Frequency Damping Research Articles

A novel locally resonance metamaterial cylindrical shell with tower-shaped lattice for broadband vibration suppression

Vibration issues in cylindrical shells are prevalent in engineering applications and can significantly impact the operational performance of systems. To address these challenges, this paper designs a novel local resonance tower structure, and establishes an analytical model to investigate vibration characteristics of the metamaterial cylindrical shell. Based on the model, a gradient design strategy is proposed to improve vibration suppression properties over a wide frequency range. Firstly, the governing equations of the cylindrical shell are derived and the dispersion analysis is conducted to predict the bandgap boundaries using the extended plane wave expansion (EPWE) method. Then, for a finite-period metamaterial cylindrical shell with specific boundary conditions, the frequency response of the structure is obtained by finite element calculations to show the bandgap behavior. The results of these two methods are basically the same. In addition, the effects of frequency spacing, damping and array period on the vibration characteristics are considered comprehensively. The results show that a wider and more stable attenuation range can be obtained by reasonably adjusting these three parameters. Finally, the comparison between experimental and numerical calculations verify that the tower structure is effective, and that the proposed design strategy can broaden the vibration attenuation region.

Damping performance of finite microperforated plates using multi-size and spatial distributions of perforations

In the context of structural dynamics, recent works by the authors showed that microperforations can be used to mitigate vibration. Microperforated plates (MPP) have been shown to exhibit substantial added damping arising from fluid-structure interactions and visco-thermal effects in the boundary layers of the perforations during relative motion between the solid and the fluid contained in the perforations. The added damping reaches a maximum for a characteristic frequency, depending only on the diameter of the perforation. Choosing the diameter of the perforation so that the characteristic frequency coincides with a given natural frequency of the plate reduces the contribution of the associated plate mode. However, the MPP studied had a single set of perforations homogeneously distributed throughout the structure. In this work, it is proposed to extend the added damping to several modes of the plate by using MPP with multi-size perforations and an optimized spatial distribution of these perforations. As an extension of the previous vibratory model of the authors, the dynamics of MPP with perforations of multiple sizes based on a homogenization model is established. In addition, the effect of the spatial distribution of perforations on the additional damping is captured by including a spatially dependent perforation ratio in the model. Experimental measurements on MPP validate the proposed analytical models. The results show that (i) MPP with multiple-size perforations feature a wider effective damping frequency band, and (ii) the added damping is accentuated when the perforations are distributed in the zone of the antinodes of the considered modes. Thus, by combining the two effects, it is possible to achieve MPP that effectively reduce the vibratory responses on several modes.

Experimental validation of a short-term damping estimation method for wind turbines in nonstationary operating conditions

Abstract. Modal properties and especially damping of operational wind turbines can vary over short time periods as a consequence of environmental and operational variability. This study seeks to experimentally test and validate a recently proposed method for short-term damping and natural frequency estimation of structures under the influence of varying environmental and operational conditions from measured vibration responses. The method is based on Gaussian process time-dependent auto-regressive moving average (GP-TARMA) modelling and is tested via two applications: a laboratory three-storey shear frame structure with controllable, time-varying damping and a flutter test of a full-scale 7 MW wind turbine prototype, in which two edgewise modes become unstable. Damping estimates for the shear frame compare well with estimates obtained with stochastic subspace identification (SSI) and standard impact hammer tests. The efficacy of the GP-TARMA approach for short-term damping estimation is illustrated through comparison to short-term SSI estimates. For the full-scale flutter test, GP-TARMA model residuals imply that the model cannot be expected to be entirely accurate. However, the damping estimates are physically meaningful and compare well with a previous study. The study shows that the GP-TARMA approach is an effective method for short-term damping estimation from vibration response measurements, given that there are enough training data and that there is a representative model structure.

An energy-efficient GMRES–multigrid solver for space-time finite element computation of dynamic poroelasticity

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver’s energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware.

