Material Damping Research Articles

Evaluation of Inherent Damping Feature of Beam Structure Based on Complex Modulus

Structural damping, which has been widely used to quantify the energy dissipation of engineering structures, plays an important role in dynamic analysis during the design phase and the assessment of existing structures. However, the development of an accurate damping model remains an open question due to the unclear mechanism. In this study, structural damping was identified based on loss factors for beam structures, which were used for presenting the damping behavior during vibrations. The equation of motion for the bending deformation of a Timoshenko beam was derived, accounting for the material damping. To identify the loss factor of the beam from the response signals at a limited number of measurement points, an inverse algorithm based on wave coefficient estimation was developed, considering the numerical stability for data interpretation. Based on the proposed loss factor identification method, several beam models with different shapes of cross-sections were investigated, focusing on the feasibility of the method of varying cross-section cases. Comparing the spectral element model with the loss factor and the finite element model with Rayleigh damping, it was confirmed that the loss factor can better describe the actual energy dissipation behavior of the structure. It provides a more accurate theoretical model for estimating structural damping in practical engineering.

Overdamping of vibration resonances by liquid crystal elastomers

This work aims to compare the capability of vibration attenuation by standard elastomeric polymers, and by the new anomalously damping nematic liquid crystal elastomer. We use the most mainstream materials in both categories, and design two testing platforms: the ASTM-standard constrained layer plate resonance geometry, and the attenuation of resonances in a commercial device (electric drill) where the damping polymers were inserted into the casing. In the standard plate resonance testing, we find that LCE outperforms all standard damping materials, moreover, it brings the vibrating plate into the overdamped condition, which is unique for a non-fluid dissipative system. In the attenuation of high-frequency vibrations of a device, we also found LCE dissipates these vibrations much better, although we did not find the optimal insertion configuration for the damping polymer, and did not reach overdamping.

Mechanical properties and restoring force model of Squeezing Rub-type Particle Damper

The sliding effect of isolation bearings has been proven to effectively mitigate the seismic effects on large-span bridges. However, it also results in excessive relative displacement between the main girder and piers during earthquakes. In this study, a pioneering Squeezing Rub-type Particle Damper (SRPD) is developed to address this issue. In order to verify the damping characteristics of SRPDs and investigate the working principle of squeezing friction energy dissipation, five quasi-static tests were conducted on SRPDs using two particle damping materials with different compactness levels. In order to compare the energy dissipation performance, comparative tests were conducted on Non-Squeezing-type Particle Dampers (NSPDs) and SRPDs. Utilizing regression analysis, two skeletal curve models for SRPDs were proposed, alongside a detailed restoring force model that incorporates considerations for both the pinching effect and stiffness degradation phenomena observed during the loading and unloading phases. The experimental results demonstrate that the maximum damping force of SRPDs can reach 16 times that of NSPDs, and the energy dissipation of each loading cycle can reach 21.06 times that of NSPDs. SRPDs exhibits improved energy dissipation performance when using high-density blended quartz sand. After sand replenishment repairs,damping force and energy dissipation per cycle of SRPDs were significantly enhanced. The proposed restoring force models of SRPDs aligns well with the experimental curves, underscoring its efficacy in accurately characterizing the hysteresis performance of SRPDs.

“Borrow-force-attack-force” by multi-scale elastic metamaterial with nonlinear damping

The powerful energy carried by low-frequency vibration is often challenging to be effectively attenuated using traditional damping materials. If low-frequency vibration can be controlled through the energy carried by the excitation itself, the cost of achieving ultra-wide low-frequency vibration control would be significantly reduced. To this end, this paper constructs a multi-scale elastic metamaterial with nonlinear damping (MEMND) to achieve the efficient suppression of ultra-wide low-frequency vibration through its unique transmission characteristics and the effect of “borrow-force-attack-force” (leveraging the excitation to dampen vibration), which is amplified with increasing external excitation. Theoretical, simulation, and experimental results demonstrate that MEMND can achieve over 10 dB damping enhancement at the expense of losing a small amount of the bandgap effect. It exhibits high sensitivity to external excitation in the low-frequency region, offering a promising opportunity for “borrow-force-attack-force”. This work integrates a natural nonlinear damping element into elastic metamaterials and leverages the nonlinear action mechanism of external excitation, presenting a different approach for nonlinear metamaterial design with potential engineering applications.

