Variation Of Elastic Modulus Research Articles

Description of nonlinear viscous and viscoelastic properties of polyacrylamide solution under loading

Background. Currently, the solution of the problem of describing the rheological behavior of viscoelastic and nonlinear viscous properties of liquid and solid-like materials is far from perfect. For successful application of polymer systems to enhance oil recovery and for preparation of fracturing fluids and drilling fluids, knowledge of their rheological properties is necessary. Objective. To determine the nonlinear viscous and viscoelastic properties of polyacrylamide solution. Material and methods. We made an attempt to describe the rheological behavior of a polyacrylamide solution depending on the shear rate and on the loading time. A binomial rheological model was used to describe steady-state stresses at different shear rates, which showed a high degree of accuracy. To describe the stress from time, we proposed to use a numerical solution of a system of two differential equations representing the well-known Maxwell and Kelvin–Voigt equations. To describe the initial section of the curves for times less than 0.05 s, a model with a variable modulus of elasticity was used. Results. A high degree of correspondence of experimental and design stresses with a time of more than 0.05 s was achieved. The overall solution was achieved by combining two solutions based on shear rate and shear stress. Relationships with high correlation coefficients were found between the elastic modulus, viscosities of Maxwell and Kelvin and the shear stress and shear rate. Conclusions. We show that in addition to the “ordinary” shear rate determined by the rotation of the viscometer cylinder, it is necessary to consider an additional shear rate due to stress changes in time. Due to this approach, a description of the stress maximum and its displacement from the shear rate can be made. We note that the additional shear rate occurred immediately after the start of loading, rather than at the time of stress drop, as commonly believed.

Quantification of elastic modulus variations during zebrafish embryo development using a 3D-printed microfluidic platform

Reliable indicators to assess embryo quality are critical for the in vitro fertilization. Increasing evidence suggests that elasticity is emerging as a potential marker to evaluate the early development of embryos. This paper introduces a 3D-printed microfluidic device to measure the elastic modulus of zebrafish embryos deformed in a circular constriction channel. Firstly, numerical simulation was performed to analyze the impact of inlet pressure, embryo size and constriction channel diameter on the maximum protrusion length of the embryo. Subsequently, the zebrafish embryos were deformed using the device to record the protrusion length which was automatically measured using U-net, before the power-law rheological model was employed to calculate the elastic modulus. Experiments showed the power-law exponent and embryo elasticity were stable as the inlet pressure was not less than 250 mbar. Embryo culturing after squeezes revealed that embryos could maintain normal development even after multiple squeezes at 150 mbar while higher pressure may be fatal. Afterward, the deformation of the yolk was found to increase elasticity by 60.4 % compared to cases where only the chorion envelope was deformed. Finally, the elasticity variation of zebrafish embryos was measured for 17 hours. It revealed that the elasticity initially increased from hour 1 to hour 7–10 and then returned to approximately the original value during culture from the cleavage to the segmentation stages. The system with the ability of precise and long-term assessment of embryo elasticity may find valuable application potentials in the mechanical evaluation and sorting of embryos.

Deep learning enabled in vitro predicting biological tissue thickness using force measurement device

Accurate perception of biological tissues (BT) thickness is essential for preliminary evaluation of medical diagnosis and animal nutrition. However, traditional thickness measuring approaches of BT require complex operation, high-cost, and trigger biological stress response. Herein this study, an novel in vitro BT thickness measuring approach integrated with force test system (FST) and the discrete multiwavelet transform convolutional neural network (DMWA-CNN) prediction model based on deep learning are proposed. Simultaneously, several comprehensive experiments and model comparisons are conducted to demonstrate the superiority of the proposed approach. By establishing a DMWA-CNN demonstrates higher estimation accuracy than other traditional algorithm, achieving 100 % accuracy for artificial BT. Moreover, the experimental results indicate that proposed approach is robust to elastic modulus variation (E), external load variation (F), and small thickness differences (Ts). In addition, four kinds of the pork’ thickness are experimentally measured, and the accuracy value is not less than 98.2 %. The thickness of BT determined using the FST and DMWA-CNN algorithm demonstrate potential application in the biomechanical parameter prediction.

Incremental Plastic Analysis of Confined Concrete Considering the Variation of Elastic Moduli

Incremental Plastic Analysis of Confined Concrete Considering the Variation of Elastic Moduli

Mechanical impact of regional structural deterioration and tissue-level compensation on proximal femur trabecular bone.