Investigation of a cutting state-independent method for identifying in-process frequency response functions of the micro milling system

Conveniently obtaining the in-process frequency response functions (FRFs) of micro milling tool is a very difficult task due to the small diameter. This article presents a method to identify the in-process FRFs of micro milling tool based on actual cutting tests, which can be at either stable or chatter cutting state. According to mode superposition principle, the in-process FRFs are predicted by integrating the mode shape with the pole, which includes damping ratio and natural frequency. The in-process mode shape of tool is modeled as being consistent with that corresponding to static state, and thus, it is calculated from the tool’s static state by combining receptance coupling substructure analysis (RCSA) with Timoshenko beam theory. The poles of in-process FRFs are acquired by modal analysis of the response signals from actual micro milling tests. To do this, cutting forces are used as excitation signals, and the velocities of tool are selected as response signals and they are measured from actual micro milling tests. With the aid of editing cepstrum and hampel outlier processing methods, a filtering method is established to remove the harmonic and useless chatter components involved in the response signals. As a result, the finally obtained FRFs are not influenced by the noises in the measured response signals, and the effectiveness of this method is verified by a series of modal tests and micro milling tests.

Variable Natural Frequency Damper for Minimizing Response of Offshore Wind Turbine: Effect on Dynamic Response According to Inner Water Level

Offshore wind turbines (OWTs) are exposed to cyclic loads resulting from wind, waves, and rotor rotation. These loads can induce resonance, thereby significantly increasing the amplitude of the structure and accelerating the accumulation of fatigue damage. Particularly, wave loads can induce the first mode of large turbines. While many studies have been conducted to suppress OWT vibrations due to external loads, research on variable natural frequency damper (VNFD), which control vibrations through changes in the natural frequency by adjusting the inner water level of the structure, is still in its infancy. Herein, the performance of a VNFD in controlling the vibration of monopile-type OWTs is analyzed by focusing on cyclic environmental loads. To analyze the amplitude minimization achieved using a VNFD, wave loads with the same period as that of the structure’s natural frequency were generated, and the structural response resulting from changes in the inner water level were analyzed. As a result, the peak displacement at the top of the tower decreased by 5.8% and 34% at the water depths of 20 m and 50 m, respectively. In terms of the peak intensity determined through Fast Fourier Transform of the displacement response, reductions of 33% and 65% were confirmed at the depths of 20 m and 50 m, respectively.

Unmanned Surface Vehicle Thruster Fault Diagnosis via Vibration Signal Wavelet Transform and Vision Transformer under Varying Rotational Speed Conditions.

Among unmanned surface vehicle (USV) components, underwater thrusters are pivotal in their mission execution integrity. Yet, these thrusters directly interact with marine environments, making them perpetually susceptible to malfunctions. To diagnose thruster faults, a non-invasive and cost-effective vibration-based methodology that does not require altering existing systems is employed. However, the vibration data collected within the hull is influenced by propeller-fluid interactions, hull damping, and structural resonant frequencies, resulting in noise and unpredictability. Furthermore, to differentiate faults not only at fixed rotational speeds but also over the entire range of a thruster's rotational speeds, traditional frequency analysis based on the Fourier transform cannot be utilized. Hence, Continuous Wavelet Transform (CWT), known for attributions encapsulating physical characteristics in both time-frequency domain nuances, was applied to address these complications and transform vibration data into a scalogram. CWT results are diagnosed using a Vision Transformer (ViT) classifier known for its global context awareness in image processing. The effectiveness of this diagnosis approach was verified through experiments using a USV designed for field experiments. Seven cases with different fault types and severity were diagnosed and yielded average accuracy of 0.9855 and 0.9908 at different vibration points, respectively.

Study on Nonlinear Dynamic Characteristics of RV Reducer Transmission System

Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters’ variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system.

