Inherent Dissipation Research Articles

Effect of entropy evolution on electromagnetic response mechanism of carbon-coated medium- and high-entropy oxides

Metal oxides have attracted much attention due to their potential in electromagnetic wave absorption. However, the inherent energy dissipation capabilities of low-entropy metal oxides pose challenges in designing materials with optimal entropy levels. The regulation of entropy structure is anticipated to facilitate the development of novel electromagnetic functional materials featuring abundant active sites, adjustable specific surface area, stable crystal structure, unique geometric compatibility, and distinctive electronic structure. This study compared the electromagnetic loss performance of low, medium, and high entropy metal oxides in carbon matrices. As entropy increases, the number of phases expands, leading to enhanced interface polarization losses and improved impedance matching. However, further increases in entropy result in performance decline due to lattice distortions and mismatches in dielectric constant and magnetic permeability. Experimental data and theoretical analysis reveal that performance enhancement in medium-to high-entropy metal oxides is attributed to their unique morphology and the synergistic effects of multiple metal components, which enhance interfacial and defect polarization mechanisms. Heterogeneous interfaces and lattice defects provide additional polarization sites, aiding in the conversion of electromagnetic energy into heat. The presence of intermediate phases effectively absorbs and dissipates electromagnetic waves, thereby enhancing the overall absorption capability.

Experimental nonlinear response of a new tensairity structure under cyclic loading

Pneumatic structures are recognized as promising thin-walled structures for their advantageous features such as lightness, portability, versatile design, and ease of installation. Although their bearing capacity under monotonic static loads can be formidable, their inherent dissipation capacity is low and thus entails significant limitations when counteracting dynamic loads. A novel tensairity structure is here proposed to overcome this drawback. The innovative design features a cylindrical inflatable element integrated with NiTiNOL cables wrapped around and affixed to a slender beam positioned along its generatrix. A laboratory-scale prototype is employed to assess how the structure behaves under cyclic loading in comparison to a standalone inflated beam and a conventional tensairity structure outfitted with steel cables. This experimental study delves into the influence of internal pressure and pretension levels of the metallic cables. Experimental results unfold a smooth softening-type hysteretic behavior under cyclic loading, which is accompanied by a slight stiffness degradation and a moderate pinching. The comparative analysis of the experimental results also demonstrates the substantially improved and consistent dissipation capacity of the presented novel concept of tensairity structure, which thus offers superior stability under cyclic loads. A parametric identification based on a modified Bouc–Wen model is finally performed to simulate the hysteretic response of the structure. A correlation is also established between the identified parameters of the phenomenological model and the internal pressure, type and cables pretension levels. The excellent agreement between numerical predictions and experimental force–displacement cycles other than those used for the parametric identification demonstrates the suitability of the adopted phenomenological modeling.

A new high-order shock-capturing TENO scheme combined with skew-symmetric-splitting method for compressible gas dynamics and turbulence simulation

The high-order shock-capturing scheme is one of the main building blocks for the simulation of the compressible fluid characterized by strong shockwaves and broadband length scales. However, the classical shock-capturing scheme fails to perform long-time stable and non-dissipative simulations since the quadratic invariants associated with the conservation equations cannot be conserved as a result of the inherent numerical dissipation. Additionally, the overall computational cost for classical shock-capturing schemes is quite expensive as a result of the time-consuming local characteristic decomposition and the nonlinear-weights computing process. In this work, based on a new efficient discontinuity indicator, which distinguishes the non-smooth high-wavenumber fluctuations and discontinuities from smooth scales in the wavenumber space, a paradigm of high-order shock-capturing scheme by recasting the non-dissipative skew-symmetric-splitting method with newly optimized dispersion property for smooth flow scales and invoking the nonlinear targeted ENO (TENO) schemes for non-smooth discontinuities is proposed. The resulting TENO-S scheme not only successfully performs long-time stable computations for smooth flows without numerical dissipation, but also recovers the robust shock-capturing capabilities with adaptive numerical dissipation. Without the necessity of parameter tuning case by case, extensive benchmark simulations involving a wide range of flow length scales and strong discontinuities demonstrate that the proposed TENO-S scheme performs significantly better than the straightforward deployment of WENO/TENO-family schemes with better spectral property and higher computational efficiency.