Osteoporosis-induced changes in bone structure and composition significantly reduce bone strength, particularly in the human proximal femur. This study examines how these changes affect the mechanical performance of trabecular bone to enhance diagnosis, prevention, and treatment strategies. A proximal femur sample was scanned using micro-CT at 40μm resolution. Five regions of interest were selected within the femoral head, femoral neck, and greater trochanter. Structural models simulating various stages of osteoporosis were created using image processing software. Micro-finite element analysis evaluated the mechanical properties of trabecular bone under different conditions of structural deterioration and tissue-level elastic modulus variations. The combined effects of structural deterioration and tissue-level mechanical properties on trabecular bone mechanical performance were further analyzed. The mechanical performance of trabecular bone generally follows a power-law relationship with its microstructural characteristics. However, in any specific region, the apparent mechanical properties linearly decrease with structural deterioration. The femoral neck and greater trochanter are more sensitive to structural deterioration than the femoral head. A 5% bone mass loss in the femoral head led to a 7% reduction in mechanical performance, while the femoral neck experienced a 12% loss. Increasing tissue-level elastic modulus improved mechanical performance, partially offsetting bone mass reduction effects. Trabecular bone in low bone mass regions is more affected by bone mass loss. Structural deterioration primarily reduces bone strength, but improvements in tissue-level properties can mitigate this effect, especially in early osteoporosis. Targeted assessments and interventions are crucial for effective management. Future research should explore heterogeneous deterioration models to better understand osteoporosis progression.

Effect of Bleaching Treatments on the Mechanical Properties of the Dentin Matrix and on Collagen Biodegradation by Endogenous Protease.

This study evaluated the mechanical properties of demineralized dentin matrix submitted to different bleaching treatments, as well as the changes in mass and collagen biodegradation brought about by endogenous protease. Dentin collagen matrices were prepared to receive the following treatments (n=12): no bleaching treatment (C-control), 10% carbamide peroxide (CP-Opalescence PF, Ultradent, South Jordan, UT, USA) 10%/8 hours/ day/14 days, and 40% hydrogen peroxide (HP-Opalescence Boost, Ultradent), 40 minutes per session/3 sessions. The dentin matrices were evaluated for elastic modulus and mass before and after treatments and ultimate tensile strength after treatments. The solution collected during storage was evaluated for hydroxyproline release. There was no statistically significant difference between CP and C in terms of the elastic modulus (p=0.3697) or mass variation (p=0.1333). Dentin beams treated with HP and C presented significant mass loss after the first session (p=0.0003). HP treatment led to complete degradation of collagen matrices after the second bleaching session. After the second session, CP showed higher hydroxyproline concentration than C (p<0.0001). Ultimate tensile strength was lower for CP than C (p=0.0097). CP did not affect the elastic modulus or the dentin collagen matrix mass but did promote hydroxyproline release by endogenous protease and reduce the ultimate tensile strength. HP significantly affected the mechanical properties of dentin and promoted complete degradation of the demineralized dentin collagen matrix.

Experimental study on the impact of sulfate attack on the performance of shaft lining concrete under sustained compressive load

To investigate the impact of sulfate corrosion on the performance of shaft lining concrete under sustained compressive loads, this study immersed samples in a 10 % sodium sulfate solution after subjecting to sustained compressive loads of 0.2fcand 0.4fc. The variation in compressive strength, ultrasonic velocity, and dynamic elasticity modulus with corrosion age were examined. The corrosion mechanisms were analyzed using field emission scanning electron microscope and energy dispersive spectrometer. The impact tendency of concrete was also evaluated. The results indicated that under sustained compressive loads of 0.2fcand 0.4fc, the compressive strength, ultrasonic velocity, and dynamic elasticity modulus are all increased with age, in the order of 0.2fc> 0.4fc>no-load. When exposed to a 10 % sodium sulfate solution under sustained compressive loads, these properties initially increased and then decreased, peaking at 90 days of corrosion age, and the order was 0.2fc> no-load > 0.4fc when the corrosion age was longer than 240 days.The shaft lining concrete exhibited weak impact tendency, with the brittleness index increasing as the corrosion age progressed. The outcome of this work might provide a reference for the further research on the design of shaft lining concrete materials.

