Local Resonance Bandgaps Research Articles

Vibro-Acoustic Performance of a Fluid-Loaded Periodic Locally Resonant Plate

The vibro-acoustic performance of a fluid-loaded periodic locally resonant (LR) plate was examined in this research, with a specific focus on the effect of water fluid on the vibration and sound radiation of the LR structure. The analytical models of the fluid-loaded LR plate’s band gap, vibration, and acoustic radiation were theoretically derived with closed-form solutions, which can be used to predict the general vibro-acoustic rules of underwater LR structure. The results show that the LR band-gap width and Bragg frequency are significantly reduced when water fluid is considered. Besides, the frequency range that can be tuned to control the vibration and sound radiation for the LR plate with fluid is much narrower than that without fluid. The reason for inducing the above effects was also given in this research, which can be physically explained by the attached mass caused by the water fluid. In addition, the reason for the enhanced radiation efficiency close above the band gap was also discussed, which is caused by the change of radiation mode from corner or edge radiation to monopole radiation. Furthermore, adding small damping into the resonator could reduce the vibration and sound radiation in the frequency range above or close below the band gap, inducing the attenuation zone to be significantly broadened. Thus, designing the periodic resonators with proper damping could be an efficient method to make the LR plate more beneficial for vibration and noise reduction in water-surrounding applications.

Investigation of a magnetorheological elastomer metamaterial sandwich beam with tunable graded stiffness for broadband vibration attenuation

Metamaterials with local resonance show promising application prospects in low-frequency vibration attenuation. However, with the drawback of narrow band gap, such potential is greatly limited. In order to broaden the local resonant band gap, a semi-active graded magnetorheological elastomer (MRE) metamaterial sandwich beam (GMREMSB) with real-time tunable graded stiffness was proposed and investigated in this study. For theoretical calculation, a mass-spring model was established for the GMREMSB. Then the calculated band gap and transmissibility using Timoshenko beam theory and spectral element method were compared. An experimental test was also conducted for verification. The results show that the bandwidth of the proposed GMREMSB can be widened by the graded stiffness arranged in ascending order. The experimental band gap of the GMREMSB under the graded current of 0.0–0.5–1.0 A is 6.4 Hz wider than the band gap of the periodic structure with the single current of 0.0 A and is 5.0 Hz wider than that of 1.0 A. The growth rate reaches 15.06% and 11.39%, respectively.

Mode purification for multimode Lamb waves by shunted piezoelectric unimorph array

Guided wave-based nondestructive testing and structural health monitoring methods have been developed to exhibit attractive potentials and best prospects for rapid and sensitive detection of defects or damage in engineering structures. Different modes of guided waves can provide different sensitivities of damage detection. However, the multimode and mode conversion nature of guided waves poses significant challenges to mode purification of received signals. This study aims to design a metamaterial-based smart transducer for mode purification of Lamb waves in a plate, which can filter out an undesired mode of the Lamb wave to enhance sensing and actuating signals of a dominated mode. The smart transducer consists of a periodic array of shunted piezoelectric unimorphs with staggered polarization directions and is bonded on the surface of a host plate. Numerical and experimental results show that a local resonance bandgap for an anti-symmetric Lamb wave, rather than a symmetric Lamb wave, can be obtained and tuned through the shunting inductance circuit. Within such mode bandgap, the wave control for propagating a specific mode of the Lamb wave can be further realized, i.e., the mode of the Lamb wave is purified. The design presented herein offers enhanced capabilities in controlling guided wave propagation for engineering applications and nondestructive testing techniques.

Vibration isolation of mechatronic metamaterial beam with resonant piezoelectric shunting

Mechatronic metamaterials are of utmost significance in vibration isolation owing to their tunable bandgaps. However, their intricate mechanisms are always challenging for environmental changing. In this study, a mechatronic metamaterial beam shunted with inductor–resistor–capacitor (LRC) shunting circuits is discussed, with the aim of obtaining tunable bandgaps. The tunable bandgap can be effectively used to achieve low-frequency vibration isolation by changing the selection of circuit parameters. The mechatronic metamaterial beam model is established using Hamilton's principle and Kirchhoff's law, and the dispersion relationship is derived by applying the transfer matrix method. An experimental rig of a mechatronic metamaterial beam is used to validate the analytical methods. The experimental results support the analytical results. Mechatronic resonant and Bragg bandgaps shown in the frequency response curves (FRCs) can block vibration transmission, thus achieving vibration isolation within a certain frequency range. Parameters studies are conducted to illustrate how the mechanic and electric parameters affect the bandgaps. It is found that the electric parameters affect the position of the mechatronic local resonant bandgap in the FRCs. Thus, low-frequency isolation can be achieved by choosing the appropriate electric parameters.

