Frequency Response Spectra Research Articles

Novel three-dimensional acoustic metamaterials with low-frequency bandgap and strong vibration and noise attenuation

The suppression of low-frequency vibration and noise has been the research focus of acoustic metamaterials. Based on the local resonance effect of the subwavelength structure, two new topology optimization methods are proposed in this paper, and two new three-dimensional single-phase material structures are obtained. Based on Bloch theorem and lattice theory, finite element simulations of the single cells with different structures are carried out to analyze and explore the bandgap properties and opening mechanism of the structures. The frequency response spectra are obtained by vibrational transport simulation of the finite-period structures. The results show that both novel metamaterial structures have good bandgap properties, the widest first bandgap width within 2000 Hz reaches 809 Hz, and the total bandgap width percentage reaches 52.7 %, and the main vibration forms of opening the bandgap are rotational and offset resonance of the internal structure and torsional resonance of part of the structure.

On the resonance frequency of the irregular shaped visco-acoustic Helmholtz cavity problem

In this paper we develop a closed-form mathematical solution for the resonance frequency of the axisymmetric irregular shaped visco-acoustic Helmholtz cavity problem. The solution is based on a conformal mapping that transforms the governing visco-acoustic equations of motion for the irregular cavity geometry into a new domain described by a set of orthogonal curvilinear coordinates. These orthogonal curvilinear coordinates have an important characteristic relative to the transformation of the physical boundary: the mapped domain is constructed such that the locus of all points for the length-wise profile of the physical boundary coincides with a constant value for a (quasi radial) coordinate in the new mapped domain. In these orthogonal curvilinear coordinates we obtain an analytical solution for the visco-acoustic equations of motion and exactly satisfy the no-slip fluid boundary conditions over the irregular shaped cavity walls by matching the coefficients of an orthogonal Legendre polynomial series representation for the non-uniform velocity on the cavity walls. The mathematical solution is an approximation to the extent that the scale factors chosen for the mapping consist of strictly the mutual-coupling terms of the true scale factors. Thus we analyze some results to understand the correlation of the analytical solution frequency response spectra with numerical finite element analyses of the idealized boundary conditions with various irregular shaped cavity geometries. The results for fundamental resonance frequency were found to exhibit good correlation with the results of finite element analyses over a significant range of fluid properties with different irregular cavity geometries. As the primary motivation for the derivation stems from the lack of a rapid yet accurate alternative to computationally intensive MultiPhysics FEA in the formulation of acoustic trendlines for sensor development, the solution’s acoustic impedance was applied as dispersive loading in a simple lumped parameter model of a fluid identification sensor for comparison. The resulting acoustic trendlines of the reduced (5 DOF) model were found to exhibit good correlation with the results of the MultiPhysics FEA (>105 DOF). Thus the solution was found to enable a closed-form analytical method for rapid construction of parametric studies in the practical design of fluid analysis sensors based on complex resonant cavity geometries.

Experimental and Numerical Study of the Flow Around Rigid and Flexible Hydrofoils for Wetted and Cavitating Flow Conditions

Abstract The hydro-elastic response of a flexible NACA 0015 hydrofoil is investigated for both wetted and cavitating flow conditions. Computational fluid dynamics (CFD) analysis are performed using a fully implicit coupling between the ISIS-CFD solver (developed by the METHRIC team at Ecole Centrale de-Nantes) and a modal approach for the structure. The Reynolds-averaged Navier–Stokes (RANS) solver is first validated for wetted and cavitating flow conditions around a similar rigid hydrofoil, with experimental results carried out at the hydrodynamic tunnel of the French Naval Academy, including lift and drag measurements and high speed camera images. Then the numerical predictions for the flexible hydrofoil response are compared with experimental bending shapes and vibrations amplitudes, with a focus on cavitating flow conditions. For wetted flow conditions, numerical results show a good agreement with the experiments, for both rigid and flexible hydrofoils. For cavitating flow conditions, the hydro-elastic response is dominated by vibrations at the hydrofoil modal frequencies and the reentrant jet instability frequency. For the lowest values of the cavitation number, a large amplitude peak is experimentally observed in the frequency response spectra, due to lock-in between the first modal frequency and the reentrant jet frequency. Strong harmonics of this dominant peak also appear in the spectra, revealing a nonlinear response of the hydrofoil. While the amplitudes of vibrations are well predicted by the computations, the frequency lock-in observed in the experiments is not captured by the numerical model.

