Low Frequency Structural Vibration Research Articles

Low-frequency chatter suppression in robotic milling using Magnetorheological Joint Damper (MRJD)

Low-frequency structural vibrations caused by poor rigidity are one of the main obstacles limiting the machining efficiency of robotic milling. Existing vibration suppression strategies primarily focus on passive vibration absorption at the robotic end and feedback control at the joint motor. Although these strategies have a certain vibration suppression effect, the limitations of robotic flexibility and the extremely limited applicable speed range remain to be overcome. In this study, a Magnetorheological Joint Damper (MRJD) is developed. The joint-mounted feature ensures machining flexibility of the robot, and the millisecond response time of the Magnetorheological Fluid (MRF) ensures a large effective spindle speed range. More importantly, the evolution law of the damping performance of MRJD was revealed based on a low-frequency chatter mechanism, which guarantees the application of MRJD in robotic milling machining. To analyze the influence of the robotic joint angle on the suppression effect of the MRJD, the joint braking coefficient and end braking coefficient were proposed. Parallel coordinate plots were used to visualize the joint range with the optimal vibration suppression effect. Finally, a combination of different postures and cutting parameters was used to verify the vibration suppression effect and feasibility of the joint angle optimization. The experimental results show that the MRJD, which directly improves the joint vibration resistance, can effectively suppress the low-frequency vibration of robotic milling under a variety of cutting conditions.

Application of multiple dynamic vibration absorbers in reducing low-frequency vibration of a floor-like lightweight joist structure: Comparison of experimental and computational results

Typical solutions to reduce excessive floor vibration and radiated sound to the room below include increasing floor mass, stiffening floor structure, and adding a floating floor in the source room. However, these methods may not be effective for lightweight floors at low frequencies. The use of dynamic vibration absorbers (DVAs) to reduce low-frequency structural vibration has attracted the attention of researchers in recent years. In this paper, an analytical model is proposed to study the effect of DVAs on the vibration of a lightweight joist structure by combining the bending modes of the plate with the bending and torsional modes of the beams. The analytical model is compared with the results from finite element models and measurements on a scaled wooden joist floor structure with fabricated spring-mass-type DVAs. A good consistency between the analytical results with results from the latter two are found in terms of the structural vibration and the DVAs’ effects.

Bandgap formation and low-frequency structural vibration suppression for stiffened plate-type metastructure with general boundary conditions

Metastructures with unique mechanical properties have shown attractive potential application in vibration and noise reduction. Typically, most of the metastructures deal with the vibration bandgap properties of infinite structures without considering specific boundary condition and dynamic behaviors, which cannot be directly applied to the engineering structures. In this research, we design a Stiffened Plate-type Metastructure (SPM) composed of a plate with periodic stiffeners and cantilever beam-type resonators subjected to general boundary conditions for low-frequency vibration suppression. The effects of boundary conditions and the number and orientation of the stiffeners on Locally Resonant (LR) type bandgap properties in SPM are further investigated. An analytical modeling framework is developed to predict the bandgap formations and vibration behaviors of SPMs in finite-size configuration. The governing equations of the SPM reinforced by various arrangements of stiffeners are derived based on the first-order shear deformation theory and Hamilton’s principle, and a Fourier series combined with auxiliary functions is employed to satisfy the arbitrary boundary conditions. Finite element analysis and experimental investigations of vibration behaviors for the SPM are carried out to validate the accuracy and reliability of the present analytical model. For practical designs of the SPMs with specific boundary conditions, it is found that there exist optimal numbers of stiffeners and resonators which can produce the significant LR-type bandgap behaviors. Furthermore, various arrangements of stiffeners and resonators are explored for different boundary conditions by breaking the requirement of spatially periodicity. It is shown that for the designed SPM, the vibration modes of its host structure should be considered to widen the frequency range in which the resonators transfer and store energy, and hence improve the performance of low-frequency vibration suppression. The present work can provide a significant theoretical guidance for the engineering application of metamaterial stiffened structures.

3D printing of fiber composite sandwich metamaterial with spiral resonators for attenuation of low-frequency structural vibration

This paper proposes a fiber composite sandwich metamaterial as a stiff structure with a low-frequency band gap. The proposed structure is a locally resonant metamaterial that inhibits the propagation of elastic waves with spiral resonators. The dispersion curves and stiffness of the metamaterial were obtained using the finite element method. The numerical analysis results indicated that the proposed sandwich structure contributes not only to the improvement of the specific stiffness but also to the widening of the band gap. From observations of the band gap boundary modes, an analytical model was developed to derive the lower and upper bound frequencies of the band gap. A metamaterial sample manufactured by 3D printing exhibited a frequency range with low vibration transmissibility, which agreed with the results of the frequency response analysis. The specific bending stiffness and band gap center frequency of the proposed metamaterial were compared with those of existing plate-type metamaterials.

