Measured Frequency Response Functions Research Articles

Research on the stability prediction for multi-posture robotic side milling based on FRF measurements

In robotic side milling, frequent chatter extremely restricts the acquisition of high surface quality due to weak stiffness, and cutting parameters optimization guided by stability boundary is regarded as an effective solution to solve the chatter problem. In this research, the influence mechanisms of stability were analyzed by evaluating the structural static stiffness and dynamic parameters, and the main factor was characterized as regenerative chatter by means of stability measurements and the theoretical prediction model. The distance-driven multi-posture frequency response function (FRF) prediction model was improved in terms of the dominant modal. Grey correlation analysis was carried out to investigate the influence law of robotic joints to modal parameters, and the difference between far-distance posture and near-distance posture was re-characterized by cross-validation of FRF measurements. Finally, the third-order Hermite–Newton approximation was employed to solve the dynamic model by considering process damping effect, and the results showed the prediction accuracy of the constructed stability boundary was over 85%.

Vibration response of in-vacuo tuneable structured fabrics

This paper presents a first survey on the vibration response of beam-like specimens formed by a vacuum plastic bag with single-layer or double-layer 3D-printed structured fabrics encompassing spherical-octahedra, octahedra and cubes truss-like rigid elements. The study reports a comprehensive analysis of the bending stiffness and energy dissipation properties with respect to the level of vacuum as well as the type and number (single or double) of overlapped fabrics. In this context, it first presents a quasi-static analysis of the bending stiffness and energy dissipation of the specimens. Then, it provides a comprehensive overview of the specimens dynamic properties with respect to measurements of the dynamic stiffness frequency response function and with reference to measurements of hysteresis loops at three characteristic frequencies, namely below, at and above the fundamental bending resonance frequency of the beam-like specimens. The study shows that the bending stiffness and thus the fundamental bending resonance frequency of the specimens can be suitably varied by increasing the level of vacuum in the bags. The specimens made with cubic mails show the highest bending stiffness and fundamental resonance frequency. Also, the specimens with double layer mails show much higher bending stiffness and fundamental resonance frequency. The level of vacuum has little effect on the energy loss, which, in general, is characterised by rather low loss factors. This suggests that once the fabric jams, there is little friction between the particles and the principal damping mechanism is offered by the material energy dissipation in the unit particles.

The Influence of Violin Tailpiece Material on Acoustic Properties of a Violin

The different mechanical properties of the materials from which the tailpieces are made have a noticeable effect on the acoustic performance of the violin. These elements are made today from ebony, rosewood, boxwood, aluminium, or plastic. The aim of this study was to check the exact impact of tailpieces made of different materials on the frequency response function (FRF) of a violin’s bridge and the timbre of the instrument’s sound. For this purpose, the bridge FRF measurement was carried out, and a psychoacoustic test was conducted. The material from which the tailpiece is made to the greatest extent affects the modal frequencies in the range 530–610 Hz (mode B1+), which mainly manifested itself in a change in the instrument’s timbre in terms of the brightness factor. The study showed that the lighter the tailpiece, the darker the sound of the violin. It was also revealed that the selection of accessories affects factors such as openness, thickness, and overall quality of the sound.

A hybrid rotordynamic modeling method for a rotor system with flexible foundation and nonlinear support force: Numerical and experimental investigation

The dynamic characteristics of a flexible foundation would greatly affect the dynamic behavior of the rotor system. In this paper, a hybrid dynamic model method in time domain combines the finite element (FE) method and the subspace-based identification method to model a rotor system with the consideration of a flexible foundation and nonlinear support forces. The state-space model of flexible foundation is identified by the subspace state-space system identification algorithm with measured frequency response functions (FRFs). To solve the calculation problem of the hybrid dynamic model in time domain, a general algorithm named the hybrid model fusion solution (HMFS) method is proposed, which combines the linear and nonlinear nodes separation method used in the FE model and the trapezoidal rule used in the state-space model, improving the calculation efficiency of solving transient response with nonlinear forces. Simulations for the hybrid dynamic model under constant speed and speed-up cases were carried out, resulting that the dynamic characteristics of the entire system can be represented when the nonlinear factors of rolling bearings and gravity were also taken into consideration. Additionally, owe to the consideration of tested dynamic behaviors of flexible base, experimental results in the laboratory test rig are well agreed with the numerical ones under two different test configurations. The investigation provides a complete modeling and highly efficient solution framework for the rotor system with a flexible foundation and nonlinear rolling bearings, with the abilities of further consideration of more nonlinear components such as squeeze film dampers and rubbing forces.