Research on high power and heat flux aerospace electronic products of integrated thermal conduction technology

In response to the increasing demand for enhanced computational capabilities within satellite systems, there has been a simultaneous rise in the heat flux density of onboard electronic components. The thermal output of these components has significantly increased compared to traditional satellite processing electronics, leading to a concurrent elevation in the heat flux density related to processing chips and the surfaces accommodating equipment installations. This paper establishes a model for conduction heat dissipation in aviation electronic products. The outlined calculation methodology facilitates a preliminary assessment of the system’s heat dissipation capacity. The article further examines the inherent heat dissipation capabilities in two commonly employed structural configurations. Additionally, it introduces an integrated design approach for structural heat dissipation, including experimental considerations and validation outcomes. The assessment methodologies and design principles detailed in this article are particularly relevant and applicable to the thermal design imperatives associated with high-power electronic products deployed for the extended operational durations typical of spacecraft.

Determining the optimal layout of energy-dissipating mechanisms for hybrid self-centering walls

To eliminate the inherent energy dissipation deficiency of self-centering walls, hybrid self-centering walls (HSWs) have been developed by employing internal or external energy dissipating (ED) mechanisms. Mild steel bars have been extensively used as energy dissipators among ED mechanisms due to their affordability and simplicity. This study investigated the effect of ED bars layout on the damage, response features, collapse probability and collapse risk of HSWs. To this end, five different layout scenarios were defined first, and their response was studied by developing numerical models. Conducting nonlinear static and dynamic analyses (IDA), the scenarios damage, response features, collapse probability and risk were estimated and further examined to determine the optimal ED bars layout. Fragility analysis was performed on global and local scales, using IDA results, to estimate scenarios collapse probability. The results revealed that the wall with ED bars at the boundary elements outperformed other scenarios. Placing ED bars at the boundary elements of HSWs decreases the self-centering capability, fundamental period, collapse probability and the extent and severity of damage (especially in toe regions), while increases the energy dissipation capacity, adjusted collapse margin ratio and structural demand. Increasing ED bars cross-sectional area increases the extent and severity of damage. Using IDA results, the wall with ED bars at the boundary elements achieved the lowest ductility ratio; moreover, the response modification factor 3 was recommended for the strength-based design of HSWs. An optimality index (OI) was proposed herein to interpret the results quantitatively and determine the optimal layout. The calculated OI showed that placing ED bars at the boundary elements or along the wall width can be considered the optimal ED bars layout for achieving better seismic performance and decreasing the collapse probability and seismic risk of HSWs.

Slosh Dynamics of the Seismically Excited Chamfered Bottom Tank with Bottom-Mounted Internal Object

The inherent energy dissipation ability of the sloshing liquid is effective in vibration control of the supporting structure. Due to the advancement in the construction techniques in structural and mechanical fields, liquid containers of different geometrical configurations were required to avoid tank interference with rigid structural or mechanical components. The quantity of liquid that participates in the connective mode determines the effectiveness of the tuned liquid damper (TLD). To reduce the impulsive liquid mass and to increase the participation of liquid mass in the convective mode, a chamfered bottom tank with a bottom-mounted internal object is proposed in this study. A 2D finite element model developed employing the potential flow theory is used for the present numerical investigation. The effect of the frequency content of ground motion on the slosh dynamics of the chamfered bottom tank has been investigated under six different earthquake ground motions classified based on frequency contents. Also, the dynamic impulsive and convective components of base shear force and hydrodynamic pressure are quantified successfully. A parametric study has been performed to quantify the influence of the bottom-mounted object on the seismic response by altering the object’s height. The developed numerical model in this study can be utilized for tuning and designing structure-coupled chamfered bottom TLDs as well as the irregular liquid containers with internal submerged components.

Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids

AbstractThis study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite‐Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth‐order‐accurate reconstructions with and without Weighted Essentially Non‐Oscillatory limiting. Acoustic‐only upwinding for pressure and mass flux terms and advective‐only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st‐order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k−5/3 to smaller spatial scales by reducing dissipation either with higher‐order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k−5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

Physical Properties and Effect of Helium-Vacancy Pair on Tungsten/Graphene Composite as Plasma-Facing Materials from First Principles

Tungsten/graphene composite was developed and demonstrated to have good mechanical and thermal properties. Density functional theory calculations were performed to investigate elastic constants, elastic anisotropies and isotropic elastic moduli, thermodynamic properties and minimum thermal conductivity of tungsten/graphene with and without a helium-vacancy pair, and tungsten/graphane and tungsten/ditungsten carbide (tungsten/W2C) composites. The results show that tungsten/graphene composite has more toughness when compared with pure tungsten metal. It is noticed that the minimum thermal conductivity of tungsten/graphene composite is higher, introducing a potential application in heat dissipation at high temperatures. We give an honest appraisal of the anisotropic and isotropic (polycrystalline) elastic properties of tungsten/graphene, tungsten/graphane, and tungsten/W2C carbide composites. In addition, the results show that the graphene layer is a strong trap for the He atom, while He affinity to the graphene layer is weaker to a single vacancy. The formation of the He-vacancy pair due to trapping effects near the W/graphene interface will help to reduce the concentration of impurities and defects in the tungsten matrix and maintain the inherent heat dissipation properties under irradiation.

Energy dissipation mechanisms in three‐dimensional rocking motion of cylindrical structures

AbstractIn recent years, there has been a growing recognition that the rocking motion of structures, especially cylindrical ones, should be evaluated with three‐dimensional (3D) models. However, dissipation mechanisms in 3D models are complex and have yet to be well established. This paper presents an analytical study on an inherent dissipation mechanism based on the rolling friction model and an external dissipation mechanism based on energy dissipators (EDs) for 3D rocking cylindrical structures. Through a variational formulation, the nonlinear equations of motion are derived considering the rolling friction model and the Bouc–Wen model. Compared with the existing inherent dissipation model in literature, the rolling friction model has a noticeable advantage that it can capture the energy dissipation behavior during free vibration under various initial conditions. Additionally, the rolling friction model is more versatile since the contact coefficient is adjustable. On the other hand, external EDs further enhance the energy dissipation of the structures. Roles of the inherent and external mechanisms in the 3D rocking motion of cylindrical structures against earthquakes are assessed using a series of near‐fault pulse‐like ground motions. Results indicate the inherent dissipation mechanism, that is, the rolling friction model, cannot avoid overturning under near‐fault pulse‐like ground motions, leading to unstable structures. This is because an uplifted cylinder will continuously absorb energy from earthquake excitations, while the amount of energy dissipated by the rolling friction model is small. Comparatively, adding external EDs is effective in mitigating seismic responses and thereby avoiding overturning.

Ultrathin acoustic metamaterial as super absorber for broadband low-frequency underwater sound

In this work, an ultrathin acoustic metamaterial formed by space-coiled water channels with a rubber coating is proposed for underwater sound absorption. The proposed metamaterial achieves perfect sound absorption (alpha > 0.99) at 181 Hz, which has a deep subwavelength thickness (lambda {/}162). The theoretical prediction is consistent with the numerical simulation, which demonstrate the broadband low-frequency sound absorption performance of the proposed super absorber. The introduction of rubber coating leads to a significant decrease of the effective sound speed in the water channel, resulting in the phenomenon of slow-sound propagation. From the perspective of numerical simulations and acoustic impedance analysis, it is proved that the rubber coating on the channel boundary causes slow-sound propagation with inherent dissipation, which is the key to meet the impedance matching condition and achieve perfect low-frequency sound absorption. Parametric studies are also carried out to investigate the effect of specific structural and material parameters on sound absorption. By tailoring key geometric parameters, an ultra-broadband underwater sound absorber is constructed, with a perfect absorption range of 365–900 Hz and a deep subwavelength thickness of 33 mm. This work paves a new way for designing underwater acoustic metamaterials and controlling underwater acoustic waves.