Investigation on the effect of the relative position between fracture and injection-production well on thermal extraction performance

The development of hot dry rock (HDR) resources is mainly through hydraulic fracturing to build fracture in low permeability high-temperature rock to form working fluid flow channels. The control mechanism of thermal transfer and conversion process in fracture system is the key to influence thermal extraction effect. In this paper, a temperature-hydraulic-mechanical (THM) coupling model of fractured rock mass is established considering the temperature variation of rock elastic modulus and Poisson's ratio. The dynamic changes of fracture aperture and permeability are investigated. Taking fractured HDR reservoir as a case study, the depletion thermal extraction process of dual-well enhanced geothermal system (EGS) is simulated, the spatial-temporal evolution of multi-field are analyzed. The results show that the cold front of the horizontal and vertical single fracture model advance in an oval shape and a rectangle shape, respectively. Over 30 years, the horizontal fracture aperture typically changes by a factor ranging from 1.02 to 1.12, permeability typically changes by a factor ranging from 5 to 15. The vertical fracture aperture typically changes by a factor ranging from 1.02 to 1.14, permeability typically changes by a factor ranging from 10 to 25.

Rock crack initiation triggered by energy digestion

The critical value of rock failure is determined by irreversible deformation (inelastic deformation, damage, and other internal dissipation) processes and external conditions before rock failure. Nevertheless, a thorough explanation of the mechanism causing cracks in rock material has not yet been provided. The strain energy theory is applied in this work to assess the initiation of rock cracks and investigate the relationship between energy digestion and rock strength. Firstly, the uniaxial compression test was conducted on sandstone samples under quasi-static loading conditions and the results of energy evolution, non-linear cumulative digestion, and stored ultimate energy were obtained. Then, a novel algorithm for assessing the initiation of rock cracks has been put forth. The concept of energy digestion index (EDI), which is the ratio of digested energy over the external loading energy, has been developed to characterize the energy absorption capacity of rock material. The result shows a relationship between the maximum growth rate of energy digestion and the increasing rate of variable elasticity modulus and crack initiation. The mechanical characteristics and peak strength of the rock material are negatively correlated with the EDI. By monitoring the digested energy status, an evaluation of the residual strength is introduced based on the relationships, which will initiate further research into in-situ monitoring and failure prediction.

CRFP Mechanical Properties—Stated Values Versus Experimental Data

Abstract This study thoroughly examines the mechanical properties of carbon fiber-reinforced polymers (CFRPs), motivated by the critical need for accurate composite property data in investigating fracture control measures for structures subjected to barely visible impact damage. We compared experimental results with manufacturer-stated values, focusing on discrepancies in fiber volume fraction and its impact on elastic modulus. Experimental findings showed an increase in elastic modulus to 190 GPa for 0 deg orientation samples, compared to the manufacturer's stated value of 159.27 GPa. The recalculated fiber volume fraction increased from the expected 57% to an actual value of 60.96%. This increase in fiber content, determined through the Voigt modulus equation and corroborated by SEM image analysis, directly contributed to the observed variations in elastic modulus. Tension tests at 0 deg and 90 deg angles exhibited average percentage errors of 14.83% and 11.57%, respectively, while compression tests at 0 deg displayed a deviation of approximately −13.92% after adjusting for values beyond 0.05% compressive strain. The study underscores the critical impact of fiber volume fraction on CFRP properties and highlights the importance of precise empirical evaluation for accurate CFRP characterization in applications such as aerospace engineering.

Grain size dependent indentation response of single-phase (CoCuMgNiZn)O high entropy oxides

Vickers indentation and nanoindentation methods were used to explore the hardness, elastic modulus, and fracture toughness of single-phase (CoCuMgNiZn)O transition metal high entropy oxides. Bulk samples with grain sizes ranging from 0.075 µm to 1.4 µm were consolidated using spark plasma sintering. Measurements reveal relatively small differences in elastic modulus and comparable hardness to Rule-of-Mixture calculations, alluding to minimal effects of entropy stabilization on mechanical properties. Hardness values exhibit a Hall-Petch relationship until an average grain size of 0.11 µm. Below this grain size an Inverse Hall-Petch relationship is observed with values decreasing up to 70 %. The measured hardness deviates from calculations of hardness using a grain interior-grain boundary composite model, indicating that other mechanisms, such as nanocracking or grain boundary sliding, contribute to the decrease in hardness at smaller grain sizes. Variations in elastic modulus are attributed to grain boundary effects, and variations in fracture toughness are attributed to the absence of grain bridging and transgranular fracture at smaller grain sizes. This grain-size dependent mechanical behavior, which is similar to behavior in MgO, must be controlled when designing (CoCuMgNiZn)O materials for various applications.