Using passive frequency response functions generated using the Operational Round Trip method to make vibration predictions at remote points

The Round Trip method was derived as a means to acquire point mobility frequency response functions at passive locations, where the term 'passive' specifies that no external known force has been applied. This allows frequency response functions to be generated at locations where the degree of freedom cannot be excited by conventional means. Vibration produced by operational sources can increase signal-to-noise ratios in large complex structures and improve the quality of the measured frequency response functions, where it can be challenging to effectively excite the system by conventional experimental means. In this study, the application of a modified version of the Round Trip method that is based on transmissibility functions, termed the Operational Round Trip method, has been investigated to determine whether forces generated by an operational source, such as a motor, could be used to generate frequency response functions at and between passive locations. Frequency response functions generated using this method have been coupled with the estimated blocked forces of an operational source to make response predictions at remote positions. Predicted responses were compared against measured responses and were shown to match those closely.

Making underwater noise predictions using frequency response functions generated by the Operation Round Trip method

The Round Trip method was derived as a means to acquire frequency response functions at passive locations, where the term ‘passive’ specifies that no external known force has been applied. This allows frequency response functions to be generated at locations where the degree of freedom cannot be excited by conventional means. Sound and vibration produced by operational sources can increase signal-to-noise ratios in large complex systems and improve the quality of the measured frequency response functions, where it can be challenging to effectively excite the system by conventional experimental means. In this study, the application of a modified version of the Round Trip method that is based on transmissibility functions, termed the Operational Round Trip method, has been investigated to determine whether the forces generated by an operational source, such as an offshore wind turbine, could be utilized to predict the frequency response functions at and between passive measurement positions within a coupled mechano-acoustical system. These predicted frequency response functions have been used with the blocked forces of a vibratory source to make underwater noise predictions at remote positions, which were validated against measured underwater noise measurements.

Improved denoising methods for smoothing frequency response functions

Measurement errors, including but not limited to noise, persist regardless of the sophistication of the experimental measurement system. Measurements contaminated with noise have proved challenging to work with from a post-processing standpoint, especially when the measurements are used directly in the analytical processing. Noise contamination in frequency response functions limits the accuracy of many applications, such as impedance modeling, requiring the direct use of measured frequency response function data. Existing approaches, such as Modal Parameter Estimation (curve-fitting), that address the de-noising of frequency response functions also suffer from various deficiencies. The errors associated with the estimation process, including modal truncation along with user interaction and interpretation, are often challenging to mitigate.Two alternative methods of frequency response function de-noising were developed in this work. The first method involves a direct approach that smooths measured frequency response functions without Modal Parameter Estimation or significant user interaction. The second approach works to alleviate the truncated effects of unmeasured modes in frequency response function synthesis more effectively than the existing upper and lower residual compensation terms. The proposed frequency response function de-noising methods are validated analytically and experimentally using various component finite element models and experimental tests.

A Novel Approach to Study the Time-Varying Additive Activity during the Electrorefining of Copper

Electrodeposition additives are key components to enhance the electrochemical deposition of metals, either in pure plating applications or during the electrorefining of metals. Many different additives, either organic or inorganic, are applied in industry, depending on the type of process. This work focusses on thiourea and chloride as common additives used for copper electrorefining. This electrochemical industrial process consumes an impure copper anode and produces a pure (99.995 %) copper cathode, while the anode impurities remain in the electrolyte. Additives assist the electroreduction process to produce smooth copper deposits, essential to avoid short circuits and the formation of unwanted cathode morphologies which can entrap impurities.Thiourea is a crucial but complex additive in copper refining. It is known to degenerate into formamidine disulfide (FDS) and both thiourea as FDS can undergo interactions with either copper ions in the solution or the cathode surface. Time dependent additive studies and fundamental knowledge of the effect of aged electrolyte on the cathodic part of the electrorefining process are scarce.The approach applied in this work enables the investigation of the time dependent effect of additives, in this case thiourea and chlorides, assisting the electroplating of copper. Fundamental knowledge of the assisted plating process is extended to create a corner stone for applied research, subsequently, semi-industrial circumstances are used to describe the additive behaviour in industrial relevant conditions. Operando Odd Random Phase Electrochemical Impedance Spectroscopy (ORP-EIS) is used to study the electrochemistry of the additive system [1,2]. Hereby, a multisine input signal is added to the DC current to perform the ORP-EIS experiment simultaneously with the plating process. This measurement technique allows an in situ monitoring of the electrochemical system for hour-long electrodeposition processes. The ORP-EIS technique enables a quantification of the nonlinearities and non-stationarities during the EIS experiment [3]. Additionally, the present non-stationarities are modelled and the nonlinearities are considered as nuisance factor to result in a best linear time-varying approximation [4,5]. An equivalent electrical circuit is used as model to extract the relevant physical parameters from the impedance data. The EIS study is complemented with an ex situ analysis of the thiourea concentration, through ion chromatography, as a function of plating time. Correlations could be made between electrochemical parameters and actual thiourea concentrations [2].[1] T. Collet, et al., An operando ORP-EIS study of the copper reduction reaction supported by thiourea and chlorides as electrorefining additives, Electrochimica Acta (2021) 138762. [2] T. Collet, et al., The time-varying effect of thiourea on the copper electroplating process with industrial copper concentrations, Electrochimica Acta (2022) 141412. [3] Van Gheem, et al., Electrochemical impedance spectroscopy in the presence of non-linear distortions and non-stationary behaviour part i: Theory and validation, Electrochimica Acta 49 (2004) 4753–4762. [4] N. Hallemans, et al., Detection, Classification, and Quantification of Nonlinear Distortions in Time-Varying Frequency Response Function Measurements, IEEE Transactions on Instrumentation and Measurement, 70 (2021) 6500814. [5] N. Hallemans, et al., Best Linear Time-Varying Approximation of a General Class of Nonlinear Time-Varying Systems, IEEE Transactions on Instrumentation and Measurement, 70 (2021) 6503814.