A Ternary Seismic Metamaterial for Low Frequency Vibration Attenuation.

Structural vibration induced by low frequency elastic waves presents a great threat to infrastructure such as buildings, bridges, and nuclear structures. In order to reduce the damage of low frequency structural vibration, researchers proposed the structure of seismic metamaterial, which can be used to block the propagation of low frequency elastic wave by adjusting the frequency range of elastic wave propagation. In this study, based on the concept of phononic crystal, a ternary seismic metamaterial is proposed to attenuate low frequency vibration by generating band gaps. The proposed metamaterial structure is periodically arranged by cube units, which consist of rubber coating, steel scatter, and soft matrix (like soil). The finite element analysis shows that the proposed metamaterial structure has a low frequency band gap with 8.5 Hz bandwidth in the range of 0–20 Hz, which demonstrates that the metamaterial can block the elastic waves propagation in a fairly wide frequency range within 0–20 Hz. The frequency response analysis demonstrates that the proposed metamaterial can effectively attenuate the low frequency vibration. A simplified equivalent mass–spring model is further proposed to analyze the band gap range which agrees well with the finite element results. This model provides a more convenient method to calculate the band gap range. Combining the proposed equivalent mass–spring model with finite element analysis, the effect of material parameters and geometric parameters on the band gap characteristic is investigated. This study can provide new insights for low frequency vibration attenuation.

Autonomous Assessment of Delamination Using Scarce Raw Structural Vibration and Transfer Learning.

Deep learning has helped achieve breakthroughs in a variety of applications; however, the lack of data from faulty states hinders the development of effective and robust diagnostic strategies using deep learning models. This work introduces a transfer learning framework for the autonomous detection, isolation, and quantification of delamination in laminated composites based on scarce low-frequency structural vibration data. Limited response data from an electromechanically coupled simulation model and from experimental testing of laminated composite coupons were encoded into high-resolution time-frequency images using SynchroExtracting Transforms (SETs). The simulated and experimental data were processed through different layers of pretrained deep learning models based on AlexNet, GoogleNet, SqueezeNet, ResNet-18, and VGG-16 to extract low- and high-level autonomous features. The support vector machine (SVM) machine learning algorithm was employed to assess how the identified autonomous features were able to assist in the detection, isolation, and quantification of delamination in laminated composites. The results obtained using these autonomous features were also compared with those obtained using handcrafted statistical features. The obtained results are encouraging and provide a new direction that will allow us to progress in the autonomous damage assessment of laminated composites despite being limited to using raw scarce structural vibration data.

Experimental study of the effect of the boundary conditions of fractured bone

Reliable fracture diagnosis monitoring and analyzing low-frequency transverse vibration data can be achieved through an in-depth understanding of the physical interactions between wave propagation and boundary conditions. The present study aims to investigate the effects of the boundary conditions on the low-frequency structural vibrations of bones. Time–frequency domain analysis of transverse vibration signals depending on the boundary conditions of bones is analyzed and investigated. These studies reveal that the responses of fractured or non-fractured bones are different and influenced by the displacement and force boundary conditions. These relationships can be considered in the development of a smart fracture diagnosis system considering the posture and boundary condition. To validate the present observations, the experiments with artificial specimens and cadaver are carried.

Persistent Protein Motions in a Rugged Energy Landscape Revealed by Normal Mode Ensemble Analysis.

Proteins are allosteric machines that couple motions at distinct, often distant, sites to control biological function. Low-frequency structural vibrations are a mechanism of this long-distance connection and are often used computationally to predict correlations, but experimentally identifying the vibrations associated with specific motions has proved challenging. Spectroscopy is an ideal tool to explore these excitations, but measurements have been largely unable to identify important frequency bands. The result is at odds with some previous calculations and raises the question what methods could successfully characterize protein structural vibrations. Here we show the lack of spectral structure arises in part from the variations in protein structure as the protein samples the energy landscape. However, by averaging over the energy landscape as sampled using an aggregate 18.5 μs of all-atom molecular dynamics simulation of hen egg white lysozyme and normal-mode analyses, we find vibrations with large overlap with functional displacements are surprisingly concentrated in narrow frequency bands. These bands are not apparent in either the ensemble averaged vibrational density of states or isotropic absorption. However, in the case of the ensemble averaged anisotropic absorption, there is persistent spectral structure and overlap between this structure and the functional displacement frequency bands. We systematically lay out heuristics for calculating the spectra robustly, including the need for statistical sampling of the protein and inclusion of adequate water in the spectral calculation. The results show the congested spectrum of these complex molecules obscures important frequency bands associated with function and reveal a method to overcome this congestion by combining structurally sensitive spectroscopy with robust normal mode ensemble analysis.