A method for measuring soil water content based on principal component analysis.

Principal component analysis (PCA) has been applied in many aspects. To address the problem of measuring water content in soil, this paper proposes a method to measure soil water content based on the PCA. We used PCA to reduce the dimension of the data and processed the soil amplitude ratio frequency response spectra. First, we designed the measuring device and measured the soil amplitude ratio frequency response data of different water content, then we used the PCA to extract features from the frequency response spectra of different water contents, established a relationship model of soil water content, and finally, we solved the model, the maximum error between the calculation results and the actual water content was no more than 0.85%. Subsequently, we carried out experimental verification, and we measured six kinds of soil with known water content by this method. The experimental results showed that the maximum error did not exceed 1.16%, and the average error was 0.71%. Thus, the proposed method can provide a useful way of measuring soil water content.

Micromagnetic frequency-domain simulation methods for magnonic systems

We present efficient numerical methods for the simulation of small magnetization oscillations in three-dimensional micromagnetic systems. Magnetization dynamics is described by the Landau–Lifshitz–Gilbert equation, linearized in the frequency domain around a generic equilibrium configuration, and formulated in a special operator form that allows leveraging large-scale techniques commonly used to evaluate the effective field in time-domain micromagnetic simulations. By using this formulation, we derive numerical algorithms to compute the free magnetization oscillations (i.e., spin wave eigenmodes) as well as magnetization oscillations driven by ac radio-frequency fields for arbitrarily shaped nanomagnets. Moreover, semi-analytical perturbation techniques based on the computation of a reduced set of eigenmodes are provided for fast evaluation of magnetization frequency response and absorption spectra as a function of damping and ac field. We present both finite-difference and finite-element implementations and demonstrate their effectiveness on a test case. These techniques open the possibility to study generic magnonic systems discretized with several hundred thousands (or even millions) of computational cells in a reasonably short time.

Seismic Site Response Analysis of MMMUT Gorakhpur of Uttar Pradesh, India

An endeavour has been made to assess the spatial fluctuation of the profundity of endured and designing bedrock in Gorakhpur Uttar Pradesh, North India utilizing Multichannel Analysis of Surface Wave (MASW) study. One-layered MASW study has been done at Madan Mohan Malaviya University of Technology, Gorakhpur campus and Shear-wave Velocity V S 30 are estimated. MASW overview at 3 location and a Standard Penetration Test SPT-N from the profound geotechnical boreholes data used for comparison of site classification. The deduction of this work might be utilized as contributions for seismic tremor risk the board by lessening the seriousness of earthquake shaking through plan of tremor Earthquake risk resilient structure strong designs. The data that collected from the MASW experimental setup is feed using the software ParkSEIS (v.3.0), we obtain Shear Wave Velocity (VS30 ). The obtained V S 30 is used to plot Response Spectra for MMMUT Gorakhpur. The Time History data used in this thesis is Nepal Earthquake 2015 data which is collected from Indian Metrological Department (IMD) Delhi, India. SPT-N value data is collected from Awas Vikas Parishad for the New Administration Building build at MMMUT campus Gorakhpur. The Time History data of Nepal Earthquake 2015 is analysed using DEEPSOIL v7 Software and a systematic layer wise study of MMMUT Campus soil is carried out, results such as Ground Motion Parameters, Response Spectra, Spectral acceleration vs Frequency plot, Tripartite Spectrum and Response spectra corresponding to 5% damping are obtained.