Theoretical study on dispersion relations of chiral acoustic metamaterials considering mass-rotation

Low-frequency vibration affects the performance of equipment such as aircraft, ships, automobiles, etc., and the noise caused by vibration harms human health. Acoustic metamaterials can dampen elastic waves at specific frequencies due to their bandgaps. In this work, an acoustic metamaterial structure is designed with the introduction of chirality to obtain wider bandgaps. Considering the rotation of the structural parts, the periodic structure is equivalent to an ideal 6-DOF-model through the introduction of Bloch's theorem, analyzed its dispersion relationship and the influence of structural parameters theoretically, and the vibration characteristics of the structure are given with the help of FEM results. The results show that the designed structure has a local resonance bandgap of around 0.12 and the maximum transmission loss exceeds 40 dB. Parametric analysis of this structure shows that structures with different parameters have up to four bandgaps in total between the second and sixth dispersion curves, and the distribution of the bandgaps is centrosymmetric. Under some parameters, the total bandwidth reaches 83.5% of the total frequency range and reduced the normalized frequency of the first bandgap to lower than 0.07. Compared with existing structures, the newly designed structure has lower bandgap frequency and higher bandwidth, and its theoretical model has outfitted with high efficiency and accuracy. This research can provide theoretical guidance and reference for designing such kinds of acoustic metamaterials.

Research on vibration reduction performance of metaconcrete based on local resonance theory

Metaconcrete is a newly manufactured construction material designed based on local resonance theory, which can reduce impact shock and structural vibration. The local resonant bandgap generated by metaconcrete cells is the key to effectively attenuating elastic waves. However, there are relatively few studies on the vibration reduction performance of the metaconcrete, and there is currently no method for designing the metaconcrete cell according to the target vibration reduction frequency range. In this study, the generation mechanism and influencing factors of the metaconcrete cell bandgap were first studied, and then the bandgap prediction formula of the metaconcrete cell was deduced based on the bandgap generation mechanism. Secondly, the vibration reduction mechanism of the metaconcrete under different frequency vibration loads was studied. Finally, a metaconcrete cell design method based on the bandgap prediction formula is proposed. The results showed that the bandgap starting frequency of the metaconcrete cell was mainly determined by the translational vibration mode of the resonator, and the resulting vibration energy is strongly coupled with the long-wave traveling energy of the matrix, thereby opening the local resonance bandgap. The cut-off frequency of the bandgap was determined by the opposite vibration mode between the resonator and the matrix, and the coupling between the two weakens, resulting in a closed bandgap. The elastic modulus and Poisson's ratio of the soft coating and the density of the matrix are the main material factors affecting the bandgap. In addition, a larger soft coating radius can obtain a lower frequency bandwidth, and a larger resonator radius and a smaller matrix side length can obtain a larger bandgap width. The metaconcrete has a shielding and attenuating effect on the vibration within the bandgap range, and the vibrational energy is dissipated through multiple conversions between the kinetic energy of the resonator and the elastic strain energy of the soft coating. The proposed method can design metaconcrete cells that meet the target vibration reduction frequency range.

Subwavelength tunable topological interface modes in metamaterial beams on elastic foundation

In this paper, by the aid of zone folding mechanism, the topological transition point (TTP) is produced in novel metamaterial beams on elastic foundation. Different from the existing topological system, the TTP is located between the locally resonant band gap (LRBG) and the transition zone, which are induced by the local resonance of resonators and Winkler foundation, respectively. The position of TTP can also be tuned effectively by the natural frequency of resonators and critical frequency of Winkler foundation. After opening the TTP by space modulation of resonators, two types of unit cells are produced, and a new topological band gap (TBG) is formed. Besides, topological properties of both types of unit cells are discussed by dispersion analysis. The band inversion and different Zak phase indicate that these two types of unit cells are topologically distinct. Therefore, the topologically protected interface mode (TPIM) will appear at the interface between two domains. The numerical simulation confirms the existence of TPIM. Meanwhile, the robustness of TPIM is investigated, including the influence of damping and defects. In detail, the transmission efficiency of TPIM is reduced with damping, while the frequency and width of TPIM are little affected. Interestingly, the introduction of mass defects is found to improve the transmission efficiency of TPIM. This novel topological system is expected to open new avenues for vibration mitigation and energy harvesting.