Monitoring and quantification of ultrasonic fatigue damage in copper based on internal friction measurement

Fatigue damage in metals and alloys would reduce their strength and should be identified as early as possible. However, fatigue damage is usually difficult to detect even using advanced nondestructive testing method. Here we developed an automated damping monitoring system for ultrasonic fatigue testing based on a quantitative electromechanical impedance method. During fatigue testing, the damping and resonance frequency of the Piezo actuator/horn/specimen system is measured regularly using an impedance analyzer. When the system damping suddenly increases, it implies that fatigue damage may be generated in the specimen. Separate impedance measurements on the copper specimen in a vacuum chamber show that the internal frictions of damaged specimens are much larger than the fresh specimens. Subsequent X-Ray micro-CT scanning shows that microcracks up to 0.8 mm in length were generated in those fatigued specimens with increased internal frictions. Further tensile testing shows that compared to the fresh specimen, specimens with fatigue damage exhibits reduced tensile strength and elongation at break. Furthermore, the larger the internal friction, the smaller the remaining yield strength and a nearly linear relationship between them holds. Finally, a damage variable DQ is defined based on internal friction which can act as a measure of fatigue damage in metals.

The potential of additively manufactured porous absorbers in the design of multi-layer microperforated absorbers

Microperforated absorbers (MPA) are a well-established technology for attenuating sound in flow carrying ducts. MPAs usually consist of a microperforated panel (MPP) in combination with a cavity as back volume. The damping maxima of MPAs occur in the range of their resonant frequencies and the effect is narrowband compared to porous or fibrous absorbers, which damp broadband at high frequencies. The resonant frequencies of MPAs decrease with increasing back volume. This provides a challenge, especially in applications with limited installation space when the damping of low frequencies is required. In the literature, the combination of MPPs and porous or fibrous absorbers is reported to reduce the required back volume. Therefore, double-layer MPAs with an additively manufactured porous absorber underneath the MPP are introduced in this work. The advantage of using additively manufactured porous absorbers as an acoustic metamaterial over conventional absorbers is that the acoustic properties can be specifically adapted to the required impedance boundary conditions. The results of this work show that the additively manufactured absorbers reduce the required back volume by up to 13% compared with liners without absorber underneath the MPP. Experimental validation underscores the robustness of the chosen design approach for double-layer MPAs.

A multi-electrode electroelastomer cylindrical actuator for multimodal locomotion and its modeling

Dielectric elastomer actuators (DEAs) have received widespread attention in human-robot interaction and biomedical engineering due to their merits of large deformation, fast response, and excellent biocompatibility. The cylindrical DEA is one of the preferred structures, combining flexibility and compactness. However, the inherent non-linear behavior between the voltage and the actuator makes predicting the output performance during the design process difficult and encumbers its application, especially for multiple degrees of freedom. Herein, a dielectric elastomer spring-roll bending actuator capable of multimodal spatial locomotion using three pairs of electrodes is proposed in this paper. The electromechanical coupling behavior of the actuator under unidirectional bending deformation is described by analyzing the stress process between the spring and the film. The system's damping and excitation frequency relationship is obtained via a semi-analytical method. The experimental results validate the actuator design and show good consistency with the theoretical model. A prototype soft robot capable of running and turning is successfully demonstrated. The actuator also achieves various spatial trajectory paths via the cooperation between electrodes. Thus, the proposed scheme and modeling shed new light on the design and control of dielectric elastomers for multimodal deformation.

Auditory perception of the thickness of plates.

This study focuses on the auditory perception of plate thickness and investigates acoustic cues that evoke thickness in the context of sound synthesis. Three hypotheses are proposed and tested through a listening test, examining the influence of damping, nonlinear phenomena, and modal frequencies on the perceived thickness of sound sources. The stimuli are generated using the numerical resolution of the Föppl-von Kármán system. We confirm that increasing the overall damping leads to an increased perceived thickness. Additionally, the emergence of an energy cascade toward higher frequencies (characteristic of thin plates) for impacts of increasing intensity evokes a thinner object.