Characterization of damping in 3D metal printed gear body using parameter optimization

With the rapid development of the global economy and the widespread use of high-speed machinery, vibration and noise pollution is becoming increasingly serious. The increased energy costs, environmental pollution, and carbon emissions have prioritized sustainable development for industry. As an important link of mechanical transmission, the gear transmission vibration and noise adversely affect the physical and mental health of operators and interfere with the normal use of machinery. This paper proposes a new metal 3D printing-made vibration-damping lightweight gear model. The solid gear web is replaced with a lightening hole structure that is expected to ensure rigidity and torsional compliance while controlling the damping effects of the gear web structure. Gears were manufactured from an additive manufacturing material using a metal 3D printing technique. This work advanced an experimental analysis of the dissipation properties of metal printed gear exploiting vibration tests. A gear frequency-sweeping excitation test bench was designed and developed to simulate in-plane excitation to produce a circumferential torsional mode of the specimen. Circumference damping estimates are guided by executing vibration exciter excitation on the setup. The half-power bandwidth and modal fitting methods were arranged and compared, relying on the measured frequency response function (FRF) single-degree-of-freedom (SDOF) approximation.

A single degree of freedom model for cracked beam

This paper presents a simplified model of cracked beam by single-degree-of-freedom system. Equivalence between the beam and SDOF models means that they have the same fundamental natural frequency and similar frequency response functions (FRFs). Similarity of FRFs is checked by using the frequency-domain assurance criterion acknowledged herein as spectral similarity index (SSI). Finally, FRFs of both the cracked beam and its simplified SDOF model have been examined versus crack location and depth using the so-called spectral damage index (SDI). Numerical results show that SDI is significantly sensitive to crack and could be used as a novel indicator for crack detection in beam by measurements of frequency response functions.

IDENTIFICATION OF THE NATURAL FREQUENCY OF THE OFFSHORE TRUSS STRUCTURE FROM MULTIPLE SIMULATED MEASURED DATA

This article presents identification methods of the natural frequency of structures from single or multiple measurements in the frequency domain and its application to identify the natural frequencies of the offshore truss structure. The simulated measurements of structural vibrations in the time domain are determined by analyzing the finite element model of the offshore truss structure subjected to random dynamic loads using SAP2000 software. The frequency domain measurements are obtained by the fast Fourier transform of time domain measurements using MATLAB software. The identification method from the multiple combined frequency response function measurements can estimate more natural frequencies than using a single measurement. A study of the considered frequency range was also performed showing the accuracy of the identification methods compared with the finite element model. By subdividing the considered frequency range, it is possible to improve the accuracy of the obtained natural frequencies.

Dynamic modelling and natural characteristics analysis of fluid conveying pipeline with connecting hose

As an important connecting component, the hoses transport fluid from pump to pipeline. However, the modeling of connecting hose has been rarely incorporated in the open research of pipeline modeling. To study the natural characteristics of fluid conveying pipeline and the effect of the connecting hose, a new dynamic model of pipeline with connecting hose is established by the finite element method. The measured support stiffness of clamp is introduced, and the equivalent boundary stiffness of connecting hose is identified based on the genetic algorithm (GA) and the measured frequency response function. The proposed model is verified by numerical examples and experimental results. Besides, the mixed finite element method (using shell element and fluid element) and the transfer matrix method are used to verify the natural characteristics of the proposed model under different fluid excitation. Moreover, the effect of fluid pressure on natural frequency of pipeline is analyzed. The results show the proposed model has higher precision than other models, and the average error is 0.55%. When the pressure increases from 0 MPa to 15 MPa, the natural frequency of pipeline decreases and the decline rate decreases with the increase of modal order. This paper provides the theoretical and experimental basis for the practical engineering requirements, and the proposed model can be more comprehensive to study the natural characteristics in fluid conveying pipeline.