Inertial amplified topological metamaterial beams

To break the limitation of large mass required for low-frequency topologically protected interface modes (TPIMs), a novel inertial amplified topological metamaterial beam is proposed in this work. Detailed analytical and numerical studies are conducted to investigate the dynamic characteristic of this system. The Dirac cone (DC) is formed at the boundary of the Brillouin zone through the zone-folding method. Thanks to the inertial amplification mechanism, the lower-frequency DC and wider local resonance bandgaps (LRBGs) are obtained without sacrificing total stiffness or increasing total mass. Besides, the DC and LRBG can be tuned effectively by the arm length ratio of the lever. In order to realize the TPIM, two topologically distinct supercells are constructed by space modulation of resonators. Transmission simulation confirms the existence of TPIM between two domains with different topological properties. The energy concentration of TPIM is quantified by the quality factor. Moreover, the tunability and robustness of TPIM are also verified. Besides, to further enlarge the response area of TPIM, the sandwich structure is proposed. Although the peak displacement is reduced with the enlargement of response area, the displacement is still well confined within the sandwich layers. This novel inertial amplified topological metamaterial beam is expected to promote the application of topological devices, especially in the low-frequency lightweight challenging conditions.

A metamaterial plate with magnetorheological elastomers and gradient resonators for tuneable, low-frequency and broadband flexural wave manipulation

Incorporating magnetorheological elastomers and multiple gradient resonators (MRE–MGRs), a novel metamaterial plate is proposed, which entails low-frequency, broadband and tuneable bandgap features. The proposed MRE-MGR design embeds an adaptive magnetic field adjustment mechanism to alter the elastic modulus of the MRE to modulate the local resonance bandgap frequency and bandwidth. A bandgap prediction model of the metamaterial plate is developed using the plane wave expansion (PWE) method. Integrated into the model through equivalent stiffness terms, the magneto-controlled modulus of the MRE can be estimated using the energy method and magnetic dipole theory. The established model allows for revealing the dispersion relation of the proposed metamaterial plate under various magnetic fields. The predicted tuneable bandgaps, vibration transmission loss and flexural wave modulation of the metamaterial plate are validated through comparisons with finite element simulations. Numerical analyses show the benefit of the gradient resonator design, which alongside the effective MRE tuning, entails broadening low frequency bandgaps at 92 Hz (relative band of 79.3% for the exponential gradient) and 72.7 Hz (relative band of 65.9% for the linear gradient). The mechanisms underpinning the observed bandgap widening phenomenon are analysed and attributed to the combined effects arising from the gradient design of the distributed resonators and the effective tuning of the MRE elastic modulus under magnetic field modulation. The proposed metamaterial plate functionally achieves simultaneous magnetron adjustment of the bandgap frequency and its width, thus holding great promise for applications such as flexural wave guiding as well as vibration and sound radiation control in planar structures.

Seismic Composite Metamaterial: A Review

The modern construction revolution throughout the past two decades has brought the need for ground vibration mitigation, and this has been one of the major study areas. These studies were mainly focused on the effect of forestation on vibration reduction as the available natural metamaterial. Physical methods such as the finite element method and the boundary conditions of 2D and 3D applications in ground vibration reduction have been developed. Many researchers, scientists, and organizations in this field have emphasized the importance of these methods theoretically and numerically. This paper presents the historical context of resonant metamaterials (MMs), the current progress of periodic 2D and 3D structures, and the possible future outcomes from the seismic metamaterials (SMs), and it relates them with their elastic counterparts to the natural metamaterial (NMs). The idea of bandgaps (FBGs) in the frequency range of interest is reviewed and discussed in some detail. Moreover, the attenuation associated with ground vibrations, noise, seismology, and the like is explained by managing the peculiar mechanisms of ground vibrations. However, a comprehensive computational review focuses on shielding MMs for ground vibration mitigation in urban areas. This phenomenon led to unique features for various techniques to control the bandgap width for various construction applications. Ecological solutions involve the creation of an economic, environmentally based seismic shield for both the Bragg scattering and the local resonance bandgaps. Reportedly, additive studies based on numerical simulation and experiments have improved the functionality of the 2D and 3D periodic structures. It was found that the mechanical properties differ (i.e., stiffness, Poisson’s ratio, and bulk density) and that the geometrical parameters (i.e., lattice, model dimensions, distance from vibration sources, and number of periodic structures) exhibited strong effects on the width and location of the derived FBGs. The geometrical properties of the used unit cell have a strong effect on the attenuation mechanism. Although deep analysis was created in much of the previous research, it was revealed, based on that research, that the attenuation mechanism is still unclear. However, this review article presents a detailed exposition of the recent research progress of the seismic metamaterials, including 2D, 3D, and the main mechanisms of the theoretical backgrounds of energy attenuation. It also summarizes the effects of the factors on the width and location of the bandgaps at a low frequency. In addition, the natural metamaterials and the study of the urban environment are surveyed. The major findings of this review involve the effectiveness of NMs for different functionalities in ground vibration attenuation, which leads to diverse purposes and applications and proposes a roadmap for developing natural materials for clean and quiet environments.