Homogeneous films from amphiphilic hyaluronan and their characterization by confocal microscopy and nanoindentation

Self-supporting films from amphiphilic hyaluronan are suitable for medical applications like wound dressings or resorbable implants. These films are typically cast from water/alcohol solutions. However, when the mixed solvent evaporates in ambient air, convection flows develop in the solution and become imprinted in the film, potentially compromising its properties. Consequently, we developed a novel film manufacturing method: drying in a closed box under saturated vapour conditions. Using this approach, we prepared a series of optically clear lauroyl-hyaluronan (LHA) films with uniform thickness and compared them to their air-dried counterparts. We first evaluated swelling ratios and elastic moduli for LHA films with varying degrees of substitution. The box-dried films swelled significantly less and were 1–2 orders of magnitude stiffer than air-dried films from the same LHA sample. Confocal microscopy revealed that box-dried films exhibited a regular microstructure, while air-dried films displayed a pore-size gradient and strong microstructure modulation due to convection flows. Local elastic modulus variations arising from these microstructures were assessed using nanoindentation mapping. Importantly, achieving the desired film stiffness requires much lower polymer modification when box-drying is used, enhancing the biological response to the material. These findings have implications for all polysaccharide formulations that utilize mixed solvents.

Random Responses of Shield Tunnel to New Tunnel Undercrossing Considering Spatial Variability of Soil Elastic Modulus

This paper investigates the effect of spatial variability of soil elastic modulus on the longitudinal responses of the existing shield tunnel to the new tunnel undercrossing using a random two-stage analysis method (RTSAM). The Timoshenko–Winkler-based deterministic method considering longitudinal variation in the subgrade reaction coefficient and the random field of the soil elastic modulus discretized by the Karhunen–Loeve expansion method are combined to establish the RTSAM. Then, the proposed RTSAM is applied to carry out a random analysis based on an actual engineering case. Results show that the increases in the scale of fluctuation and the coefficient of variation of the soil elastic modulus lead to higher variabilities of tunnel responses. A decreasing pillar depth and mean value of the soil elastic modulus and an increasing skew angle strengthen the effect of the spatial variability of the soil elastic modulus on tunnel responses. The variabilities of tunnel responses under the random field of the soil elastic modulus are overestimated by the Euler–Bernoulli beam model. The results of this study provide references for the uncertainty analysis of the new tunneling-induced responses of the existing tunnel under the random field of soil properties.

Study of Surface Chemistry, Temperature and Strain Rate on the Tensile Properties of Monolayer Graphene Oxide

The mechanical properties of graphene oxide (GO) during tensile fracture were studied using molecular dynamics methods, and the influence of hydroxyl and epoxy groups on the mechanical properties of GO was explored. In addition, the changes in mechanical properties of GO under different temperatures and strain rates were studied to gain a deeper understanding of its mechanical behavior. The results indicate that hydroxyl and epoxy groups have a significant influence on the elastic modulus, ultimate stress, and ultimate strain of GO. The presence of hydroxyl and epoxy groups can alter the molecular structure of GO, thereby affecting its ultimate stress and strain. When the number of hydroxyl groups is 16 and the number of epoxy groups is 20, the ultimate stress decreases by about 31% and the elastic modulus decreases by about 20%. The variation of elastic modulus, ultimate stress, and ultimate strain of GO with temperature was studied at three temperatures: 300[Formula: see text]K, 500[Formula: see text]K, and 800[Formula: see text]K. As the temperature increases, the amplitude of atomic vibration increases and internal defects and cracks in GO continue to form and expand. At the same time, its coefficient of thermal expansion also increases, causing deformation and loosening of the crystal structure, resulting in a decrease of about 10% in the ultimate stress of GO, and a slight decrease in the ultimate strain and elastic modulus. Finally, the influence of different strain rates on the mechanical properties of GO was studied. As the strain rate increases, the intermolecular interactions within GO are rapidly altered, and the previously loose structure gradually becomes tightly ordered, resulting in an increasing trend in the elastic modulus, ultimate stress, and ultimate strain of GO.