A magnetic levitation-based tristable hybrid energy harvester for scavenging energy from low-frequency structural vibration

A magnetic levitation-based hybrid energy harvester is proposed in this work. The new harvester consists of a tri-stable nonlinearity-enhanced mechanism that not only enhances the energy transfer throughresonant inter-well oscillations, and also offers a wider bandwidth under low-frequency excitation levels. This integrated unit that combines a slider-driven electromagnetic generator (EMG) and a sliding-mode triboelectric nanogenerator (TENG) can harness more energy from vibration motions, thus resulting in a higher power density. In this study, both theoretical modelling and experimental studies are presented to investigate the dynamic characterization of the mechanical design, in which only four outer magnets are deployed on a plane to establish a triple-well nonlinear behaviour. Magnetic forces of this harvester are calculated by the magnetizing current method and the formation of tri-stable potential wells in the dynamic system is verified by a bifurcation analysis. In addition, a prototype of the harvester is fabricated and tested by an electrodynamic shaker system. The results show that the prototype exhibits a frequency bandwidth of 3–8 Hz and generates an output power of 6.9 mWand 6.44 mW in both horizontal and vertical orientations at a frequency of 8 Hz and 1 g acceleration, respectively. A performance study is also conducted to show that the proposed technique can produce sufficient power output as compared to other electromagnetic-triboelectric devices.

Classification and prediction of multidamages in smart composite laminates using discriminant analysis

A supervised machine learning framework is proposed for local assessments of delamination and transducer debonding in smart composite laminates while using their low-frequency structural vibrations. Load independent discriminative features were identified through a system identification algorithm and several supervised machine learning algorithms were employed to distinguish between the healthy and damaged structures. Linear discriminant analysis was shown to outperform other classifiers. The issue of overfitting of the training data was addressed by evaluating the predictive performance of the classifier on independent test cases. The proposed approach could help provide insightful guidelines for the assessment of multidamages in smart composite laminates.

Effects of high-amplitude low-frequency structural vibrations and machinery sound waves on ultrasonic guided wave propagation for health monitoring of composite aircraft primary structures

A reliable damage diagnostic by ultrasonic guided wave (GW) based structural health monitoring (SHM) can only be achieved if the physical interactions between wave propagation, the SHM system and environmental factors are fully understood. The purpose of this research was to gain knowledge about the effects of high-amplitude low-frequency structural vibrations (HA-LFV) and audible sound waves (SW) on ultrasonic GW propagation. Measurements were performed on a stiffened panel of a full-scale composite torsion box containing barely visible impact damage. Time-domain analysis of the filtered GW signals revealed that the main effect of HA-LFV was the presence of coherent noise. This was interpreted as the consequence of superposition of multiple dispersive wave groups produced by mode conversion at the moment of reflection on the corrugated panel surfaces during propagation. It was also observed that the coherent noise amplitude depends on the amplitude of the HA-LFV, and on the ratio between the HA-LFV frequency and the ultrasonic excitation frequency. These relationships can potentially be explored for the development of a HA-LFV compensation mechanism to enable in-service GW based damage diagnostics. In contrast, GW signals in the cases with audible SW present were almost unaffected. It was concluded that there is strong evidence supporting the hypothesis that ultrasonic GW propagation with HA-LFV effects can be analysed under the assumption of a permanently corrugated structure.