Analysis of low frequency vibration attenuation and wave propagation mechanism of graded maze structure

In this paper, a new graded maze metamaterial with a single phase is proposed. Based on the finite element method and Bloch's theorem, the bandgap characteristics of graded maze structures in different regions are analyzed, and the mechanism of bandgap opening and closing is explored by vibration patterns. Subsequently, the mechanism of elastic wave propagation within different structures is comprehensively analyzed from four perspectives, such as group velocity and phase velocity. And the damping performance is further verified by frequency response spectra. The results show that the new structure has excellent low-frequency bandgap and damping performance, the local resonance of the graded maze plays an important role in the expansion of the bandgap, and there is directionality and regionality of wave propagation within the structure. This paper provides a new idea for wave propagation control and analysis, and low frequency damping of single-phase materials.

Optimizing steady and dynamic hydroelastic performance of composite foils with low-order models

Predicting and controlling the steady and dynamic hydroelastic performance is a crucial challenge in marine composite lifting surface design. Excessive flow-induced vibrations and accelerated fatigue can be severe issues if not considered in the initial design. Most design optimizations only consider steady performance and neglect critical dynamic aspects of the marine environment, such as lower resonance frequencies and different band gaps between modal frequencies in water compared to in air. This work uses lower-order models to capture the steady and dynamic fluid–structure interaction behavior and optimize the design of composite hydrofoils. We formulate new objectives and constraints that consider the natural frequencies, damping, and frequency response spectra in addition to steady hydroelasticity to achieve the design intent. The optimization method is heuristic, which is appropriate for this level of model fidelity where holistic parameter trends are more of interest. Results for a 1/3 length-scale hydrofoil model showed a significant improvement in the optimized performance over the baseline. By tailoring geometric and material variables of the composite hydrofoil, we produced an optimal design. This design meets the steady design condition requirements and avoids excessive vibrations and dynamic load amplifications due to lock-in, resonance, flutter, and modal coalescence.

The geometric mean is a superior frequency response averaging method for human body vibration

The frequency response data of human body vibration are often used for standardisation, design of transport vehicles and occupational health and safety measures. This article shows that the commonly used methods of averaging frequency response spectra, such as arithmetic averaging in the complex or magnitude domain and median averaging, are not as suitable as the less commonly used geometric averaging in the complex domain. This is because it is necessary to minimise the deviation of the measured values about the mean value and to minimise the bias from the true mean value due to noise, distortion and nonlinearity. Practitioner summary: For averaging frequency response spectra, it is necessary to minimise the bias from the true mean value. This research shows that the commonly used averaging methods, such as arithmetic averaging in the complex or magnitude domain and the median, are not as suitable as geometric averaging in the complex domain. Abbreviations: H1 Estimator: frequency response function estimation method using the cross-spectrum of the output with the input divided by the auto-spectrum of the input; ISO: International Organization for Standardization; NHK: Nippon Hatsujo Kabushiki Kaisha; PCB: PCB Group ("PCB" is abbreviation for "PicoCoulomB"); RMIT: Royal Melbourne Institute of Technology; r.m.s.: root mean square

Output-Only Modal Parameter Identification of Systems Subjected to Various Types of Excitation

This study presents a novel modal parameter identification method enabling approximation of the mode shapes of linear systems using white-noise or earthquake inputs. The majority of well-established existing system identification methods perform successfully when the system is excited by broadband white-noise excitation. However, they encounter serious limitations when analyzing the vibrations triggered by nonstationary earthquake inputs. Thus, the presented technique extends the applicability of system identification and modal-based structural health monitoring methods. The method operates in modal space and is based on mode superposition in short windows. The mode shapes are identified using an optimization algorithm minimizing the weighted sum of cross-correlation of frequency response spectra. The technique is validated analytically using simulation results of a simple three-dimensional (3D) structure representing a simplified model of a real bridge pier structure, which enables exact comparison with known properties. The results show the method provides relatively good identification accuracy of modal parameters of systems excited by white-noise and earthquake inputs. The identified modal frequencies showed <1% error, where the mode-shape coefficients were identified within 5% error. The method performs robustly even for high levels of simulated sensor noise and can be readily applied to more complex multiple degree of freedom (MDOF) systems.

A Guide to Concentration Alternating Frequency Response Analysis of Fuel Cells.