Damage detection, quantification, and localization for resonant metamaterials using physics-based and data-driven methods

Resonant metamaterials have attracted significant research interest in mechanical and acoustic engineering with applications in the fields of sound and vibration control thanks to their integrated tuned mass dampers. One prevailing issue regarding industrial application of such structures is the high probability of local damage for their resonating parts. Accurate and efficient health state estimation methods for resonant metamaterials are therefore urgently required. In particular, the quantification and localization of damaged resonators represent key pieces of information for the operator of a structural asset. This work presents for the first time an investigation into quantifying and identifying damaged oscillators in a resonant metamaterial based on the measured frequency response function (FRF) data. Both data-driven and physics-based methods are implemented and corresponding results are exhibited. Manufacturing-induced structural uncertainty is quantified through physical measurements and taken into account in this work. It is demonstrated that such uncertainty may have a rather significant impact on the response of 3D printed resonant metamaterials, leading to difficulties vis-a-vis damage quantification. The proposed theoretical developments are able to properly account for such uncertainties, providing probabilistic estimation indices for the existing damage level and location. Both simulated and experimental case studies are presented to validate the two proposed methodologies and comparisons are also exhibited and discussed.

Towards a low cost method for measuring the airborne sound insulation of partitions

BS EN ISO 10140-2 outlines a method for estimating the airborne sound insulation of a partition using adjacent rooms. In this paper, a new method is presented by which the airborne sound insulation is obtained without the need for a transmission suite. Using a stand-alone partition, a representative blocked pressure field is applied numerically to a measured frequency response function matrix characterising the partition. The incident and transmitted powers are determined from the blocked pressure and velocity field on the source and receiver sides, respectively. Results of several partitions measured using the proposed methodology will be compared against estimates obtained according to BS EN ISO 10140-2.

Novel FRF-based fast modal testing of multi-storey CLT building in operation using wirelessly synchronised data loggers

This paper presents a novel input–output frequency-response function (FRF) based field modal testing (MT) of an operational and fully occupied tallest cross-laminated timber (CLT) building in the U.K. A custom-built MT system and testing protocol were developed to facilitate exceptionally fast field testing work lasting only 10 h, including all instrumentation and field testing work.This yielded eight fundamental and higher-order modes of vibration with natural frequencies up to 12 Hz. The higher order modes are normally not possible to measure well enough using the standard output-only operational modal analysis (OMA). An FE model was developed prior to the testing to assure quality and facilitate the fast testing process. The FE model, based on the best engineering judgement, proved to be able to predict very well the key features of the test building. This includes close matching and correct clustering of the FE-calculated and MT-estimated natural frequencies, as well as a very reasonable prediction of the static stiffness at the top of the building. The in-situ measured horizontal static stiffness at the top of the CLT building is a considerable benefit of the field FRF measurements and is not possible in the standard OMA. It was shown that the preliminary best practice FE model was over-predicting the static stiffness in the two orthogonal directions by only up to 22% of the measured values.Curve-fitting of the good quality FRF data yielded damping ratio values for the higher order modes of vibration, typically above 3%. This is quite high for a full-scale multi-storey residential building.

Active vibration control for milling operations including frequency response function uncertainties

Active vibration controllers are designed to mitigate chatter vibrations and increase the productivity of machines. Such controllers, however, often do not perform well in real applications if uncertainties are present in the system. In this study, a controller design is presented for a test configuration, where the actuation is utilized by an electromagnetic actuator. The robust stability charts, which take into account the bounded uncertainties in the measured frequency response functions (FRFs), are calculated in frequency domain using the zero-order approximation method. The predictions for the experimental configuration are validated in cutting tests.