An accurate and practical numerical solver for simulations of shock, vortices and turbulence interaction problems

Numerical simulations of high-speed compressible flows remain challenging in engineering as the appearance of shock waves poses difficulties for high-resolution schemes as well as explicit large eddy simulation methods. Therefore, in this work, we propose a practical numerical solver for simulations of shock-vortex and shock-turbulence problems with the implicit large eddy simulation approach and newly developed low-dissipative schemes. In order to handle the multi-scale raised in the shock-vortex and shock-turbulence problems, it is required that the flow solver can simultaneously solve the large-scale flow structures such as shock waves with numerical oscillation-free, the resolvable flow structures above the grid scale with low-dissipation, and the under-resolve isotropic sub-grid scale with numerical stability. To this end, a low-dissipative, structure-preserving scheme with rigorously adjusted numerical dissipation is employed in the proposed solver. The structure-preserving property of this scheme can ensure that the large-scale structure is solved without numerical oscillations and the low-dissipative property of this scheme can produce high-resolution results for the resolvable flow scales. Moreover, the sub-grid scale is solved and stabilized by the inherent numerical dissipation in the shock-capturing scheme. The proposed numerical solver is then applied to simulate a wide range of shock-vortex and shock-turbulence interaction problems including supersonic planar jets, transonic flows past a deep cavity and impingement of a supersonic jet on a cone mounted on a flat plate. A comparison is also made with the solver using conventional total variation diminishing schemes. The numerical results of the supersonic planar jet have demonstrated that the proposed solver can resolve the small-scale structure such as Kelvin–Helmholtz instability involved in shock and shear layer with high-resolution. Through the results of transonic flow past a deep cavity and comparisons with the experimental data, it is verified that the proposed solver can reproduce the turbulence statistical data. Furthermore, the proposed solver resolves the complex turbulent fluid mechanical phenomena in the impingement of a supersonic jet on a cone, which demonstrates the proposed solver can robustly handle irregular geometry. The proposed solver also enjoys simplicity without using the explicit sub-grid scale model and involving the complexity of very high-order schemes. Thus, this work provides an accurate and practical numerical solver for shock-vortex and shock-turbulence problems in high-speed flows.

Cyclic Response of Buckling-Restrained Stainless Steel Energy Dissipating Bars. I: Experimental Investigations

The seismic performance of structures could be enhanced by the inclusion of supplemental components that dissipate the earthquake-induced energy. This is especially crucial for rocking structures that possess low energy dissipation properties due to their damage avoidance mechanism. Amongst variously developed yielding-type energy dissipaters (EDs), buckling-restrained energy dissipating carbon steel bars have received considerable attention as they make the most use of the inherent energy dissipation of steel and are easy to fabricate. However, maintenance, repair costs, and performance disruptions owing to corrosive environments have been mostly disregarded in past investigations. Employing stainless steel can be a viable solution to overcome such issues. The work described in this two-part study sheds light on various aspects of the buckling-restrained stainless steel EDs through experimental and finite element (FE) investigations. The mechanical properties of type 304L stainless steel including uniaxial monotonic response, strain sensitivity, and cyclic hardening are characterized. It is shown that the material possesses high ductility along with substantial hardening characteristics. In the first phase of testing, energy dissipating bars with different fuse diameters and lengths are designed. Load and strain capacities and bar-tube interactions of the buckling-restrained energy dissipation device are studied through quasi-static tests. In the second phase of testing, various EDs are designed, fabricated with stainless and mild steel, and tested under quasi-static loading to validate the findings of the FE investigations. The test results demonstrate a stable hysteresis response of the buckling-restrained stainless steel EDs with a cyclic average strain capacity of 10%. The FE modelling procedure, calibration, and parametric studies are presented in the companion paper as Part II.