Progress in Seismic Isolation Technology Research in Soft Soil Sites: A Review

Soft soil sites can amplify the peak acceleration by a factor of 1.5 to 3.5 and exhibit the filtering effect on seismic waves. This effect results in the attenuation of high frequencies, amplification of low frequencies, and extension of the predominant period of ground motion. Consequently, soft soil sites have a more pronounced impact on isolation buildings constructed on them. The seismic isolation structure design typically involves assuming rigid foundation for calculations. However, the soil properties can significantly impact the dynamic response of the structure, affecting factors such as input ground motion, changes in vibration characteristics, radiation energy dissipation, and material damping energy dissipation. Therefore, neglecting these influences and relying solely on the rigid foundation assumption for calculations can lead to significant errors in the final seismic response analysis of the structure. Currently, there are numerous LNG storage tanks, museums, and other isolation buildings constructed on soft soil sites. Therefore, research on seismic isolation measures for soft soil sites holds significant practical importance. In light of this, this paper, firstly, provides a systematic summary of seismic isolation strategies and engineering applications for soft soil sites. Secondly, it further discusses advancements in research on the dynamic interactions of soil–isolated structures, covering analytical methods, numerical investigations, and experimental studies on soft soil sites. Lastly, the paper concludes with insights on current research progress and prospects for further studies.

Method for Predicting Environmental Vibration Impact of Existing Subway Lines and Its Practical Application

To predict accurately the impact of track vibrations caused by subway trains on adjacent buildings and address the problem of their excessive dynamic response, a method for predicting the environmental vibration impact of existing subway lines is proposed in this paper. A coupled numerical dynamical model of the train/track/tunnel system is established using the multi-scale method. Using field-measured soil vibration data, empirical formulas for soil frequency and material damping coefficient are calibrated. By combining the numerical model and the empirical formulas, buildings’ indoor vibrations and noise level can be assessed. At the same time, a solution to the problem of excessive vibration of buildings along a subway line is also proposed that optimizes the track fastener parameters. Field tests verified the accuracy of the prediction method and the effectiveness of the optimized track parameters. These research results provide a reference for predicting the vibration of buildings along subway lines and using the proposed preventive solutions.

A Novel Approach of the Viscoelasticity of Axially Functional Graded Bar and Application of Harmonic Vibration Analysis of an Isotropic Beam as Support

The use of smart materials and passive controllers in modern technologies has stimulated the study of vibration in elastic systems with viscoelastic damping. It is also possible to create components with precise material distribution coefficients and distinct properties, such as Functionally Graded Materials. This work investigates the resonant frequency characteristics of a beam supported at its ends by Axially Functionally Graded (AFG) viscoelastic bars using the finite element method. The set of equations governing motion is obtained by assuming Euler–Bernoulli beam theory for the beam and bar theory for the bars using Lagrange’s equations. The material properties of the functionally graded bar is assumed to vary through the length according to the power law distribution. The longitudinal loss factor values are used to define the internal damping coefficient, which is also dependent on the Young’s modulus value varying along the bar. The effects of the length-varying material properties and internal damping of the FG support bars on the force transmission TR and frequency parameters λ are examined in detail. No study has been found in the literature on the vibration of viscoelastic FG bar-supported beams subjected to a harmonic force at the centre point. It is shown that using bars formed with combinations of different materials considering material damping will be useful to keep the vibration level and force transmission at a certain value and control the frequency parameters.