Thomson scattering-induced bandgap in planar chiral phononic crystals

Releasing the dependence of the low-frequency and broad bandgaps on low stiffness and bulky masses has been an intractable bottleneck. Although inertial amplification is a terrific candidate for addressing the barrier, numerous extended ideas are limited to the classical models, thus, slowing or stalling the advances in this demand. To break this limit, we report a kind of planar chiral phononic crystal based on Thomson scattering. Different from the optimization effect produced in the locally resonant phononic crystals, the mirrored chirality can open a Thomson scattering-induced broad bandgap when the local resonant sub-structure is discarded. In addition, while simplifying the material components, we lower the starting frequency of the bandgap with a virtually unchanged width for the same lattice constant, stiffness and mass. Consequently, the starting frequency of the attenuation can be in the same order of magnitude as the local resonance bandgap, while the width is significantly better than the latter. Our proposal may open a new way to manipulate broadband elastic waves and validate that Thomson scattering is a promising alternative approach and mechanism for bandgap formation.

Bandgap characteristics of the two-dimensional missing rib lattice structure

In this paper, the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem. The tuning of the width and position of the bandgap is achieved by changing the local structural parameters, i.e., the rotation angle, the short beam length, and the beam thickness. In order to expand the regulation of the bandgap, the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed. The results show that the mass density and stiffness of the structure have significant effects on the bandgap, while Poisson’s ratio has no effect on the bandgap. By analyzing the first ten bands of the reference unit cell, it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction, and these bandgap widths are wider. The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure, and this dipole resonance originates from the coupling of the bending deformation of the beam elements. In the band structure, the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance, which is different from that with the conventional negative slope formed by the coupling of two resonance modes. This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials, as well as for the regulation of bandgaps and the suppression of elastic waves.

Surface wave attenuation by periodic hollow steel trenches with Bragg band gap and local resonance band gap

The use of phononic crystals and elastic metamaterials has been a significant concern as an efficient approach to attenuate the surface waves of ambient vibration and seismic vibration. In previous research, elastic metamaterials with periodic array of pillars or other forms of standing structures (such as H-fractal steel or built-up structural steel) erected on soil substrate can achieve a low frequency surface wave band gap (BG). However, such metamaterials with standing structures occupy land and affect the esthetics of cities, and buried metamaterials such as cross-like-cavity or hollow-cylinder structures with large size in soils necessitate continual maintenance for the stability of cavity soil structure. Thus, this study proposes two types of periodic hollow steel trenches exhibiting both a Bragg BG and a local resonance BG, the steel plates are used to support the soil on both sides of the trench to meet the stability requirements of cavity soil structure and avoid toppling or landslide of soils. The dispersion relations of periodic hollow steel trenches are calculated by using finite element method and the mechanism of generation for two kinds of BGs are interpreted by the eigenmodes. Furthermore, the effectiveness of periodic hollow steel trenches on isolating surface waves within the BGs is demonstrated in both frequency domain and time domain analysis. Several significant geometrical and material parameters on BGs that can affect the BG are studied as well. This study provides a new approach using the coupling effects of Bragg BG and local resonance BG to simultaneously attenuate the surface waves induced by the ambient and seismic vibration in a more practical way.

