Thickness Of Damping Layer Research Articles

Optimization of the Geometric Characteristics of Damping Layers for Acoustic Black Hole Beams Based on the Backpropagation Algorithm

In real-world scenarios, it is common to apply a damping layer of a specific thickness to the surface of an acoustic black hole (ABH) beam to boost its energy dissipation capacity. However, it has become apparent that excessive damping layers might result in negative consequences. The present study suggests employing the backpropagation (BP) algorithm to refine the positioning, thickness, and contour of the damping layer for optimal results. This study begins with the derivation of a semi-analytical solution for the vibration characteristics of an ABH beam under a harmonic load using the Gaussian expansion method (GEM). This process results in the preliminary identification of a thickness profile for the damping layer that exhibits significant potential for energy dissipation. Subsequently, a BP neural network is trained on the data produced by the semi-analytical solution to further optimize this thickness variation function. The findings reveal that the geometry of the damping layer has a more complex influence on performance than previously recognized. The optimization guided by the BP neural network suggests that achieving a strong ABH effect does not require uniform application of the damping layer across the entire ABH section. Rather, the most effective approach is to concentrate the damping layer thickness at the ABH tip, with a rapid decrease in thickness as one moves away from this point. It is also determined that applying a damping layer in areas far from the tip is unnecessary. Additionally, an innovative strategy is proposed to enhance the system’s energy dissipation capabilities without changing the truncation thickness of the ABH beam. This research contributes to a deeper understanding of how the damping layer affects the energy dissipation performance of ABH beams.

Response of existing lining subjected to closed blasting in zero-spacing twin tunnels and its damping measures

The blasting excavation of a new tunnel significantly impacts the lining of existing tunnels during the construction of zero-spacing twin tunnels. In this study, a field test was first carried out to study the vibration velocity of an existing lining in zero-spacing twin tunnels. LS-DYNA software was then employed to investigate the dynamic response characteristics under various blasting factors. Finally, the use of damping layer was considered to analyze its effects on the dynamic response of the existing tunnel lining. The maximum vibration velocity was found at the hance adjacent to the new tunnel, with a value of 17.51 cm/s in the tests. The maximum principal tensile stress(PTS) from the simulation was also shown at the same hance of the existing lining to have an intensity of 3.27 MPa. Additionally, the blasting of the rock mass close to the existing tunnel in the first step would result in a higher PTS intensity of 3.54 MPa within the lining, compared to the blasting of the rock mass away from the existing tunnel in the first step. However, the cumulative stress disturbance caused by the former to the lining was smaller than that of the latter. The maximum PTS at the hance was also found to linearly decrease with the reduction of the excavation footage and the maximum PTS was 2.3 MPa at an excavation footage of 0.9 m. The damping layer of the existing tunnel would contribute to a significant reduction of PTS. Therefore, a damping layer thickness of 2.5 cm was suggested in the study considering the effects of the damping and mechanics of the lining.

Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions

Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (Hi ), and inversion layer Froude number (Fri ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere’s buoyancy frequency or buoyant perturbations’ time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

Design and vibration characteristics of sandwich constrained damping gasket for diaphragm air pump

There are certain problems of vibration reduction and isolation relevant to the working stability of diaphragm air pumps. To make the diaphragm air pump meet the use requirements, a sandwich-constrained damping gasket is designed and prepared in this paper. The research focuses on examining the impact of varying damping layer thickness on the efficacy of damping gaskets in reducing and isolating vibrations. Meanwhile, with the increase of the damping layer thickness, the total vibration severity of the diaphragm air pump body continues to increase, indicating a weakened performance of vibration reduction, while the vibration isolation performance is gradually improved.

Aseismic performances of constrained damping lining structures made of rubber-sand-concrete

Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures. In this study, a constrained damping structure for underground tunnel lining, using a rubber-sand-concrete (RSC) as the aseismic material, is proposed. The aseismic performances of constrained damping structure were investigated by a series of hammer impact tests. The damping layer thickness and shape effects on the aseismic performance such as effective duration and acceleration amplitude of time-domain analysis, composite loss factor and damping ratio of the transfer function analysis, and total vibration level of octave spectrum analysis were discussed. The hammer impact tests revealed that the relationship between the aseismic performance and damping layer thickness was not linear, and that the hollow damping layer had a better aseismic performance than the flat damping layer one. The aseismic performances of constrained damping structure under different seismicity magnitudes and geological conditions were investigated. The effects of the peak ground acceleration (PGA) and tunnel overburden depth on the aseismic performances such as the maximum principal stress and equivalent plastic strain (PEEQ) were discussed. The numerical results show the constrained damping structure proposed in this paper has a good aseismic performance, with PGA in the range (0.2–1.2)g and tunnel overburden depth in the range of 0–300 m.