An experimental setup capable of generating a periodic concentration input perturbation of oxygen was used to perform concentration-alternating frequency response analysis (cFRA) on proton-exchange membrane (PEM) fuel cells. During cFRA experiments, the modulated concentration feed was sent to the cathode of the cell at different frequencies. The electric response, which can be cell potential or current depending on the control applied on the cell, was registered in order to formulate a frequency response transfer function. Unlike traditional electrochemical impedance spectroscopy (EIS), the novel cFRA methodology makes it possible to separate the contribution of different mass transport phenomena from the kinetic charge transfer processes in the frequency response spectra of the cell. Moreover, cFRA is able to differentiate between varying humidification states of the cathode. In this protocol, the focus is on the detailed description of the procedure to perform cFRA experiments. The most critical steps of the measurements and future improvements to the technique are discussed.

Understanding nonlinearity in electrochemical systems

Commonly applied electrochemical methods for the analysis and diagnosis of the processes in and state of electrochemical cells, such as Electrochemical Impedance Spectroscopy and Current Interrupt analysis, are either limited to linear analysis or the signal is quite unspecific which hampers to extract significant and precise nonlinear information. We present a systematic insight into how significant information can be extracted from a promising alternative nonlinear dynamic electrochemical analysis technique, Nonlinear Frequency Response Analysis. Further, we present a fundamental and in-depth study of impact of processes at electrodes on nonlinear behavior. Model based analysis of a reaction process with Butler-Volmer kinetics and of a diffusion process are thereby used to understand and interpret the excitation of higher harmonics. A reaction with a symmetric current potential relation thereby causes an excitation of the third harmonic, whereas for the diffusion process the second and third harmonic are excited. Nonlinearities caused by diffusion are limited to low frequencies. Further, parameter variations of exchange current density, double layer capacitance and diffusion coefficient as well as variation of the input signal show that the symmetry of the nonlinear behavior between current and potential is responsible for the excitation of the second and third harmonic. The tangent method is presented as a suitable method to quantitatively evaluate and compare influences of each process and parameter on spectrum features and the related characteristic frequency range. The work thus serves as a guideline for using and interpreting nonlinear frequency response spectra.

Vibration and modal analysis of a rotating disc using high-speed 3D digital image correlation

Abstract Rotating structures are of interest in many engineering fields, where knowing their dynamic behaviour is important to prevent undesired operating states. However, the experimental measurement of vibrations in rotating structures is still a relatively demanding task that requires the use of special measurement technique or method. The paper deals with the application of high-speed digital image correlation in vibration analysis of rotating structures. The method introduced in this research is based on the elimination of rigid body motion components contained in the primary responses measured by cameras. The process of separation and subsequent elimination of these components is given by numerical post-processing of three-dimensional displacement fields. The basis is to determine rotation matrix and translation vector that optimally describe rigid transformation between two positions of an analysed object. The proposed method is applicable for measuring under both constant and variable speed of rotation. Practical application is presented by three experiments in which vibrations of a flat rotating disc were analysed. The first experiment is focused on determine the operating deflection shapes of the disc rotating at 4700 rpm. The second one is a run-up analysis under variable rotational speed that ranges from 0 to 4700 rpm. The aim of the third measurement is to obtain natural frequencies and modal shapes of the disc rotating at 4800 rpm. The results of the experiments show that the elimination of rigid body motions leads to a higher accuracy of measurement and provides more pronounced frequency response spectra.

Nonlinear dynamics of a flexible rotor on tilting pad journal bearings experiencing rub–impact

Rub–impact phenomenon occurring in hydrodynamic journal bearings is one of the main malfunctions in rotating machines and causes undesirable dynamic behavior. In order to investigate such a phenomenon, nonlinear dynamics due to rub–impact within tilting pad journal bearings supporting a flexible rotor is studied. In simulating rub–impact between the journal and the associated pads, this paper employs mixed lubrication theory along with elasto-plastic asperity contact model between pads and journal. Periodic, quasiperiodic and chaotic vibrational behaviors of system are studied by varying the unbalanced load magnitude and the rotational speed of the rotor as control parameters. Phase plane orbits, waterfall frequency response spectra and bifurcation diagrams are used to show various dynamic responses of rotor when the control parameters are changed. The Poincare maps are used to determine the onset of irregular motions. Presented results provide better understanding of strongly nonlinear vibrations occurring due to rub–impact in TPJBs supporting industrial rotating machines.