Sensitivity Analysis and Robust Assignment of Natural Frequencies for Vibrating Systems Using the Receptance Method

This paper presents a new receptance-based method for the robust assignment of natural frequencies. This method aims to address the deviation of the actually achieved natural frequencies for target natural frequencies when assigning natural frequencies, which usually arises due to uncertainties in passive structural modifications (i.e. mass and stiffness modifications). The mathematical expression is derived for the sensitivity of the target natural frequency to the uncertainties in modification parameters, which are subsequently employed to characterize the potential deviations of the target natural frequencies in the total differential form. The obtained deviation expression is integrated into the optimization calculation of the natural frequency assignment as an extra penalty term to boost the acquisition of highly robust modification parameters. The proposed robust assignment method, as a non-probabilistic technique, can be employed without any knowledge of the probabilistic distribution of uncertainty in modification parameters. Moreover, it uses only the measured frequency response functions (FRFs), preserving the advantage of the receptance method not needing a numerical model. Two numerical examples and a comparison with a typical eigenstructure assignment method (reported in the literature) demonstrate that the proposed method can provide highly robust modification parameter solutions. The application of the proposed method to the natural frequency assignment of a laboratory water-filled pipeline system gives experimental evidence of its effectiveness.

An experimental investigation on the effectiveness of damping changes for damage detection in a Fibre Reinforced Plastic Plate

Fibre reinforced plastics (FRP) are extensively used because of their high specific strength and stiffness. However, throughout their service life, such materials are susceptible to damages, which when accumulated may result in catastrophic failure. Studies on effects of stiffness loss due to damage has been exercised by quite a large number of researchers but very less investigators have involved the variations in dissipative behaviour in combination with such stiffness loss. However, damage in these structures not only causes local reduction of stiffness but is also observed with increased dissipation behaviour. One of the most convenient ways to carry out health monitoring exercise to detect damages is to conduct systematic vibration testing. The present study investigates the likely changes in natural frequencies and mode shapes of a rectangular FRP composite plate along with damping factors due to the induced damage. The FRP plate considered has been modal tested and dynamic responses i.e., natural frequencies, mode shapes and modal damping factors are derived through curve-fitting technique from the frequency response function measurements. In this study, changes in dynamic responses due to a locally induced damage in the FRP plate is studied. For this, in order to maximize the effects of local reduction in the stiffness on the modal parameters, a partial-cut is provided in a localised region of the plate in the first damage case. In the second damage scenario, the partially-cut area has been filled with epoxy resin matrix to create a region with localised change in material properties and with limited stiffness loss. Damping changes has been observed to be significant and more sensitive than variations in natural frequencies and mode shapes. The study suggests that damping parameters along with stiffness changes together can be put into practice to develop an effective vibration-based health monitoring scheme

Experimental acoustic modal analysis of a tenor saxophone.

This paper presents an application of the Experimental Acoustic Modal Analysis (AMA) on a vintage 10 M Conn tenor saxophone. This technique originates from the traditional Modal Analysis which is commonly adopted to determine the dynamic behaviour of solid structures. The methodology is based on the measurement of Frequency Response Functions (FRFs) as a ratio of the acoustic pressure, measured by means of a set of microphones positioned along the saxophone body, and the volume velocity produced by an acoustic source and measured at the instrument input. The microphones are housed on the stripped saxophone keys by means of tailored three-dimensional printed adapters. The AMA makes use of the FRFs to extract modal parameters, such as resonance frequencies, loss factors, and mode shapes. These parameters pertain to the cavity modes of the saxophone passive resonator. The analysis has been performed for three different notes (B ♭, B, and C) and for two registers of the instrument in order to show the potential of the technique. Moreover, the influence of the mouthpiece volume on the cavity modes has been shown. The information obtained by AMA can find useful application in the validation of analytical or numerical models of this kind of musical instruments.

Scavenging energy from aeroelastic vibrations for hybrid stall control in a fixed-wing micro aerial vehicle

Scavenging energy from aeroelastic vibrations was considered for a self-powered hybrid passive-active stall control system intended to improve the aerodynamic performance of fixed-wing micro aerial vehicles without exhausting available batteries. It was found that the passive component of the system generates intense streamwise vortices, which give rise to vortex-induced vibrations. Measured frequency response functions indicated accelerations in a wing prototype up to 0.1 g at relatively low frequencies, when it was operated at simulated flight conditions in a wind tunnel. Aiming to use this resource for additional power, a piezoelectric energy harvesting device was installed inside the wing and tuned for resonant response. Two electromechanical modeling approaches for the piezoelectric harvester were investigated, namely, an analytical model and finite elements simulations. A comparison with experimental results has shown that the latter approach is better equipped to deal with advanced designs, yielding accurate predictions in the present study. Extracted power and generated voltage were quantified as a function of the electric loading resistance. The reported data demonstrated that the proof of concept was achieved, so that a lightweight, low-consumption actuator for the active component of the stall control system can be powered by the energy of structural vibrations.