Free vibration of co‐curing damping sandwich composites with different lay‐up angles

AbstractIn this article, the dynamic characteristics of Co‐curing Damping Sandwich Composites with Different Lay‐up Angles (CDSCDLA) are studied by means of modal analysis and numerical simulation to optimize the structure of co‐curing composites. The vibration equilibrium equation of CDSCDLA is derived according to first order shear deformation theory and Hamilton equation. The dynamic model of the structure is established by finite element simulation to verify the accuracy of the theoretical calculation. The influence of different lay‐up angle and the damping film thickness on the free vibration of CDSCDLA is explored under the condition of constant skin thickness. The theoretical derivation and finite element simulation results reveals that the overall dynamic characteristic of damping sandwich composite with a lay‐up angle of 45° is optimal when the damping film thickness is constant. In particular, when the thickness of the damping film is 0.1 mm, the first‐order mode damping and mode frequency of composite plate with a lay‐up angle of 45° reach the maximum value of 0.1495 and 747.9 Hz, respectively. The first order damping loss factor of the CDSCDLA with different layup angles is maximum when the damping film thickness is 0.3 mm. However, blindly increasing the damping layer thickness can not always improve the damping performance of the composite structure, but will greatly reduce the stiffness of the composite. The work provides a reference for dynamic performance optimization and structural design of sandwich plate with high strength and large damping loss factor.Highlights Free vibration of sandwich composites with lay‐up angles is investigated. The dynamic analytical model of the structure is established. The validity of the derived theory is verified by numerical simulation.

Damped Cantilever Microprobes for High-Speed Contact Metrology with 3D Surface Topography.

We addressed the coating 5 mm-long cantilever microprobes with a viscoelastic material, which was intended to considerably extend the range of the traverse speed during the measurements of the 3D surface topography by damping contact-induced oscillations. The damping material was composed of epoxy glue, isopropyl alcohol, and glycerol, and its deposition onto the cantilever is described, as well as the tests of the completed cantilevers under free-oscillating conditions and in contact during scanning on a rough surface. The amplitude and phase of the cantilever's fundamental out-of-plane oscillation mode was investigated vs. the damping layer thickness, which was set via repeated coating steps. The resonance frequency and quality factor decreased with the increasing thickness of the damping layer for both the free-oscillating and in-contact scanning operation mode, as expected from viscoelastic theory. A very low storage modulus of E'≈100kPa, a loss modulus of E″≈434kPa, and a density of ρ≈1.2gcm-3 were yielded for the damping composite. Almost critical damping was observed with an approximately 130 µm-thick damping layer in the free-oscillating case, which was effective at suppressing the ringing behavior during the high-speed in-contact probing of the rough surface topography.

Structural optimization to improve the dynamic performance of novel co‐curing damping sandwich composites

AbstractCo‐cured damping composite structures have broad application prospects in high‐tech fields such as aerospace and space vehicles because of their low weight, large damping, and sufficient stiffness. In order to improve dynamic properties of conventional composite structures, a new type of damping composites embedded with multilayer viscoelastic film is proposed in this paper. Based on the complex modulus theory and vibration mechanics of composite plates and shells, vibration differential equation of composite plates with multilayer viscoelastic film is derived. The constitutive relation of the complex structure is established. The consistency of theoretical derivation and numerical simulation results provides a reference for the optimization of dynamic performance of damping sandwich composites. The effects of the distribution of viscoelastic film and the geometric structure parameters on dynamic performance of co‐cured damping composites are also discussed. The results show that the embedding of multi‐layer viscoelastic film can greatly enhance the loss factors of co‐cured composite structures under same damping layer thickness. This work lays a foundation for optimization of dynamic performance of lightweight and large damping composite structures.