A Study on Efficacy of Wavelet Transform for Damage Identification in Reinforced Concrete Buildings

Structural damage and its extent can be detected by vibration-based techniques to avoid failure or to minimize maintenance. Among different damage identification techniques, modal curvature approaches are widely researched and applied one. On the contrary, wavelet transformation (WT) methods are gaining popularity in damage identification of real life buildings because of their suitability for non-stationary signals and non-dependency on baseline data. This paper presents a novel approach utilizing complex continuous wavelet to effectively locate change in physical properties of reinforced concrete (RC) buildings by virtue of variation in frequency and mode shapes due to small change in mass and stiffness. In this paper, the effect of variation of mass and stiffness of a building on the modal parameters is established analytically using theequation of motion for a multi-degree freedom system under forced vibration condition. A 3-D finite element model was developed for predicting the modal frequencies and mode shapes of the scaled down six storey RC building and the effect of addition of mass on a particular level of structure on the modal parameters was studied. Further, acceleration time histories were recorded with variation in mass on 3rd story of building using wireless tri-axial accelerometers and the time histories were processed to arrive at Curvature Damage Factor and wavelet coefficients for identification of the additional load on the particular floor. Vibration responses from all floors of RC building in ambient and loaded conditions were analyzed for frequency response spectra (FRS). Mode shapes were drawn for unloaded case and loaded cases. It was observed that the modal frequency of building decreases with the increase in mass at floors. It is observed that CDF approach could detect the change in mass in both numerical and experimental results. However, CDF algorithm could not detect the addition of load in case 1, 2 and 3, i.e. when load was less than 25 kg, i.e. only 2.6% of floor mass (960 kg). The acquired data for the above stated load cases were analyzed using complex Gaussian ‘cgau5’ wavelet in MATLAB toolbox to determine the singularity in the signal in terms of wavelet coefficient modulus. It is observed that the WT approach is able to precisely locate the change in physical parameters of the RC model building. However, it is seen that additional load could not be detected in case where only 9 kg, i.e. 0.93% of the total floor mass, was placed on 3rd floor. From the research work, it is observed that CDF technique is inefficient in damage detection and always demand prior baseline information, which is usually difficult to obtain in practice. However, the wavelet transform-based approach more accurately detects the location of change without relying on intact state vibration data.

Damage Identification for Hysteretic Structures Using a Mode Decomposition Method

AbstractThis article investigates structural health monitoring (SHM) of multidegree of freedom (MDOF) structures after major seismic or environmental events. A recently developed hysteresis loop analysis (HLA) SHM technique has performed robustly for single degree of freedom (SDOF) and single mode dominant MDOF structures. However, strong ground motions can trigger higher vibration modes, resulting in irregular hysteresis loops and making this otherwise robust identification difficult. This study presents a new filtering tool, enabling reconstruction of single mode dominant restoring force‐displacement loops which can be readily used for HLA.The proposed filtering tool is based on a classic modal decomposition using optimized mode shape coefficients. The optimization process is carried out in a modal space and is based on decoupling frequency response spectra of interfering modes. Application of modal decomposition using the optimized mode shape coefficients allows for reconstruction of single‐mode dominant hysteresis loops, which can be effectively identified using HLA. The proposed filtering tool is validated on the reconstruction of hysteresis loops on an experimental bridge pier test structure with notable contributions from at least two modes.The results show the method eliminates the influence of all higher modes that contain significant energy content and yields the reconstruction of “smooth” single mode dominant hysteresis loops. The resulting SHM analysis on the reconstructed experimental hysteresis loops identified degradation in the elastic stiffness profiles, indicating damage within the structure and matching prior published results based on physical inspection of damage. The overall method presented increases the breadth of potential application of the HLA method and can be readily generalized to a range of MDOF structures.