Enhanced vibration suppression using diatomic acoustic metamaterial with negative stiffness mechanism

This paper presents a diatomic-chain locally resonant acoustic metamaterial (LRAM) structure with negative-stiffness mechanism for enhanced suppression of vibration transmission. The bandgap properties of the diatomic configuration were studied and shown to enhance performance benefits by introducing two extra bandgaps that exploit Bragg scattering, located on both sides of the local resonant bandgap. The upper band-folding-induced bandgap exhibits better performance than the lower band-folding-induced bandgap. Converting a monoatomic configuration into a diatomic configuration is shown to be beneficial. A dispersion relation analysis is performed and new phenomena are revealed from the viewpoint of the vibration power flow and wave transmittance, demonstrating the potential application of negative stiffness for performance improvement. A geometrical nonlinear mechanism is studied, and the results demonstrate the possibility of providing a constant negative stiffness under specific material parameters. With the application of this negative-stiffness mechanism for the critical, effective stiffness value, the locally resonant bandgap of the metamaterial configuration shifted toward the lower frequency range, effective from zero frequency, thus achieving ultralow frequency vibration control. The proposed implementation of the negative-stiffness mechanism in a diatomic metamaterial structure is shown to yield desirable bandgap properties, providing potential benefits for vibration suppression.

Vibration Control of Footbridges Based on Local Resonance Band Gaps

Vibration Control of Footbridges Based on Local Resonance Band Gaps

Double-beam metastructure with inertially amplified resonators for flexural wave attenuation

A new type of double-beam metastructure with periodically attached inertially amplified (IA) resonators is designed to attenuate the flexural wave propagation in the low-frequency range. An analytical approach based on the spectral element method (SEM) and the Wittrick-Williams algorithm is developed. The results of SEM show superior accuracy and an order of magnitude higher computational efficiency compared to the finite element method (FEM). Employing the developed approach, the wave attenuation behavior is presented as a function of the parameters including truss angle, beam thickness, IA mass, spring, and damper location to exhibit the perfect adjustability of bandgaps realized by the proposed structure. The local resonance bandgap frequencies are effectively lowered under the effect of inertial amplification. In addition, the damping amplification is also achieved by the IA structure, which is advantageous for extending the wave attenuation range. Finally, multibody dynamics numerical simulations are carried out to validate the reliability of the theoretical method and the rationality of simplifications used in the theoretical derivation. Furthermore, the formation mechanism of bandgaps is revealed by exploring the eigenmode shape on dispersion curves to obtain a thorough understanding of the structure.

Acoustic attenuation characteristics of the muffler phononic crystal with hybrid resonators

Aiming at achieving broadband and strong sound attenuation in the duct, this study proposes one compact and hybrid muffler phononic crystal. The two-dimensional (2D) transfer matrix method is applied to calculate the transmission loss (TL) of one unit cell validated by the numerical simulation and experiment. On this basis, the unit cell dispersion theory is employed to predict the bandgap properties of the infinite periodic mufflers. The sound reduction mechanism in the hybrid muffler is disclosed, while the effect of the period number on the acoustic performance is examined. It demonstrated that the acoustic resonant behaviors of the short-length mufflers are conducive to the continuous and superior attenuation band through the compact structure. The number of the TL domes and the boundary length of the short chamber could be evaluated by the cut-off frequency at the (0,1) radial mode and the first passing frequency for the muffler. Although each resonant-type component of the hybrid muffler is responsible for the TL peaks at different frequency ranges, via the coupling effect, they provide remarkably improved performance over a wide frequency range. The unit cell periodicity brings two types of bandgap, the locally resonant bandgap (LRG) and Bragg bandgap (BG), further enhancing the attenuation amplitude. Utilizing the different resonance mechanisms as well as the merging of the LRG and BG, the hybrid muffler phononic crystal is improved, which possesses a wide attenuation range with a tinier structure. The results develop new approaches for broadband and strong sound attenuation using the concept of the phononic crystal and offer a promising application in duct noise control.

Q-Factor Enhancement of Coupling Bragg and Local Resonance Band Gaps in Single-Phase Phononic Crystals for TPOS MEMS Resonator.