Effect of acoustic black hole parameters on vibration suppression of rectangular plate

The acoustic black hole has the ability to gather and manipulate the flexural wave in the structure, and can be used to achieve vibration suppression of the structure. A group of FEM models for the vibration analysis of the rectangular plate embedded with acoustic black holes were established in this paper. Four monitoring points on the ABH plate were selected to calculate their vibration velocity response in 100 Hz-3 kHz frequency interval. In order to study the effects of acoustic black hole geometric parameters and damping layer geometric parameters on the vibration response of the ABH plate, 15 combinations of different parameters of the maximum ABH diameter, the truncated thickness of the ABH, the power index of the ABH, and the damping layer thickness, the maximum diameter of the damping layer were selected to calculate the vibration velocity response of the four monitoring points. The calculation result can help us understand the effects of acoustic black hole geometric parameters and damping layer geometric parameters on the vibration suppression of rectangular plate.

Flexural fatigue behavior of novel co-curing damping composite structures

In order to investigate the flexural fatigue performance of novel carbon fiber reinforced bismaleimide resin matrix damping sandwich composite structure prepared by co-curing process, three-point flexural fatigue tests were carried out on composite structure embedded with damping films of different thickness. The flexural fatigue failure mode, fatigue life and damage evolution law of sandwich beam were obtained, and different damage mechanisms of sandwich beam under flexural fatigue load were analyzed. The S-N curves of undamped composite were fitted by three-point flexural fatigue test. The fatigue characteristics of the undamped composite and damping composite were compared and analyzed. The results showed that the fatigue life of damping composite decreased with the increase of damping layer thickness under the same cyclic load. A numerical simulation model of three-point flexural fatigue performance of damping composite was established. The fatigue life variation trend of damping composite under different damping layer parameters (number of damping layers, location of damping layers, distribution of damping layers) was further simulated, which provided theoretical basis for the fatigue design of damping composite.

Vibration suppression of a rotating functionally graded beam with enhanced active constrained layer damping treatment in temperature field

This paper investigates the vibration control of a rotating functionally gradient material (FGM) beam under thermal environment by using an enhanced active constrained layer damping (EACLD) treatment. The present model is extended from a newly developed dynamic model for composite EACLD beams. The difference is that the base beam is composed of temperature-dependent FGM that was widely used in the aerospace industry as advanced heat-resisting composite and the temperature dependence of viscoelastic material in the constrained layer is also considered. The active piezoelectric layer has edge elements at both ends, which are modeled as equivalent springs and mass points. The Lagrange’s equation is used to derive the dynamic equations of the system and the deformation of the beam is described by the assumed-mode method. Based on the rigid-flexible coupling dynamic theory, the dynamic responses of the rotating FGM beam with various temperature differences are investigated. Simulation results show that the vibration suppression performance of the EACLD beam is better than the ACLD beam. The equivalent springs have more significant influences on the structural vibration suppression effect than the mass points. The larger the temperature difference is, the larger the thermal induced flutter of the structure is. The influences of VEM damping layer thickness, rotating speed, and control gain on the vibration of the structure with EACLD treatment are also discussed.

Wave-based analysis of the cut-on frequency of curved acoustic black holes

The curved acoustic black hole (ABH), a thin structure with a curved baseline and a thickness that tapers according to a power law, has been proposed and investigated numerically and experimentally as a candidate for an effective and compact absorber of flexural waves. To understand physically the wave motions within a curved ABH and to utilize a spiral ABH in practical applications, systematic investigations of the effects of geometrical parameters such as the curvature or the damping-layer thickness are needed, as well as a theoretical approach to facilitate fast and accurate calculations. In this paper, we propose a wave-based theoretical method and investigate the “cut-on frequency” of a curved ABH, the frequency from which waves start to propagate within the ABH, using this method. The governing equation of the wave motion is derived using Hamilton's principle, and the solution of the governing equation is obtained numerically by recasting the original equation into impedance-equation form. Using the proposed method, we calculate the reflection coefficients of arc ABHs and Archimedean spiral ABHs with various geometrical parameters and frequencies to investigate their cut-on frequencies. The cut-on frequency increases almost linearly in proportion to the curvature in arc ABHs, and decreases with increasing gap distance in spiral ABHs.

