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Free vibration mode shapes for Metaconcrete B with low stiffness compliant layers, i.e. silicon rubber, during damping frequency of 5000 Hz. Resonant frequency at effective modal mass percentage respectively -(i) Mode 1: 260.45 Hz at 76.28 % , (ii) Mode 2: 1517.06 Hz at 3.28 %.
Source publication
In this contribution, a reduced‐order homogenization approach is adopted and extended to incorporate the linear viscoelasticity effect. A homogenized enriched model emerges from the homogenization framework, which is utilized here for the analysis of blast wave propagation in metaconcrete with linear viscoelastic compliant layer(s). A semi‐discrete...
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Citations
... However, metaconcrete based on local resonance commonly has the defect of narrow bandgaps. Once artificial aggregate structures are formed, they can only play a role in wave attenuation for specific frequency loads [7][8][9]. Therefore, researchers have conducted extensive research on the configuration of artificial aggregates to increase the bandgap width of the structure. Mitchell et al. [3] derived the relationship between the resonant frequency of artificial aggregates and the elastic layer modulus, thickness, as well as the core radius and density. ...
This paper proposes a novel protective material that enhances the impact resistance of meta-concrete by integrating rubber aggregates. The study delves into the mesoscopic mechanisms of wave attenuation in this material and the regulation of its performance accordingly. It first explores the effect of various design parameters of engineering aggregates on bandgap formation and then further investigates the influence of material viscoelastic properties on its bandgap width. Mesoscale simulations of spalling tests demonstrate that incorporating rubber aggregates can effectively expand the bandgap range, enhance energy absorption, reduce damage to the mortar matrix, and ultimately improve the impact resistance of metaconcrete. Simulation results in the present study highlight the effectiveness of rubber aggregates in strengthening meta-concrete's impact resistance.
... Numerical studies have been carried out demonstrating the reduction for both longitudinal and transverse vibration modes of metaconcrete [12][13][14][15][16][17][18][19] , in addition to experimental validations endorsing this behavior [20][21][22] , even if the inclusions are dispersed in a random 23,24 or quasi-random arrangement 25 . Furthermore, a simplified analytical model for metaconcrete filled with randomly distributed resonators has been proposed 26 . ...
... Xu et al. (2021bXu et al. ( , 2022a conducted impulsive load experiments to investigate the influence of different kinds of aggregates and bandgaps on the stress wave mitigation of metacnocrete rod. Tan et al. (2019) developed a homogenized enriched model for analyzing the blast wave propagation in metaconcrete with viscoelastic compliant layer. Liu et al. (2021Liu et al. ( , 2022 designed single-resonator and double resonator metconcrete spcimen and studied the vibration attenuation effect of metaconcrete specimen by frequency sweeping vibration experiment. ...
... Most multiscale studies on acoustic metamaterials have been restricted to linear elastic material except for the work [17,32], where hyperelastic or viscoelastic model was con-sidered for the rubber coating. While developing a classical FE 2 method with nonlinear materials is not easy, including different material models in the Direct FE 2 method is straightforward. ...
This paper presents an extension of Direct \(\hbox {FE}^{2}\) method for the study of dynamic problems in heterogeneous materials. The proposed method can be formulated based on either the Hill–Mandel principle or the extended Hill–Mandel principle, the latter of which enforces the energy contributed by the internal force and the inertial force consistent at two scales. Unlike the traditional \(\hbox {FE}^{2}\) method, it is not necessary to conduct two levels of finite element simulations linked by extensive information interchange. Instead, we reformulate the macroscopic variational statement with the microscopic contributions, leading to only a single coupled boundary value problem. The classical microscopic boundary condition used in the traditional \(\hbox {FE}^{2}\) method can be employed but it is implemented through kinematical constraints between the macro nodes and the micro nodes in the Direct \(\hbox {FE}^{2}\) method. The proposed method is illustrated by two numerical examples including a fiber-reinforced composite and an acoustic metamaterial. The results are verified by direct numerical simulations and it is shown that micro-inertia effects are not important in modeling low-velocity impact behavior of the composite but they are essential in capturing wave attenuation performance of locally resonant acoustic metamaterials.
