SMF). The validation of the proposed simplified estimation method of the maximum deformation of the base isolation system by using the equivalent linearization method and the validation of the design shear force of the superstructure are investigated from results of the nonlinear dynamic response analysis. In recent years, the constructions of steel office buildings with seismic isolation system are proceeding even in Indonesia where the risk of earthquakes is high. Although the design code for the seismic isolation structure has been proposed, there is no actual construction example for special moment frame steel structure with base isolation. Therefore, in this research, the SMF and BI-SMF buildings are designed by Indonesian Building Code which are assumed to be built at Padang City in Indonesia. The material of base isolation system is high damping rubber bearing. Dynamic eigenvalue analysis and nonlinear dynamic response analysis are carried out to show the dynamic characteristics and seismic performance. In addition, the seismic loss function is obtained from damage state probability and repair cost. For the response analysis, simulated ground accelerations, which have the phases of recorded seismic waves (El Centro NS, El Centro EW, Kobe NS and Kobe EW), adapted to the response spectrum prescribed by the Indonesian design code, that has, are used.