Natural Frequency and Foundation Damping of Colocated and Hybrid Systems Sharing Wind Turbine Monopiles under Operational Conditions

Natural Frequency and Foundation Damping of Colocated and Hybrid Systems Sharing Wind Turbine Monopiles under Operational Conditions

Advancing the temporal direct deconvolution method with spatial regularization

This study continues the exploration of temporal large-eddy simulation, particularly the extension of the temporal direct deconvolution method (TDDM) with a regularization term based on spatial dissipation. Furthermore, we aim to put insight stemming from previous work to test. Specifically, the hypothesis is that the temporal residual-stress leads to a reduction of the required artificial dissipation in under-resolved simulations. Moreover, this work seeks corroborate earlier discoveries with a posteriori results. We perform a numerical examination of two different spatial regularization terms in conjunction with TDDM: a spatial variant of selective frequency damping, functioning as a relaxation term that gradually drifts the velocity toward the filtered velocity, and the dynamic Smagorinsky model incorporating a prefactor. We test various cases, including the Taylor–Green vortex flow with a Reynolds number of Re = 3000, forced homogeneous isotropic turbulence with Reλ=200, turbulent channel flow at Reτ=590, and the flow over a periodic hill with Re = 10 935. Additionally, we also analyze the various dissipation contributions in TDDM as well as their interrelations. We also discuss grid artifacts and energy budget errors using these to compare the different models. Our results confirm the hypothesis that residual-stress dissipation reduces the necessary artificial dissipation. Because of the numerical ill-conditioning of deconvolution, whether temporal or spatial, there are practical limitations in the size of the filter width. Due to these limitations, the impact remains relatively minor. The a posteriori results of the new spatial regularization term show it to be effective in eliminating energy from the high wavenumber range.

Experimental Verification of Dynamic Properties of a Hollow Aluminum Beam

In this study, analytical and computational analyses are performed to determine the dynamic properties of an aluminum hollow beam and an experimental analysis is also performed. The experimental model is taken as a reference model and the computational model is updated accordingly using model updating tools. The damping behavior inherent in all physical structures is measured experimentally. According to the results of the cross-correlation modal assurance criterion, the experimental and computational results match well. The average error between the computational and experimental results for the first five damped natural frequency values is 1.5%.

Optimization and analysis of Sic reinforced copolymer blend composite structural springs

The design of lightweight leaf springs plays a crucial role in reducing fuel consumption and improving vehicle comfort by minimizing road shock transmission and vibration. Composite materials have shown great potential in significantly reducing leaf spring weight. epoxy, being a desirable thermoset polymer widely used in various applications such as electrical devices, ships and automobiles, exhibits limitations in terms of brittleness, fracture resistance and impact strength. To overcome these drawbacks while preserving its beneficial properties, epoxy can be blended with other polymers and reinforcements. In this study, polysulfide (PS) was selected as a suitable solution to enhance epoxy brittleness, offering an effective yet underutilized approach. Furthermore, the incorporation of silicon carbide (Sic), known for its superior characteristics, aimed to further enhance the mechanical properties of the epoxy-PS copolymer blend. The microstructural analysis was inspected using Fourier transform infrared. The blending and reinforcement process followed a Taguchi L8 static design to evaluate the impact of different composite blending percentages (represented as input factors) on leaf spring tensile strength, damping properties, impact resistance and hardness (represented as responses). The responses were analyzed using S/N ratios, ANOVA, main effect plots and interaction plots, while regression equations were employed to predict the responses under varying factors. The analysis demonstrated a robust model for manufacturing leaf springs. Experimental results indicated a 7.4% reduction in hardness with the addition of PS polymer. Conversely, reinforcing the epoxy-PS copolymer with 10–20% wt. of Sic resulted in a 3–5% increase in hardness. The natural frequency of the composite exhibited a gradual decrease upon the incorporation of PS and Sic. Evaluating the damping ratio revealed that the maximum value was achieved when the epoxy-PS copolymer was reinforced with 20% Sic. Additionally, while the copolymer blend displayed the greatest logarithmic decrement, epoxy exhibited the highest damping frequency.