This paper presents a type of single-phase double “I” hole phononic crystal (DIH-PnC) structure, which is formed by vertically intersecting double “I” holes. By using the finite element method, the complex energy band curve, special point mode shapes, and different delay lines were calculated. Numerical results showed that DIH-PnC yielded ultra-wide band gaps with strong attenuation. The formation mechanism is attributed to the Bragg-coupled local resonance mechanism. The effects of the pore width in DIH-PnC on the band gaps were further explored numerically. Significantly, as the pore width variable, the position of the local resonance natural frequency could be modulated, and this enabled the coupling between the local resonance and the Bragg mechanism. Subsequently, we introduced this DIH-PnC into the thin-film piezoelectric-on-silicon (TPOS) resonator. The results illustrated that the anchor loss quality factor () of the DIH-PnC resonator was 20,425.1% higher than that of the conventional resonator and 3762.3% higher than the of the cross-like holey PnC resonator. In addition, the effect of periodic array numbers on was researched. When the reached 1.12 × 106, the number of the period array in DIH-PnC only needed to be 1/6 compared with cross-like holey PnC. Adopting the PnC based on the coupling Bragg and local resonance band gaps had a good effect on improving the of the resonator.

Propagation of elastic waves in metamaterial plates with various lattices for low-frequency vibration attenuation

Elastic wave propagation characteristics of elastic metamaterial plates embedded scatterer with various lattices are explored numerically and experimentally in this study, for the attenuation of in-plane longitudinal and out-of-plane flexural waves in the subwavelength frequency region. Firstly, the mathematical models of the elastic metamaterial plates are established, and the dispersion relations are derived by the plane wave expansion (PWE) method based on Bloch's theorem. Furthermore, the applicability of the irreducible Brillouin zone (IBZ) for different lattices is also investigated through iso-frequency contours. The analysis of the bandgap formation mechanism indicates that the proposed metamaterial plates can enlarge the bandgaps (BGs) in the low-frequency range by coupling Bragg and local resonance BGs. Moreover, the influences of the scatterer shapes, geometric and material parameters on the BGs are investigated, and which combination of parameters has positive significance for opening low-frequency broadband is also discussed. The results show that the vibration transmittance obtained by experiment and numerical calculation is in good agreement with the predicted results of band structures. Therefore, the elastic metamaterial plates should be promising in the application of low-frequency wave mitigation.

A self-sensing and self-actuating metamaterial sandwich structure for the low-frequency vibration mitigation and isolation

Sandwich structures (SSs) are widely deployed in engineering applications, such as for the low-frequency vibration or acoustic mitigation and isolation. However, it is challenging to enhance their low-frequency vibration mitigation and isolation performance while maintaining their multi-functionalities, such as lightweight, high bending stiffness, and high impact absorption ability, etc. To achieve this objective, local resonators are introduced into a hollow-tube core lattice sandwich structure (HLSS) in this paper, which is referred to as the metamaterial sandwich structure (MMSS-1). The proposed MMSS-1 is composed of periodically distributed thin-walled hollow tubes with attached resonators as the core, and two thin cover-plates or face-sheets. The band structures and the corresponding eigenmodes of the unit-cell of the MMSS show that both the Bragg scattering and the local resonance band-gaps coexist in the proposed MMSS-1. The influences of the key geometrical and material parameters of the MMSS-1 on the band-gaps are analyzed in details. Then, the piezoelectric patches are attached to the top and bottom face-plate surfaces of the MMSS-1 and resonators to form the MMSS-2, and they are shunted via an active feedback control to build the MMSS-3. The effects of the displacement feedback control gains on the band-gaps of the MMSS-3 are studied. Based on the active displacement feedback control and differential evolution (DE) optimization algorithm, a self-sensing and self-actuating strategy is developed to lend the self-adaptive capability to the MMSS-3, which is referred to as the self-adaptive MMSS. The vibration or flexural wave propagation in the finite-sized self-adaptive MMSS is numerically simulated to demonstrate its outstanding ability for low-frequency vibration mitigation and isolation. It shows that the proposed self-adaptive MMSS can evolve different control parameters automatically to widen and merge Bragg scattering band-gaps and local resonance band-gaps without human intervention. In addition, the vibration attenuation inside the band-gaps is also enhanced. The proposed self-sensing and self-actuating strategy can improve the vibration mitigation and isolation performance of the HLSSs significantly in the low-frequency range. The proposed self-adaptive MMSS may pave a novel and feasible way for the design and applications of the HLSSs for the low-frequency vibration mitigation and isolation in civil engineering, mechanical engineering, and aerospace engineering etc. Moreover, the proposed self-adaptive strategy via self-sensing and self-actuating can be also applied to other types of the SSs for improving their vibration mitigation and isolation performance, and for the NVH (noise, vibration and harshness) of vehicles, high-end equipment and high-precision instruments.