The influence of papaya shape on its mass model and mechanical properties

AbstractPostharvest handling tasks include fruit grading and minimizing loss. Fruits are often packaged into grades based on size and mass for uniformity and proper handling. Losses caused by mechanical damage can be reduced by understanding the fruit's response to loads. Papaya's (cv. Exotica) irregular shape and short shelf‐life are important factors for proper handling. This study aimed to develop a model for papaya mass based on geometric properties and to characterize its mechanical behavior when compressed along its major axis. For mass prediction, single‐ and multiple‐variable regression models using papaya's geometrical variables were developed. Despite its irregular shape, similar performance was observed in the best single‐ and multiple‐variable mass models (R2 ≈ 0.95, RMSE ≈ 82 g). However, the single‐variable model is likely more practical because only two axial lengths are needed and can be extracted from 2D images. For papaya's mechanical behavior, the results for elastic properties indicate some variations (p &gt; 0.05) in elastic modulus, and failure stress and strain along the major axis, while results for viscoelastic properties indicate significant variation (p &lt; 0.05) in the relaxation moduli. Overall, the bottom section is less resistant to deformation compared to the top. Therefore, reducing compression in the section could potentially reduce damage. Using the mechanical properties described here in computer simulation studies may provide more detailed load distribution. Mass modeling can aid the automation of papaya grading, while mechanical response characterization provides valuable information for designing postharvest handling systems.Practical ApplicationsPostharvest handling tasks include fruit grading and minimizing loss. Fruits are often packaged into grades based on size and mass for uniformity and proper handling. Losses caused by mechanical damage may be reduced by understanding the fruit's response to loads. Papaya's irregular shape and short shelf‐life are important factors for proper postharvest handling. Mass modeling can assist the automation of papaya sorting, while characterizing its mechanical response can assist the design of postharvest handling systems. The mass model result indicates that papaya's mass (cv. Exotica) can be predicted using two axial lengths, which can be easily obtained using 2D images. The advantage is that this task can be combined with other tasks using imaging data. While the mechanical properties of papaya indicate that its bottom section is more susceptible to deformation compared to the top when they are stored in an environment with minimal movements over an extended period. Therefore, in this setup, applying the compression load at the top section while minimizing compression load at the bottom may be more effective in preventing and minimizing mechanical damage.

Multiscale Characterization and Biomimetic Design of Porcupine Quills for Enhanced Mechanical Performance.

The mechanical properties of porcupine quills have attracted the interest of researchers due to their unique structure and composition. However, there is still a knowledge gap in understanding how these properties can be utilized to design biomimetic structures with enhanced performance. This study delves into the nanomechanical and macro-mechanical properties of porcupine quills, unveiling varied elastic moduli across different regions and cross sections. The results indicated that the elastic moduli of the upper and lower epidermis were higher at 8.13 ± 0.05 GPa and 7.71 ± 0.14 GPa, respectively, compared to other regions. In contrast, the elastic modulus of the mid-dermis of the quill mid-section was measured to be 7.16 ± 0.10 GPa. Based on the micro- and macro-structural analysis of porcupine quills, which revealed distinct variations in elastic moduli across different regions and cross sections, various biomimetic porous structures (BPSs) were designed. These BPSs were inspired by the unique properties of the quills and aimed to replicate and enhance their mechanical characteristics in engineering applications. Compression, torsion, and impact tests illustrated the efficacy of structures with filled hexagons and circles in improving performance. This study showed enhancements in maximum torsional load and crashworthiness with an increase in filled structures. Particularly noteworthy was the biomimetic porous circular structure 3 (BPCS_3), which displayed exceptional achievements in average energy absorption (28.37 J) and specific energy absorption (919.82 J/kg). Finally, a response surface-based optimization method is proposed to enhance the design of the structure under combined compression-torsion loads, with the goal of reducing mass and deformation. This research contributes to the field of biomimetics by exploring the potential applications of porcupine quill-inspired structures in fields such as robotics, drive shafts, and aerospace engineering.

Modelling deformable boundary by spherical particle for normal contact

The normal contact of the elastic spherical particle with deformable boundary is investigated in terms of the Discrete Element Method (DEM). The particle of the prescribed radius is moving under gravity and the initial velocity. The deformable boundary is treated as rigidly fixed spherical particle with variable elasticity modulus and variable radius. The limit case, approaching the infinite radius presents an elastic half-space, while increasing of the elasticity modulus presents the rigid boundary, respectively.&#x0D; The linear model and the nonlinear Hertz contact model used in the discrete element method are investigated numerically by applying the 5th-order Gear’s predictorcorrector integration scheme. The numerical model is tested by comparing it with analytical solution. The time variations of the particle positions, velocities and accelerations are presented. On the basis of simulation results the limit values of the boundary particle parameters are evaluated and recommendations for the boundary article parameters required in DEM simulation are drown.