Mid-frequency propagation path analysis on vehicle body using structural intensity

With the penetration of electric vehicles, reduction of structure-borne road noise gets important issue to realize comfortable vehicles for customers.Sound generation mechanism of structure-borne road noise on vehicle body is analyzed basically by modal analysis in low-frequency range. On the other hand, as frequency increases, modal analysis cannot clarify vibration mechanism because vibration wavelength gets shorter, mode density gets high and mode shape gets complicated. Therefore, it is difficult to identify efficient countermeasure parts and inefficient damping materials are added to response panels in mid-frequency range. So alternative analytical methods in mid-frequency range are under research to understand vibration mechanism. In this paper, Structural intensity (SI) analysis is introduced to clarify sound propagation mechanism. This analysis method makes it possible to clarify the main energy propagation path from input point to vibrating panels on vehicle body. The results show that SI analysis unveils the main energy propagation path and gives the opportunity to reduce the panel vibration efficiently by controlling the energy propagation path in body frame structure without damping materials.

The use of ensembles trees machine learning method in estimating damping of granular materials

Granular Materials (GM) employed within the mechanism of particle dampers attenuate the vibration energy due to their interparticle and particle-wall interactions. Estimating their damping effect using the analytical equivalent single mass approach overlooked the particles' individual losses that are built into the total damping. Alternatively, the numerical techniques (e.g., Discrete Element) are time-inefficient and computationally demanding. Therefore, this study explores the implementation of Machine learning (ML) algorithms to estimate the damping effect of GM. The ML model in this study will rely on a Data-Driven Modeling approach (DDM) incorporating the ensemble tress nonlinear regressor method. The models' training and testing data were obtained from an experimental setup of an acrylic beam internally integrated with Stainless Steel (SS) and glass spheres undergoing low excitation amplitude (RMS <1N). The main aim was to map between seven input features (e.g. filling ratio) and one targeted output: the beam's damped frequency response. Three ensemble trees' algorithms were used to create the DDM; Decision Tree, Random Forest, and XGBoost. The hyperparameter combination based on the Gridsearch CV function increases the prediction accuracy of each model. The developed ML models provided high accuracy (86-93%) in predicting the damping effect of the granular materials spheres.

Sound transmission loss of constrained layer damping composites featuring elastic plates embedded with acoustic black hole

This paper preliminarily investigates the influence of an elastic layer with an acoustic black hole (ABH) on the airborne sound insulation of a constrained layer damping (CLD) composite plate. ABHs represent a continuous impedance reduction in a local area of the structure, achieved by reducing material thickness. They efficiently dampen structure-borne sound in plate-like structures, resulting in excellent airborne sound attenuation performance. In the CLD composite structure, a damping layer is inserted between the elastic layers. This configuration achieves noise reduction and provides excellent airborne sound attenuation performance. By incorporating an ABH on one side of the elastic layer within the constrained damping composite structure and utilizing the damping layer as the terminal damping material for ABH, we achieve a lightweight structure with outstanding airborne sound insulation performance. Using finite element numerical calculations, we assess the airborne sound transmission loss of ABHs embedded within the CLD plate. Our analysis compares their transmission losses within the frequency range of 10 to 4000 Hz under normal-incidence and random incidence acoustic field excitations. While the ABH does not enhance the overall sound isolation performance of the CLD plate, it significantly improves the sound isolation dip at the resonance frequency.

Experimental characterization of acoustic damping materials

AbstractDue to their ease of use and low cost, passive damping methods are a preferred mean for the reduction of noise in many engineering applications. This applies in particular to foam materials, which exhibit good acoustic and mechanical damping properties. The selection of suitable materials is usually carried out experimentally and can be very labor‐intensive and time‐consuming. For this reason, it is helpful to develop qualified numerical methodsthat can be used for material design and selection. Hence, foam materials must be characterized experimentally in order to enable a later comparison with vibroacoustic simulations. This contribution, therefore, aims at providing suitable parameters for the use in numerical analyses and their validation. Firstly, the microstructure of a foam specimen is captured by means of a CT scan. In addition to providing the geometry for the multi‐physics simulations, this measurement is also used to determine characteristic foam features, for example, strut thickness and pore size distribution. In the second step, the frequency‐dependent stiffness and damping properties of the material are determined by a special experimental setup utilizing an electrodynamic shaker. Here, the dynamic system is approximated as a single‐mass oscillator, which is sufficiently accurate for low frequencies. These properties will later be used in the numerical model to evaluate different parameter identification approaches. In the third and last step of the experimental campaign, measurements with an impedance tube are conducted to obtain the coefficient of absorption. This material parameter is particularly suitable for comparing experiments and simulations. Finally, the correlation between the experimental results is examined to provide a deeper understanding of the foam materials.