... The effects on attenuation bands of inclusion shape, size, and volume fraction and the sensitivity to material properties were investigated numerically by Xu et al. [11]. Enriched homogenization techniques to describe the effective behavior of metaconcrete with viscous inclusion coatings have been introduced by Tan et al. [12] as a promising approach for the analysis of large structures. Numerical and experimental tests by Barnhart et al. [13] on an elastic metamaterial containing five-layer spherical resonators demonstrated the possibility of obtaining two attenuation regions that can be combined or overlapped by suitably tuning geometric and material parameters. ...
Background
Metaconcrete is a new concept of concrete, showing marked attenuation properties under impact and blast loading, where traditional aggregates are partially replaced by resonant bi-material inclusions. In a departure from conventional mechanical metamaterials, the inclusions are dispersed randomly as cast in the material. The behavior of metaconcrete at supersonic frequencies has been investigated theoretically and numerically and confirmed experimentally.
Objective
The feasibility of metaconcrete to achieve wave attenuation at low frequencies demands further experimental validation. The present study is directed at characterizing dynamically, in the range of the low sonic frequencies, the—possibly synergistic—effect of combinations of different types of inclusions on the attenuation properties of metaconcrete.
Methods
Dynamic tests are conducted on cylindrical metaconcrete specimens cast with two types of spherical inclusions, made of a steel core and a polymeric coating. The two inclusions differ in terms of size and coating material: type 1 inclusions are 22 mm diameter with 1.35 mm PDMS coating; type 2 inclusions are 24 mm diameter with 2 mm layer natural rubber coating. Linear frequency sweeps in the low sonic range (< 10 kHz), tuned to numerically estimated inclusion eigenfrequencies, are applied to the specimens through a mechanical actuator. The transmitted waves are recorded by transducers and Fast-Fourier transformed (FFT) to bring the attenuation spectrum of the material into full display.
Results
Amplitude reductions of transmitted signals are markedly visible for any metaconcrete specimens in the range of the inclusion resonant frequencies, namely, 3,400-3,500 Hz for the PDMS coating inclusions and near 3,200 Hz for the natural rubber coating inclusions. Specimens with mixed inclusions provide a rather uniform attenuation in a limited range of frequencies, independently of the inclusion density, while specimens with a single inclusion type are effective over larger frequency ranges. With respect to conventional concrete, metaconcrete reduces up to 90% the amplitude of the transmitted signal within the attenuation bands.
Conclusions
Relative to conventional concrete, metaconcrete strongly attenuates waves over frequency bands determined by the resonant frequencies of the inclusions. The present dynamical tests conducted in the sonic range of frequencies quantify the attenuation properties of the metaconcrete cast with two types inclusions, providing location, range and intensity of the attenuation bands, which are dependent on the physical-geometric features of the inclusions.
To mitigate shock wave propagation, a conventional engineered aggregate (EA) consisting of solid core coated with relatively soft material was designed to be tuned at targeted frequencies based on the local resonance mechanism. Previous studies demonstrated that metaconcrete consisting of conventional engineered aggregates (EAs) exhibited favourable attenuation performance of impulsive loading effects on structures. However, it was also found that the existence of the soft coating on conventional EA caused a reduction in the compressive strength of metaconcrete. In this study, a new type of EA by adding a relatively stiff shell outside the soft layer of the conventional EA was developed to overcome the issue of strength reduction whilst keeping its favourable wave attenuation properties. Quasi-static mechanical properties of metaconcrete consisting of conventional and newly developed EAs were examined through standard compression tests. The dynamic responses of the cylindrical metaconcrete specimens subjected to non-destructive and destructive impulsive loadings were also tested to investigate its wave attenuation capacity. The failure processes and the failure modes of metaconcrete made of different types of EAs under destructive tests were compared. It was found that adding a stiffer shell to the conventional EAs can improve the mechanical properties of metaconcrete while still keeping its good performance in mitigating stress wave propagation under both destructive and non-destructive loads.
To mitigate shock and vibration, metaconcrete with single-mass-coating resonators and double-mass-coating resonators was designed based on local resonance mechanism. The resonator is constructed by metallic ball coated with thin and soft rubber layer. Dynamic analysis method for finite-size metaconcrete is developed to predict the effective bands for vibration attenuation, which is verified by frequency-sweeping vibration experiment. Local resonance of the mass-coating system endows finite-size metaconcrete excellent vibration attenuation ability at the desired frequency band. Having two local resonation frequencies, double-mass-coating system effectively expands the vibration attenuation band from one to two and much wider compared with single-mass-coating system. The finite-size metaconcrete block designed in this research can dissipate 56.4% more energy than the common concrete block.
