Phononic Crystal Beam Research Articles

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

Viaduct-Like Phononic Crystal Beams with Point Elastic Supports for Robust Transverse Wave Transport

Viaduct-Like Phononic Crystal Beams with Point Elastic Supports for Robust Transverse Wave Transport

Low-Frequency Bandgap Characterization of a Locally Resonant Pentagonal Phononic Crystal Beam Structure.

This paper proposes a local resonance-type pentagonal phononic crystal beam structure for practical engineering applications to achieve better vibration and noise reduction. The energy band, transmission curve, and displacement field corresponding to the vibration modes of the structure are calculated based on the finite element method and Bloch-Floquet theorem. Furthermore, an analysis is conducted to understand the mechanism behind the generation of bandgaps. The numerical analysis indicates that the pentagonal unit oscillator creates a low-frequency bandgap between 60-70 Hz and 107-130 Hz. Additionally, the pentagonal phononic crystal double-layer beam structure exhibits excellent vibration damping, whereas the single-layer beam has poor vibration damping. The article comparatively analyzes the effects of different parameters on the bandgap range and transmission loss of a pentagonal phononic crystal beam. For instance, increasing the thickness of the lead layer leads to an increase in the width of the bandgap. Similarly, increasing the thickness of the rubber layer, intermediate plate, and total thickness of the phononic crystals results in a bandgap at lower frequencies. By adjusting the parameters, the beam can be optimized for practical engineering purposes.

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

In this paper, a new defective phononic crystal (PC) microbeam model in a thermal environment is developed with the application of modified couple stress theory (MCST). By using Hamilton’s principle, the wave equation and complete boundary conditions of a heated Bernoulli–Euler microbeam are obtained. The band structures of the perfect and defective heated PC microbeams are solved by employing the transfer matrix method and supercell technology. The accuracy of the new model is validated using the finite element model, and the parametric analysis is conducted to examine the influences of size and temperature effects, as well as defect segment length, on the band structures of current microbeams. The results indicate that the size effect induces microstructure hardening, while the increase in temperature has a softening impact, decreasing the band gap frequencies. The inclusion of defect cells leads to the localization of elastic waves. These findings have significant implications for the design of microdevices, including applications in micro-energy harvesters, energy absorbers, and micro-electro-mechanical systems (MEMS).

Mechanical vibration absorber for flexural wave attenuation in multi-materials metastructure

Vibration isolation is a promise to suppress mechanical vibration from a host structure, similarly, a mechanical vibration absorber, a simple but effective device to attenuate flexural wave propagation, which has been implemented in civil and mechanical engineering. This paper presents a type of composite sandwich phononic crystal to attenuate the flexural wave propagation in a beam structure, which can effectively suppress mechanical vibration in a broad band gap by repetitively arranging phononic crystal. First, the elastic wave dispersion characteristic in a composite sandwich beam structure is derived, and a triangular shape phononic crystal for flexural wave attenuation by taking advantage of destructive interference is presented. Then two dimensional phononic crystals are designed by assembling four different unit-cells of metabeam. Finally, numerical experiments are conducted to verify the effectiveness of the proposed mechanical metamaterial absorbers to attenuate flexural wave propagation, the numerical results indicate that the proposed metamaterial is of good performance in mechanical vibration suppression, which can effectively mitigate structure vibration in low-frequency domain than the structure without phononic crystal and single layer metamaterial beam structure. It is the first attempt to design a mechanical metamaterial absorber with the mechanism of destructive interference with composite sandwich phononic crystal.

Ultrahigh frequency vibration control in a piezoelectric phononic crystal beam at the nanoscale considering surface effects

Ultrahigh frequency vibration control in a piezoelectric phononic crystal beam at the nanoscale considering surface effects

Widening the Band Gaps of Hourglass Lattice Truss Core Sandwich Structures for Broadband Vibration Suppression

Abstract This paper proposes a novel phononic crystal sandwich beam (PCSB) for low-frequency and broadband vibration suppression. The representative volume element (RVE) consists of two hourglass truss unit cells with the same span but different rod radii. After validating the modeling method, a model of the PCSB is established to calculate band structure and transmittance response, and the results show good agreement. It is found that the PCSB can open wider and lower band gaps compared to a traditional sandwich beam (TSB). The band-folding mechanism is applied. The PCSB breaks the spatial symmetry, becomes diatomic, and opens the folding points, finally leading to two band-folding-induced gaps. The experiment is conducted on the PCSB, and the vibration band gap property is confirmed. Subsequently, the impacts of geometric parameters on the PCSB’s band gaps are investigated in detail. Design guidelines for tuning the geometric parameters toward lower frequency and broadband band gap are provided based on the parametric study results. In addition, the higher-order band-folding strategy is proposed. It is shown that a multi-folding PCSB can produce more band gaps. However, through two examples, i.e., second-folding and third-folding PCSBs, it is known that simply increasing the folding order may not be effective and even could deteriorate the vibration attenuation ability. In summary, this work explores a general strategy for designing sandwich beams with low-frequency and broadband vibration suppression ability.