A Comprehensive Review on the Viscoelastic Parameters Used for Engineering Materials, Including Soft Materials, and the Relationships between Different Damping Parameters.

Although the physical properties of a structure, such as stiffness, can be determined using some statical tests, the identification of damping parameters requires a dynamic test. In general, both theoretical prediction and experimental identification of damping are quite difficult. There are many different techniques available for damping identification, and each method gives a different damping parameter. The dynamic indentation method, rheometry, atomic force microscopy, and resonant vibration tests are commonly used to identify the damping of materials, including soft materials. While the viscous damping ratio, loss factor, complex modulus, and viscosity are quite common to describe the damping of materials, there are also other parameters, such as the specific damping capacity, loss angle, half-power bandwidth, and logarithmic decrement, to describe the damping of various materials. Often, one of these parameters is measured, and the measured parameter needs to be converted into another damping parameter for comparison purposes. In this review, the theoretical derivations of different parameters for the description and quantification of damping and their relationships are presented. The expressions for both high damping and low damping are included and evaluated. This study is considered as the first comprehensive review article presenting the theoretical derivations of a large number of damping parameters and the relationships among many damping parameters, with a quantitative evaluation of accurate and approximate formulas. This paper could be a primary resource for damping research and teaching.

A Thermal Model for a Hybrid Gas Bearing System in Oil-Free Turbochargers

Abstract With little drag friction, gas bearings operate at high rotor speed and high temperature and thus enable long operating life along with material damping for mechanical energy dissipation. However, most computational tools for modeling gas bearings are not accessible to bearing manufacturers or potential end-users, and the models are restricted to specific geometries and operating conditions or are missing important features, thus limiting their utility. This paper presents the thermal energy transport in a hybrid gas bearing for oil-free turbochargers with integrated heat and fluid flow models to produce a comprehensive thermo-hydrodynamic analysis predictive tool, and to design and evaluate air-lubricated gas bearings by predictions and experiments. An efficient algorithm couples the solution of the Reynolds equations and the thermal energy transport equations in the film between the rotor and a pad of the hybrid gas bearing, and updates the temperature-dependent viscosity and film thicknesses during the iterative process. The test repeats and averaged for each rotor speed from 2 krpm to 22 krpm at intervals of 2 krpm, for supply pressure varying along 25 psi to 100 psi and predicted film temperature matches well with the measured one. The parameters of interest in this analysis include the gas supply condition, bearing configuration, and the gas properties at high altitudes and high rotation speeds. The parametric study results show the density and kinematic viscosity are the most dominant properties of the gas lubrication for the film temperature.

An automatic simulation pipeline for coupled simulations of acoustic damping materials

AbstractFoamed materials are widely used to reduce noise due to their comparably good acoustic damping behavior. However, out of a large variety of these materials a suitable candidate has to be identified for each application. This is a challenging process that is typically guided by experiments and experience. While numerical simulations could support these experiments and reduce the effort to a great extent, no suitable discretization approach has yet been established that can fully capture the complex geometry of the foam. A fully resolved model is desirable in order to yield reliable predictions that can then be used to establish homogenized models. We established a monolithic coupling approach based on the finite cell method (FCM) that realizes a vibroacoustic simulation in this sense. The fluid and the structure domain are discretized by Cartesian grids and the geometry defined based on computed tomography scans is accounted for during the quadrature of the weak form. Our simulation in the time domain makes use of explicit time marching schemes and is therefore limited by a critical time step size. This is known to be arbitrarily low for discretizations with the FCM containing cells with arbitrarily small support. As a remedy against this we use the classical ‐stabilization technique and investigate its potentials and limitations.