Review of Topside Interconnections for Wide Bandgap Power Semiconductor Packaging

Due to their superior material properties, wide bandgap (WBG) semiconductors enable the application of power electronics at higher temperature operation, higher frequencies, and higher efficiencies compared to silicon (Si). However, the commonly-used aluminum wire bonding as topside interconnection technology prevents WBG semiconductors from reaching their full potential, due to inherent parasitic inductances, large size, heat dissipation, and reliability issues of wire bonding technology. Therefore, this article presents a comprehensive review of topside interconnection technologies of WBG semiconductor power devices and modules. First, the challenges and driving factors for the interconnection of WBG semiconductor dies are discussed. Second, for each widely commercially used WBG semiconductor, i.e., silicon carbide and gallium nitride, technical details and innovative features of state-of-the-art interconnection techniques in packages are reviewed. Then, the majority of existing topside interconnection materials for WBG semiconductors are categorized and compared, followed by a discussion of their advantages, challenges, and failure modes. Based on this elaborate discussion, potential future directions of the interconnection technology development are given. It is concluded that the superior performance of WBG semiconductors can be obtained by combining novel materials with innovative designs for the topside interconnections.

Broadband low-frequency sound absorbing metastructures composed of impedance matching coiled-up cavity and porous materials

In this work, we propose a sound absorbing metastructure based on impedance matching coiled-up cavity embedded with porous materials (IMCCP), which demonstrates tremendous broadband (e.g., 4.55 times compared to conventional designs) low-frequency absorption capability with deep subwavelength thickness (e.g., ∼λ/10.96 at 602 Hz), without considering multiple units coupling. By tuning the geometric parameters of the non-coupled unit, relative bandwidths ranging from 111.07 % to 142.55 % are achieved. In particular, two notable perfect absorption peaks are obtained in the low- to mid-frequency range by changing the number of coiled-up channels. Theoretical predictions, numerical simulations and experimental measurements are conducted to investigate the acoustic characteristics of IMCCPs, and the results agree well with each other. Physically, the bandwidth broadening stems from the impedance matching effect which increases the degree of smoothness of sound wave propagation inside coiled-up space with strong inherent dissipation. The bandwidth broadening effect is generally confirmed for diverse geometrical and transport parameters of IMCCPs. This work contributes to understanding the sound wave propagation inside porous coiled-up space and designing broadband porous metastructures.

Low-frequency underwater sound absorption of hybrid metamaterials using dissipative slow-sound

In this work, a hybrid metamaterial is proposed as a new type of underwater absorber, which is composed of carefully designed periodically arranged units. Each unit consists of a perforated panel, a water chamber and a coiled water channel coated with rubber on the channel walls. The coiled channel is designed to reduce the thickness of the structure. The introduction of the rubber coating changes the boundary condition of the coiled channel from rigid to non-rigid, resulting in dissipative slow-sound propagation in the coiled channel. The slow-sound propagation leads to the decrease of resonant frequency, and its inherent dissipation can consume sound energy, resulting in perfect low-frequency sound absorption at subwavelength thickness. Theoretical and numerical results show that the proposed hybrid metamaterial exhibits more than 99% sound energy absorption at 155 Hz, and the thickness of the structure is only 1/456 of the wavelength of sound wave. This work paves the way for the design of ultrathin underwater low-frequency absorbers.