Improving interfacial shear strength of co-cured sandwich composites by designing novel damping layer

The purpose of this work is to improve the interfacial bonding performance of traditional sandwich damping composite. The glass fiber reinforced damping composites with four different damping film thickness were prepared by introducing the interface reaction between damping polymer and resin matrix. The co-cured damping composite specimen is composed of sandwich damping film (0.1 mm–0.4 mm) and upper and lower skin (1 mm). The outstanding characteristic of the co-cured damping composite is that the resin matrix and damping material maintain the same reaction process. The interface bonding behaviors were experimentally investigated using interfacial shear strength test and microstructure analysis. The interfacial shear strength of specimens with the damping layer thickness of 0.1, 0.2, 0.3, and 0.4 mm was increased by 72.55%, 51.29%, 47.30% and 36.39% compared with traditional damping sandwich composite. It was found that the interfacial shear strength was significantly enhanced by interleaving the tailored damping material. The analysis exhibited that sandwich damping layer and lamina were well combined. The FTIR and XPS characterization showed that rubber and resin were chemically bonded at the interface, which further explained the interface bonding mechanism. The results reveal that the novel damping composites show a broad application prospect.

Fabrication and investigation on damping performance of novel co‐curing sandwich composites

AbstractA new kind of co‐cured sandwich composite was manufactured via inserting tailored damping materials between the lamina to enhance vibration characteristics and sound insulation performance of traditional sandwich composite. The sandwich material was investigated based on the theory of co‐curing, which was superior to the preparation process of traditional sandwich composite. The viscous flow characteristics of epoxy resin and rubber sandwich were considered in the preparation process. The damping characteristics and sound insulation properties of the sandwich composite were determined by the single cantilever beam vibration test and the standing wave tube method. The loss factor of the sandwich composites with damping layer thickness of 0.1 mm reaches 3.384%, which increases by 102.81% compared with that of the undamped composite. The experimental results reveal that the novel damping polymer enhances the damping characteristic and sound insulation performance of laminates significantly compared with previous sandwich composite. The conclusion indicates that the co‐cured composite structures show a strong ability of vibration reduction and sound insulation.

Energy absorption and impact resistance of sandwich composite alloy structures under dynamic impact

Abstract A new sandwich composite structure is prepared based on warm rolling process. The dynamic mechanical property of the sandwich composite structure is investigated through split Hopkinson pressure bar (SHPB) experiment. The Johnson–Cook constitutive model is modified based on the SHPB experiment result, taking into account the synergy between strain softening and strain rate softening. Projectile penetration simulation is performed on the sandwich composite structure using projectile penetration schemes for different angles and different structural dimensions to examine how penetration angle and structural dimensions affect the dynamic energy absorption property of sandwich composite structures. Vibration equations of sandwich structures are inferred based on Hamilton’s theory to reveal the dynamic energy absorption mechanisms of these structures. The results show that symmetric structures have better damping performance than asymmetric structures; maximum stress will display a rise-fall-rise profile with increasing penetration angle; for symmetric structures with damping layer thickness of 4 mm, the projectile deflection angle will first increase and then reduce with increasing penetration angle and the projectile deflection angle will approximate 40°at penetration angle 10°.

Effects of Acoustic Black Hole Parameters and Damping Layer on Sound Insulation Performance of ABH Circular Plate

The acoustic black hole (ABH) can be utilized to achieve aggregation of flexural wave in structures with the feature that the thickness gradually reduced to zero with a power exponent no less than 2. The above characteristics could be applied in vibration reduction, noise attenuation or improving sound insulation. Previous literatures on vibration and acoustic characteristics of ABH structures mainly focus on the structural response under mechanical force excitation, while the transmission loss (TL) of circular plates embedded with two-dimensional ABHs investigated in this paper is a vibro-acoustic coupling procedure under excitation of diffuse sound field. Series of vibro-acoustic coupling finite element models (FEM) for TL analysis of ABH circular plates were established by automatic matched layer (AML) method in this paper and an experimental platform for measuring TLs of ABH circular plates and uniform plates was constructed. The accuracy of the FEM analysis was verified by experimental measurements. To systematically analyze the influence mechanism of parameters of the ABH on TLs of ABH circular plates, the effects of diameter, orientation, number, and truncation thickness of ABHs on TLs of ABH circular plates were further studied. The effect of the damping layer on TLs of circular plates embedded with 1 and 19 ABHs was also analyzed and it reveals that the influence of damping layer mainly concentrates on the first-order resonance frequency and damping-controlled region of the plate, and at some frequencies, the greater the damping layer thickness, the worse the sound insulation performance, despite that the modal damping loss factor has been increased in the whole frequency domain.