Experimental studies in finite element model updating of vibro-acoustic cavities using coupled modal data and FRFs

The NVH design of cavities in aircraft, cars and other transportation equipment are mainly based on use of vibro-acoustic FE models to analyze low frequency structural vibration and interior noise. In order to improve the accuracy and reliability of these vibro-acoustic models, uncertainties associated with modeling of boundary conditions, joints, damping and acoustic absorption properties of cavity surfaces in acoustic domain, must be taken into account. Finite element (FE) model updating is now recognized as an effective approach to reduce modeling inaccuracies present in an FE model. This paper presents experimental studies in updating of FE model of vibro-acoustic cavity. Two experimental studies are presented. The first experimental study is about updating of structural FE model of the cavity incorporating acoustic loading using modal data based on an inverse eigen-sensitivity approach. The second study involves updating of structural and acoustic parameters of the vibro-acoustic model using frequency response functions based on a constrained optimization based approach. Thus, FE model and experimental coupled modal data and FRF data are integrated to obtain a more accurate vibro-acoustic model. Experimental example of a 3D rectangular-box cavity with a flexible plate is presented. The studies demonstrate that the improvement of the vibro-acoustic FE models through FE model updating can be an effective approach to obtain more accurate vibro-acoustic predictions.

Structural vibration-based classification and prediction of delamination in smart composite laminates using deep learning neural network

This paper proposes a Convolutional Neural Network (CNN) based approach for the classification and prediction of various types of in-plane and through-the-thickness delamination in smart composite laminates using low-frequency structural vibration outputs. An electromechanically coupled mathematical model is developed for the healthy and delaminated smart composite laminates, and their structural vibration responses are obtained in the time domain. Short Time Fourier Transform (STFT) is employed to transform the transient responses into two-dimensional spectral frame representation. A convolutional neural network is incorporated to distinguish between the damaged and undamaged states, as well as various types of damage of the laminated composites, by automatically extracting discriminative features from the vibration-based spectrograms. The CNN showed a classification accuracy of 90.1% on one healthy and 12 delaminated cases. The study of the confusion matrix of CNN provided further insights into the physics of the problem. The predictive performance of a pre-trained CNN classifier was also evaluated on unseen cases of delamination, and physically consistent results were obtained.

Multi-channel adaptive active vibration control of piezoelectric smart plate with online secondary path modelling using PZT patches

Abstract Reducing the vibration of smart structures based on adaptive active vibration control (AAVC) has been extensively studied in recent years, because it is a light weight and effective method for reducing low-frequency structural vibrations. The multi-channel AAVC methodology based on the filtered-X least mean square (FXLMS) algorithm is widely implemented in active control applications owing to its self-adjustment ability to adapt to dynamically varying structures. In this paper, a new multi-channel FXLMS with online secondary path modelling (SPM) is designed based on the auxiliary random noise technique. Through a defined indirect error signal, the proposed variable step-size (VSS) strategies can ensure that every online SPM filter and every active control filter have their own exclusive step size to update the coefficients. Moreover, the proposed auxiliary noise power scheduling (ANPS) strategy can ensure that the variation rules of auxiliary noise power applied to different secondary paths are different. A complete multi-channel AAVC real-time experimental system based on NI compact RIO is set up to conduct the experimental investigation. A series of AAVC control experiments on a piezoelectric smart cantilever plate with PZT sensors and actuators are conducted to demonstrate the validity and efficiency of the proposed method. The experimental results show that the vibration of the smart cantilever plate could be effectively attenuated with a high convergence rate. The proposed methodology has an important advantage in applications where active vibration control of piezoelectric smart structures is required.

Dispersed Sensing Networks in Nano-Engineered Polymer Composites: From Static Strain Measurement to Ultrasonic Wave Acquisition.

Self-sensing capability of composite materials has been the core of intensive research over the years and particularly boosted up by the recent quantum leap in nanotechnology. The capacity of most existing self-sensing approaches is restricted to static strains or low-frequency structural vibration. In this study, a new breed of functionalized epoxy-based composites is developed and fabricated, with a graphene nanoparticle-enriched, dispersed sensing network, whereby to self-perceive broadband elastic disturbance from static strains, through low-frequency vibration to guided waves in an ultrasonic regime. Owing to the dispersed and networked sensing capability, signals can be captured at any desired part of the composites. Experimental validation has demonstrated that the functionalized composites can self-sense strains, outperforming conventional metal foil strain sensors with a significantly enhanced gauge factor and a much broader response bandwidth. Precise and fast self-response of the composites to broadband ultrasonic signals (up to 440 kHz) has revealed that the composite structure itself can serve as ultrasound sensors, comparable to piezoceramic sensors in performance, whereas avoiding the use of bulky cables and wires as used in a piezoceramic sensor network. This study has spotlighted promising potentials of the developed approach to functionalize conventional composites with a self-sensing capability of high-sensitivity yet minimized intrusion to original structures.