Experimental Study on the Mechanical Properties of Rock–Concrete Composite Specimens under Cyclic Loading

The foundations of bridges and other tall buildings are often subjected to cyclic loads. Therefore, it is essential to investigate the mechanical properties of rock–concrete composite foundations under cyclic loads. In this paper, uniaxial cyclic loading and unloading tests were conducted on rock–concrete composite specimens using the TFD-2000 microcomputer servo-controlled rock triaxial testing machine. The stress–strain curves, elastic modulus variation, and energy dissipation were analyzed. The results showed that the stress–strain curves of composite specimens under uniaxial cyclic loading and unloading conditions formed hysteresis loops. The hysteresis loop exhibited a sparse–dense–sparse pattern under the upper stress of 27.44 MPa, which was 90% of the uniaxial strength. The elastic modulus, as well as the dissipated energy, decreased rapidly in the first few cycles and then gradually decreased at a constant rate, with the upper stress increasing to 27.44 MPa. Both the elastic modulus and the dissipated energy exhibited an accelerated stage before specimen failure. The primary failure mode of the composite specimen was split failure from concrete to sandstone. A damage variable was derived to better reflect the laws governing the damage evolution of the composite under cyclic loads.

Characterization of Ti-6Al-4V Bar for Aerospace Fastener Pin Axial Forging

Ti-6Al-4V warm forged fasteners are a critical part of the aerospace industry, as they are used in vast quantities for mechanical joining of components for the fuselage, wing-skin and aero-engine. These components are produced in vast quantities at rapid production rates through multi-blow axial forging However the rate that they are manufactured means that manufacturers rely upon periodic part conformance testing to understand if the part is within tolerance or if any undesirable manufacturing defects such as cracks or underfilling are present. Thus, a right-first-time manufacturing approach is essential to minimize non-conformant scrap. An analysis of the Ti-6Al-4V supplied raw material for axial forging, in a variety of different bar diameter sizes and from different industrial suppliers, was conducted. This was to attempt to understand whether material property variation or operator variation was the root cause for some material behaving differently during the manufacture route. Experimental testing was performed through microstructure characterization and mechanical testing methods. The volume fraction of the β-phase was noted to be marginally higher in material with good forgeability. The hardness of the inner core of the bar appears to be a critical material property for the Ti-6Al4V bar, with an overly hard bar-core hindering forgeability of the bar. This is believed to be due to the hotter central region malleability being key for forgeability. Micro-void porosity was also noted which could lead to stress concentration locations, or crack initiation, and as such is a deleterious property for forgeability. The experienced forgeability of the Ti-6Al-4V bars have been demonstrated to be sensitive to rather small variation in measured microstructure and mechanical property. It is believed that cumulative impacts of small differences, 1% variation in α-phase volume fraction, small variations in elongation to failure, 1% variation in elastic modulus and microhardness profile variation at the center of the bar of less than 10 HV0.3, can combine to significantly impact the forgeability of Ti-6Al-4V bar.

Vibration and acoustic characteristics of acoustic black hole plates with variable elastic modulus

Acoustic black hole (ABH), as a new wave manipulation technique, shows excellent applications in vibration and noise reduction of structures. Nowadays, most ABHs use materials with a fixed elastic modulus, limiting their low-frequency performance. Herein ABH plates with variable elastic modulus (VM-ABH) is designed, and its vibration and acoustic radiation characteristics are investigated by using numerical analysis. The results show that the vibration response of VM-ABH has a decrease of 5–13.2[Formula: see text]dB relative to that of the uniform texture ABH (UT-ABH) in the frequency range of 10–5000[Formula: see text]Hz, and the degree of energy aggregation is significantly improved. Moreover, the sound pressure level was reduced by 3.6 dB. Meanwhile, by linearly varying the elastic modulus in the center region of the VM-ABH, the effects of gradient index and terminal elastic modulus on the damping characteristics and dynamic response are revealed. The research results provide new objects for the study of vibration and noise reduction of ABH.