A combined volume penalization/selective frequency damping approach for immersed boundary methods: Application to moving geometries

High-order numerical techniques and immersed boundary methods (IBMs) are gaining popularity to avoid constructing body-fitted meshes while accurately resolving complex flows on Cartesian grids. Recently, we have presented a new treatment for the immersed boundary method based on the combination of volume penalization and selective frequency damping (SFD) [J. Kou and E. Ferrer, “A combined volume penalization/selective frequency damping approach for immersed boundary methods applied to high-order schemes,” J. Comput. Phys. 472, 111678 (2023).], that offers improved accuracy for nonmoving geometries. The objective of SFD is to remove nonphysical, high-frequency oscillations inside the solid body and by doing so enhance the accuracy in the fluid region. The present paper extends the new immersed boundary treatment to moving geometries. The convergence of this approach is first validated by the method of manufactured solutions, where we design a one-dimensional advection–diffusion case, with a moving interface, to validate the numerical accuracy. Second, we simulate an unsteady flow past a plunging circular cylinder (Navier–Stokes solver). In this case, we show that the combination of volume penalization and SFD provides improved accuracy for moving geometries.

Dynamic Compensation Strategy for Scanning Error of Contact Probe Based on Damping Ratio and Frequency Mapping

Dynamic Compensation Strategy for Scanning Error of Contact Probe Based on Damping Ratio and Frequency Mapping

Experiment and optimization of a damping structure system with distributed multiple unidirectional single-particle dampers

Although particle dampers are characterized by a wide damping frequency band, flexible arrangement, and applicability to harsh environments, they have three shortcomings: their performance is difficult to simulate, insufficient research has been conducted on the damping effect they exert on multi-story structures, and there are no methods for evaluating their performance. Therefore, the aim of this research was to develop a Multiple Unidirectional Single-Particle Damper (MUSPD). Firstly, the simulation element of the MUSPD was established by analyzing its damping mechanism, following which the values of the parameters in the element were determined. Secondly, a series of shaking table tests were performed to investigate the damping effect of the MUSPD and demonstrate the accuracy of the simulation. Thirdly, the optimal layout of the MUSPD was proposed based on an analysis of the relationship between particle mass, particle movement distance, and damping effect. Fourthly, a dynamic method for evaluating the damping effect of the MUSPD was proposed. Finally, the rationality and feasibility of the optimal layout scheme and the method for evaluating the MUSPD in multi-story structures were verified by a case analysis. The test results demonstrated that the damping rate of MUSPD for displacement peaks in multi-story structures reached 21.40 %, with a root mean square damping rate of 36.50 %. Additionally, for acceleration peaks, MUSPD achieved a damping rate of 25.12 %, with a root mean square damping rate of 38.10 %. MUSPD exhibited a significant damping effect on multi-story structures. The comparison between test results and simulation results showed that the simulation element of the MUSPD exhibited good accuracy; Simulation analysis results revealed that the optimal layout scheme and dynamic evaluation method were reasonable and effective.

Influence of water hammer effect on low frequency oscillation of grid-connected hydropower station system

This paper aims to investigate the influence of the water hammer effect on low-frequency oscillations (LFO) in power systems, mainly quantifying and revealing the characteristics of hydraulic damping of LFO. The models of the grid-connected hydropower stations considering the water column elasticity (elastic model) and without considering it (rigid model) are respectively established and used as time domain validation models. The corresponding analytical formulas for the mechanical damping torque coefficients (MDTC) are derived to obtain the system's damping frequency characteristics. Finally, a method for quantifying the nonlinear system's damping is proposed. The results show that due to the effect of the water hammer wave, the system's damping frequency characteristics have changed, and damping peaks and valleys appear. The corresponding frequencies are determined by the frequency of the water hammer wave. The system has a critical oscillation frequency. When the frequency of LFO is below the critical frequency, water column elasticity must be considered. When the frequency of LFO is consistent with the frequency of the water hammer wave, the negative damping reaches its maximum. Finally, the proposed quantitative method was used to clarify the influence of the water hammer effect on the system's damping characteristics while considering nonlinear head loss.