Dynamic Property Investigation of Sandwich Acoustic Black Hole Beam with Clamped‐Free Boundary Condition

The geometric parameters of the acoustic black hole (ABH) structure are changed in power exponent, and this feature can be used to control the flexural wave to achieve energy concentration, vibration attenuation, or noise reduction. However, in practice, the ABH structure often has a truncation due to the limitation of manufacturing, which will cause the reflection coefficient to increase significantly and seriously affect the ABH effect. In this paper, a semianalytical model of the sandwich‐truncated ABH beam structure with aluminum in the middle layer and steel in the upper and lower layers is constructed based on the energy principle. The ABH effect of the sandwich beam under the clamped‐free boundary condition is analyzed. Meanwhile, the effects of damping layer parameters, middle layer material, and thickness on the vibrational acceleration response of the ABH region and the uniform beam region of the sandwich beam are also studied. It is observed that, for the sandwich ABH beam structure, the influence of damping layer thickness on the acceleration response peak values of both the ABH region and the uniform region is very obvious in middle and high frequencies and the peaks at about 9 kHz are completely suppressed when the damping layer thickness reaches 3 mm. It also reveals that the use of aluminum as the middle layer material can bring a vibration attenuation at around 9 kHz both for the ABH region and the uniform beam region compared with using steel as the middle layer material. Experiments are carried out to verify the accuracy of simulation analysis.

Dynamics characteristic of steady fluid conveying in the periodical partially viscoelastic composite pipeline

Abstract In this paper, the dynamic stability of the fluid-conveying in the periodically composite pipeline (FCPCP) is researched, and the FCPCP system is divided into two parts: pipeline with partial viscoelastic composite part and the conveying-fluid part. The in-plane variables of the first part are calculated by the Zig-Zag laminated shell theory, and the equilibrium equations are obtained by Hamilton's principle. Meanwhile, the equilibrium equations of the fluid part are mainly obtained by Newton's Second law. The govern equations of the FCPCP system can be determined by combining the equations obtained of the two parts, and considering the boundary conditions, and the instability of the current structure can be obtained by solve the govern equation system. The factors (Such as the thickness ratio of the pipeline, the thickness of viscoelastic damping layer and the viscoelastic composite fraction, etc.) which affected the instability of FCPCP is thoroughly examined, and validate is performed finally.

An Experimental Investigation of Acoustic Black Hole Dynamics at Low, Mid, and High Frequencies

The acoustic black hole (ABH) has been developed in recent years as an effective, passive, and lightweight method for attenuating bending wave vibrations in beams and plates and reducing the sound radiation and structural-acoustic response of structures. The ABH effect utilizes a local change in the plate or beam thickness to reduce the bending wave speed and increase the transverse vibration amplitude. Attaching a viscoelastic damping layer to the ABH results in effective energy dissipation and vibration reduction. Surface-averaged mobility and radiated sound power measurements were performed on an aluminum plate containing an array of 20 two-dimensional ABHs with damping layers and compared to a similar uniform plate. Detailed laser vibrometer scans of an ABH cell (including the ABH and surrounding homogeneous plate) were also performed to analyze the vibratory characteristics of individual ABH cells and compared with mode shapes calculated using finite elements. The results showed that the surface-averaged mobility was reduced by up to 14 dB for the fully damped ABH plate compared to a uniform reference plate while also reducing the mass of the plate. The results demonstrated that the dynamics of plates with embedded ABHs can be characterized by low, mid, and high frequency ranges, with low-order local ABH modes contributing significantly to low frequency ABH performance. The effects of damping layer thickness and diameter were also investigated to assess ABH performance optimization. It was shown that the damping layer can have the added benefit of mass loading the ABH and enhancing low frequency performance. The results will be useful for designing the low frequency performance of future ABH systems and describing ABH performance in terms of design parameters.

Vibration and noise reduction properties of different damped rails in high-speed railway

Wheel/rail rolling noise is the major composition of railway noise pollution. With the rapid development of high-speed railway, the increasing vehicle speed results in higher railway vibration and noise level. Setting damping material on rail waist is an effective control method for mitigating wheel/rail vibration and noise at the source. Damping treatments of rails can be classified into monolayer constrained damped rail, multilayer constrained damped rail and labyrinth constrained damped rail according to structure type. In order to select an appropriate type of damped rail for ballastless track in high-speed railway, vibration and acoustic radiated characteristics of standard rail and the three typical damped rails were compared using vibro-acoustic radiation models for ballastless track system established by the collaborative simulation of FEM/BEM, and the wheel/ rail tread roughness was converted into high-speed wheel/rail interaction force as external excitation. By comparison, using labyrinth constrained damped rail in high-speed railway is recommended, and the suggested value for the damping layer thickness is also provided.