A comparative study of low cyclic loading effects on plastic strain, nonlinear damping, and strength softening in fiber-reinforced recycled aggregate concrete

The incorporation of fibers significantly enhances the properties and structural performance of recycled aggregate concrete. This study introduces Fiber-Reinforced Recycled Aggregate Concrete (FRAC) by integrating steel fibers (SF) and polypropylene fibers (PPF) into the recycled aggregate concrete (RAC) matrix. A comprehensive series of cyclic loading tests, including reload and unload sequences, were conducted to meticulously analyze the deterioration of strength and energy dissipation capabilities of SF/PPF-reinforced RAC. The research examines the effects of fiber characteristics, volume ratios, lengths, and diameters on strength degradation after the peak stress along the stress-strain curve. Degradation models based on plastic strain were proposed for both SF-reinforced RAC and PPF-reinforced RAC. The study further investigates the fluctuation of strain energy in FRAC under low cyclic loading, revealing the correlation between plastic strain energy and equivalent viscous damping ratio. A nonlinear viscous damping model that accounts for the influence of the reinforcing index (RI) is proposed. This model effectively predicts the degradation of strength, the evolution of plastic strain, and the dynamics of nonlinear viscous damping in composite materials with varying fiber content. Ultimately, this research provides essential technical insights for the practical engineering application of RAC.

Torsion of end-bearing pile foundations in layered anisotropic geomaterials

ABSTRACT An analysis for the torsional dynamic response of end-bearing pile foundations embedded in a layered transversely isotropic geomaterial (soil/rock) is presented. The deformation of the transversely isotropic soil or rock is described by the method of separation of variables. The elasticity theory for a viscoelastic medium with frequency independent hysteretic material damping, and the Extended Hamilton’s Principle are utilised to derive the differential equations describing pile and soil motions. The differential equations are solved analytically in an iterative algorithm. The accuracy of the analysis is verified with existing studies reported in the literature for pile foundations embedded in a homogeneous and layered soil deposit. The effect of the degree of anisotropy on the pile-soil response – dynamic pile-head stiffness, distribution of pile rotation and torque with depth, dimensionless soil displacement function for various values of pile slenderness and pile-soil stiffness ratios in a homogenous soil deposit is investigated. Design charts of static pile-head stiffness in a homogeneous soil deposit for a wide range of pile-soil stiffness and pile slenderness ratios, and degree of anisotropy are also reported. The effect of soil layering for a pile embedded in a two-layered soil deposit is also studied.

Control Mechanism and Noise Reduction Effect of CVDM on Rail Transit Steel Bridge: Experimental and Numerical Study

Steel bridge, as one of the main structural types in bridge design, has been widely used in rail transit. However, the train-induced vibro-acoustic problem of the bridge has become increasingly prominent. The vibration and noise characteristics must be more significant and complex than steel truss bridge because of too many components. Viscoelastic damping materials (VDMs) have the characteristics of both viscous liquid and elastic solid, and have better damping performance than other damping materials. Therefore, VDM plays an important role in vibration and noise reduction technology. In applications, VDM is usually combined with constraining materials to form composite viscoelastic damping materials (CVDM). In this paper, based on the dynamic receptance method and superposition principle, the coupling model of vehicle–track–bridge in the frequency domain is first established, and then the vibration and noise prediction model of a steel truss bridge with CVDM is established based on RUK theory and statistical energy analysis (SEA) method. Based on the prediction model, the natural dynamic characteristics of typical components of steel truss bridges with CVDM were investigated, and the control mechanism and influence rule of CVDM on train-induced vibration and noise of steel bridges were revealed.

Model order reduction of time-domain acoustic finite element simulations with perfectly matched layers

This paper presents a stability-preserving model reduction method for an acoustic finite element model with perfectly matched layers (PMLs). PMLs are often introduced into an unbounded domain to simulate the Sommerfeld radiation condition. These layers act as anisotropic damping materials to absorb the scattered field, of which the material properties are frequency- and coordinate-dependent. The corresponding time-domain model size is often very large due to this frequency-dependent property and the number of elements needed per wavelength. Therefore, to enable efficient transient simulations, this paper proposes a two-step method to generate stable reduced order models (ROMs) of such systems. Firstly, the modified and stable version of PMLs is projected by a one-sided split basis, which gives a stable intermediate ROM. Secondly, the intermediate ROM is modified to satisfy the stability-preserving condition by applying the modal transformation. Applying any one-sided model order reduction method on this modified model leads to a stable and small ROM. This two-step method is further extended to account for the locally-conformal PML model by reformulating it in curvilinear coordinates, which works for arbitrary convex truncated domains. The proposed method is successfully verified by several numerical simulations.