Structure-soil-structure interaction effects on structures retrofitted with tuned mass dampers

This paper investigates the dynamic structure-soil-structure interaction (SSSI) between two adjacent sway frames, replicating closely spaced residential buildings in an urban setting subjected to seismic input motions. The structures are considered with and without external damping mechanisms by means of tuned mass damper (TMD) configurations. Geotechnical centrifuge tests were conducted to address the current lack of experimental case studies into SSSI and uniquely explore the influences from the presence of TMDs and variations in their configurations on SSSI. SSSI was found to significantly alter the response of proximally located urban structures, as was evident from significantly larger rocking amplitudes and changes in frequency response spectra. TMD effects under SSSI were mostly found to amplify an adjacent structure's peak roof acceleration response and inter-storey drift – this was most aggravated when the damper was de-tuned. TMD effects were found to be relatively more pronounced under smaller earthquakes and could certainly cause occupational inconvenience or even damage in adjacent buildings.

Effect of proton irradiation on extended wavelength In0.83Ga0.17As infrared detector

Extended wavelength In0.83Ga0.17As infrared detectors have been irradiated with 2MeV proton with a fluence of 1×1015cm−2. Dark current–voltage characteristics, low frequency noise (LFN) and response spectra were measured before and after irradiation at room temperature (RT) to investigate the irradiation effect. The results showed that dark current and LFN increased after irradiation, and the responsivity decreased. The performance degeneration of detectors is generally related to the defects originated from the displacement effect of irradiation. The analysis of dark current mechanisms indicates that the irradiation mainly results in the increase of shunt component. The degeneration of LFN is attributed to the increase of all noise components, i.e. 1/f noise, g–r noise and white noise. The annealing behaviors of dark currents were observed at RT. The dark currents decreased by about 17% on average by the 19th hour and then hardly recovered by the 225th hour after irradiation. The InGaAs/InAlAs multilayer epitaxial material used to fabricate the detector was also irradiated. The Photoluminescence (PL) measurements at 77K showed that PL intensity of InGaAs layer decreased much greater than that of InAlAs layer after irradiation.

Dynamic behaviors of a geared rotor system under time-periodic base angular motions

The dynamic behaviors of a geared rotor system under time-periodic base motions are studied in this paper. The equations of motion for a spur gear pair system are derived based on the energy theorem and Lagrange's principle. Three base angular motions, including the rolling, pitching and yawing motions, are assumed to be sinusoidal perturbations superimposed upon constant terms. Considering the time-varying base movements and gear meshing, the second order differential equations of the system will not only have time-periodic gyroscopic and stiffness coefficients, but also the multi-frequency external excitations. Numerical method is utilized to obtain the lateral and torsional responses of the geared system under transmission error and unbalanced mass excitations. The effects of various base angular motions on both frequency response and response spectra are discussed in detail. Compared with the other two types of periodic base motions, the rolling base motion has the greatest impact on the dynamic behaviors of the geared system. The transient response of the geared rotor system is always greatly enhanced no matter which type of base angular motion is in operation.

Frequency Response Spectra Applied to Assess Efficiency of the Training Techniques

The purpose of the research is to assess the increase of the muscle strength and power. Movement of the human body when the moving one impacts a stationary or moving body is taken under consideration. The waveform produced by an impact is transformed into frequency domain. The acceleration record is transformed as a complex spectrum, by the use of a Discrete Fourier Transformation. In this paper the applications of the discrete Fourier transform is discussed and it was pointed out that it can be fruitfully applied to analyze movement techniques during competition or training exercises. The acceleration response spectrum contains knowledge about efficiency of certain techniques. It has distinct features which can show that the energy is concentrated around several discrete frequencies. Data from the shape of a frequency response spectra curve can provide the coach and the performer with valuable information on technique and also give information on recommendations with respect to corrections and adjustments that can lead to performance enhancement. In this paper, the technique of a database creation is proposed what allows us to establish a particular set of circumstances under a specified protocol to observe and evaluate the implications of the resulting observations.