Underwater pipeline impact localization using piezoceramic transducers

Reports indicated that impact events accounted for 47% of offshore pipeline failures, which calls for impact detection and localization for subsea pipelines. In this paper, an innovative method for rapid localization of impacts on underwater pipelines utilizing a novel determination technique for both arrival-time and group velocity (ATGV) of ultrasonic guided waves with lead zirconate titanate (PZT) transducers is described. PZT transducers mounted on the outer surface of a model pipeline were utilized to measure ultrasonic guided waves generated by impact events. Based on the signals from PZT sensors, the ATGV technique integrates wavelet decomposition, Hilbert transform and statistical analysis to pinpoint the arrival-time of the designated ultrasonic guided waves with a specific group velocity. Experimental results have verified the effectiveness and the localization accuracy for eight impact points along a model underwater pipeline. All estimations errors were small and were comparable with the wavelength of the designated ultrasonic guided waves. Furthermore, the method is robust against the low frequency structural vibration introduced by other external forces.

Broadband electrostatic device for power harvesting

This paper introduces a prototype energy harvester device with integrated MEMS capacitive plate and two impact oscillators for transferring energy from low frequency structural vibration with varying mechanical spectra to a vibration of a high resonance frequency cantilever. The use of the two impact oscillators not only harvested energy at low frequencies but also had demonstrated exceptionally sufficient and optimum dynamic responses to a broad frequency bandwidth between 13 Hz and 39 Hz, the bandwidth covering wide range of residual vibrations in structures and systems, without reduction in output power. The device was designed with a MEMS capacitor fixed at the free end of an aluminium cantilever clamped at one side, with a high resonance frequency of 605 Hz matched with the single-cavity capacitor, and two cantilevers made of Al sheet with low resonance frequencies of 18 Hz and 25 Hz. The results clearly demonstrates the device's ability for frequency up- conversion and harvesting power on a wide range from 13 Hz to 39 Hz at 1g excitation.

Wave propagation in metamaterial plates with periodic local resonances

Vibration characteristics of metamaterial plates manufactured from assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures has been shown to exhibit a unique stop band behavior extending to very low frequency ranges. A finite element model (FEM) is developed to predict the modal and frequency response of different configurations of the metamaterial plates. A Floquet–Bloch approach is exercised to demonstrate the stop band and mechanical filtering capabilities over a broad range of frequencies. The predictions of these theoretical models are validated experimentally when the plates are excited by a mechanical shaker over a frequency range of up to 5kHz. It is observed that there is a good agreement between the theoretical predictions and the experimental results for different configurations of the metamaterial plate. The obtained results emphasize the potential of such plates to provide significant vibration attenuation and exhibit stop bands extending to low frequencies. Such characteristics indicate that metamaterial plates are more effective in attenuating and filtering low frequency structural vibrations than plain periodic plates of similar size and weight.

The effect of modelling acoustic media in cavities of lightweight buildings on the transmission of structural vibrations

Determining the dynamic behaviour of lightweight buildings by means of finite element analyses requires models representing the geometry involved in great detail, resulting in systems having many millions of degrees of freedom. It is, therefore, important to avoid unnecessarily detailed models by carefully considering what is essential to include in the models and the level of details required for describing the phenomena of interest accurately. In the study presented here, it was investigated whether or not air and insulation in cavities of multi-storey wood buildings affect the transmission of low-frequency structural vibrations. It was concluded, by means of numerical studies, that including air and insulation in cavities, modelled as acoustic media, affects the transmission from a floor to the underlying ceiling and surrounding walls.

Crack detection technique for operating wind turbine blades using Vibro-Acoustic Modulation

This article presents a new technique for identifying cracks in wind turbine blades undergoing operational loads using the Vibro-Acoustic Modulation technique. Vibro-Acoustic Modulation utilizes a low-frequency pumping excitation signal in conjunction with a high-frequency probing excitation signal to create the modulation that is used to identify cracks. Wind turbines provide the ideal conditions in which Vibro-Acoustic Modulation can be utilized because wind turbines experience large low-frequency structural vibrations during operation which can serve as the low-frequency pumping excitation signal. In this article, the theory for the vibro-acoustic technique is described, and the proposed crack detection technique is demonstrated with Vibro-Acoustic Modulation experiments performed on a small Whisper 100 wind turbine in operation. The experimental results are also compared with two other conventional vibro-acoustic techniques in order to validate the new technique. Finally, a computational study is demonstrated for choosing a proper probing signal with a finite element model of the cracked blade to maximize the sensitivity of the technique for detecting cracks.