Application of High-Order WENO Scheme in the CFD/FW–H Method to Predict Helicopter Rotor Blade–Vortex Interaction Tonal Noise

The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation of the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting rotor BVI noise using a high-resolution numerical method based on the Reynolds-averaged Navier–Stokes and the Ffowcs Williams–Hawkings equations. The seventh-order improved WENO-Z scheme is utilized to minimize the inherent numerical dissipation of the reconstruction method in the monotone upstream-centered scheme for conservation laws (MUSCL), thereby improving the rotor wake resolution and the BVI noise-prediction accuracy. The three-layer dummy cell method is used to ensure that the flux at the boundary maintains seventh-order accuracy. The effectiveness of the flow solver and the acoustic solver is validated using the Helishape-7A rotor and the UH-1H rotor, respectively. The flow field and BVI noise characteristics of the OLS rotor obtained from the fifth- and seventh-order WENO-Z schemes are compared with that of the third-order MUSCL for coarse and fine background grids. The wake resolution, noise-prediction accuracy, and computational cost of the three schemes are compared. The results show that the high-order WENO scheme provides higher accuracy for flow field simulation and BVI noise prediction than the MUSCL, but the computational cost of the WENO scheme increases substantially as the grid resolution increases. However, the WENO scheme can predict BVI using a coarser grid than the MUSCL. The computational cost of the WENO scheme is relatively low under the same flow field simulation resolution.

Protection of Kapton from atomic oxygen attack by SiOx/NiCr coating

SiOx/NiCr coatings with different SiOx thicknesses were deposited by the combination of ion implantation (IIP), filter cathode vacuum arc (FCVA), and electron beam (E-beam) evaporation methods to protect flexible Kapton from atomic oxygen (AO) attack. Due to the ion stitching effect and mechanical interlocking of implanted Ni+, the ductility and supporting effect of the fcc γ (Ni-Cr) alloy layer, and the low growth stress of the SiOx, the SiOx/NiCr coatings showed high adhesion and toughness. Exposure tests indicated that the AO erosion yield of the 1 μm-thick SiOx/NiCr-coated Kapton was 5.6 × 10−26 cm3 atom−1, which was attributed to the formation of a compact and continuous thin SiO2 layer. In addition, the inherent kinetic energy and oxidation performance dissipation of AO on the thick inner walls of cracks helped to reduce the cavity cross-sectional area and maximum width in the matrix.

Material parametrization of natural rubber based compound and characterization of crack propagation under consideration of dissipative effects

Most concepts to characterize crack propagation were developed for elastic materials. When applying these methods to elastomers, the question is how the inherent energy dissipation of the material affects the cracking behavior. This contribution presents a numerical analysis of crack growth in natural rubber taking energy dissipation due to the visco-elastic material behavior into account. For this purpose, experimental tests were first carried out under different load conditions to parameterize a Prony series as well as a Bergström–Boyce model with the results. The parameterized Prony series was then used to perform numerical investigations with respect to the cracking behavior. Using the FE-software system ANSYS and the concept of material forces, the influence and proportion of the dissipative components were discussed.

Inherent Dissipation of Upwind‐Biased Potential Temperature Advection and its Feedback on Model Dynamics

AbstractHigher order upwind‐biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and antidiffusive fluxes are interpreted here as the effect of irreversible sub‐gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore, the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes. The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one‐dimensional advection‐dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.

Optimization of Viscoelastic Metamaterials for Vibration Attenuation Properties

Metamaterials (MMs) are composites that are artificially engineered to have unconventional mechanical properties that stem from their microstructural geometry rather than from their chemical composition. Several studies have shown the effectiveness of viscoelastic MMs in vibration attenuation due to their inherent vibration dissipation properties and the Bragg scattering effect. This study presents a multiobjective optimization based on genetic algorithms (GA) that aims to find a viscoelastic MM crystal with the highest vibration attenuation in a chosen low-frequency range. A multiobjective optimization allows considering the attenuation due to the MM inertia versus the Bragg scattering effect resulting from the periodicity of the MM. The investigated parameters that influence wave transmission in a one-dimensional (1D) MM crystal included the lattice constant, the number of cells and the layers’ thickness. Experimental testing and finite element analysis were used to support the optimization procedure. An electrodynamic shaker was used to measure the vibration transmission of the three control specimens and the optimal specimen in the frequency range 1–1200[Formula: see text]Hz. The test results demonstrated that the optimized specimen provides better vibration attenuation than the control specimens by both having a band-gap starting at a lower frequency and having less transmission at its passband.