Modelling Low-Frequency Vibration and Defect Detection in Homogeneous Plate-Like Solids

The inspection of thick-section sandwich structures with skins around core materials such as honeycomb, balsa, and foam relies on low-frequency vibration techniques to identify defects through changes in amplitude or phase response. However, current industrial methods are often limited to detecting specific types of defects, potentially overlooking others. Moreover, these methods do not gather detailed information about the defect type or depth, as they only analyse a small portion of the available data instead of the full relevant response spectrum. This paper explores the scientific basis of using low-frequency vibration in the pitch-catch variant for defect detection in homogeneous solids, through analysis of the full relevant frequency spectrum (5–50 kHz). Defects in structures lead to reduced local stiffness and mass in the affected area, causing resonance in the layer above, resulting in amplified vibrations known as local defect resonance (LDR). In this work, an aluminium plate with a 40 mm diameter circular flat-bottomed hole (FBH) at a depth of 1 mm (representing a skin defect) is excited with a chirp signal of 5–50 kHz, and the response is monitored 17 mm away from the excitation point. Finite-element analysis (FEA) is used for the numerical model, addressing challenges in creating an accurate model. The process to optimise the numerical model and the reduce model-experiment error is outlined, including challenges such as the lack of knowledge of material damping. The study emphasizes the importance of modelling the probe’s stiffness and damping effects for achieving agreement between the model and experiment. After incorporating these effects, the maximum LDR frequency error decreased from approximately 3 kHz to less than 1 kHz. In addition, this study presents a method with the potential for defect classification through comparison to modelled responses. The minimum difference error was used to quantify the resonance frequencies’ error between the model and the experiment. Since the resonant frequencies are a function of the defect’s shape, size, and depth, a relatively low root mean squared (RMS) error across the resonance frequency error spectrum indicates the defect’s characteristics. Finally, defect detection and sizing using the pitch-catch probe are explored with a wide-band excitation signal and a line scan through the mid-plane of the defect. A method for defect sizing using a pitch-catch probe is presented and experimentally validated. Accurate defect sizing is achieved with the pitch-catch probe when the defect width is at least ≥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ge $$\\end{document} twice the 17 mm pin-spacing of the probe.

Perbandingan Tingkat Kebisingan Berbagai Bahan Peredam pada Knalpot Sepeda Motor Racing

The use of racing exhausts on motorised vehicles can cause uncomfortable and dangerous noise pollution if it exceeds the threshold set by the Minister of Environment. Based on the Decree of the Minister of Environment No 07/2009, the noise limit for motorbikes with engine capacity below 80 cc is 77 dB, 80-175 cc is 80 dB, and above 175 cc is 83 dB. This study aims to observe the comparison of noise levels of various silencer materials on racing motorbike exhausts in order to find the most effective material in reducing noise in accordance with these regulations. The noise measurement method follows the ISO 5130 standard, carried out when the engine is running idle and at engine speed range from 0 to 8000 RPM with a variety of different damping materials. The results show that at idle conditions, yellow Glasswool is the best damping material with the lowest noise level of 90.31 dBA, while Stainless wool shows the worst performance with an average noise level of 100.81 dBA. In contrast, in the 0-8000 RPM rotation condition, Stainless wool became the most superior silencer material with a noise level of 105.4 dBA, while grandma's hair Glasswool (fibreglass) became the worst with the highest noise level of 106.4 dBA. The conclusion of this study is that the optimal choice of silencer material can differ depending on the operating conditions of the racing exhaust, with yellow Glasswool being more effective at idle conditions and Stainless wool being more effective at maximum revs.