Study on Band Gap Characteristics of Phononic Crystal Double-Layer Beam Structure Attached by Multilayer Cylinder

Intended for the vibration and noise control problems faced by many engineering fields, a fresh variety of phononic crystal beam structure was constructed by attaching a one-dimensional periodic multilayer cylinder to a double-layer beam structure. Utilizing the finite element method and the Bloch theorem, the vibration modes of the band structure, the critical point of the band gap and the associated finite structure’s vibration transmission is estimated, and then the band gap characteristics of the structure are comprehensively studied. The results show that reasonable parameter design can achieve vibration and noise control in a certain frequency range. Based on the modal analysis, the mechanism of band gap opening is revealed. By comparing the single-layer beam and double-layer beam with the same parameters, the advantages of the double-layer beam in vibration reduction and noise reduction are shown. The study’s findings offer a fresh concept for ship engineering disciplines including vibration and noise reduction technology.

Investigation on band gap mechanism and vibration attenuation characteristics of cantilever-beam-type power-exponent prismatic phononic crystal plates

This study proposes a novel phononic crystal (NPC) configuration composed of power-exponent prismatic phononic crystal (EPC) and cantilever beams to address the vibration problem of the ship plate structure. Through the dispersion curve, it is found that NPC has complete flexural band gaps of low-, medium-, and high-frequency. The medium-frequency and high-frequency band gaps are the coupled band gaps induced by local resonance under the superimposition between the resonance of cantilever beams and the energy concentration effect in the primary structure. It is found that the addition of cantilever beam can make EPC produce low-frequency, and medium-frequency band gaps and broaden high-frequency band gap. Changing the parameters of the cantilever beam can adjust the low-, medium-, and high-frequency band gaps at the same time. Changing the parameters of the power index prism can adjust the medium-frequency and high-frequency band gap without changing the low-frequency band gap. The present simulation and model tests validated the above conclusions. Compared with the traditional embedded ABH model, NPC cannot weaken the structural strength with greater flexibility in application, suggesting broad application prospects in ship structure engineering. The present research results can support the vibration control of ship structures.

Complex band structure and evanescent wave propagation of composite corrugated phononic crystal beams

Complex band structure and evanescent wave propagation of composite corrugated phononic crystal beams

Flexural wave bandgap properties of phononic crystal beams with interval parameters

Uncertainties are unavoidable in practical engineering, and phononic crystals are no exception. In this paper, the uncertainties are treated as the interval parameters, and an interval phononic crystal beam model is established. A perturbation-based interval finite element method (P-IFEM) and an affine-based interval finite element method (A-IFEM) are proposed to study the dynamic response of this interval phononic crystal beam, based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined. Finally, two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM. Results show that the safe bandgap range may even decrease by 10% compared with the deterministic bandgap without considering the uncertainties.

Meta-Kagome lattice structures for broadband vibration isolation

One-dimensional (1D) phononic crystal (PC) beams have been extensively studied due to their bandgap properties, but the idea of using this functional beam components to form three-dimensional (3D) periodic structures has rarely been mentioned. In this paper, the PC beam element is used to replace the ordinary member of the conventional Kagome lattice structures, thus, a meta-Kagome lattice (MKL) structure is innovatively constructed with broadband vibration isolation performance. The dispersion analysis is performed to reveal the mechanism of bandgap formation and the reason of getting broad bandgaps. Three kinds of MKL structures, namely, with triangular, rectangular and hexagonal pyramids are designed. The vibration transmission properties of the MKL columns with or without interfaces are studied to illustrate the isolation effect. Moreover, the vibration isolation performance of the sandwich structures composed of MKL cores is also studied, and the influence of the skin characteristics on the properties is discussed. Vibration transmission tests were conducted to verify the results. This work provides a new method to develop 3D multi-functional lattice structures, especially for load-bearing and vibration reduction.

Broadband and controllable topological interface state of longitudinal wave in pillared phononic crystal beams

We design one-dimensional broadband and controllable pillared phononic crystal (PC) beams composed of magnetic pillars deposited on an Aluminum beam to realize the tunable topological interface state of longitudinal wave. Relying on the adjustable geometrical parameters in a unit cell (i.e., the distance between magnetic pillars and the number of magnetic pillars), the topological transition point can be easily generated and tuned, the controllable topological interface state of longitudinal wave can be obtained within band gap and at the interface of two pillared PC beams with different topological phases. The localization of topological interface state decreases gradually through increasing the number of magnetic pillars. The topological interface state has also been experimentally verified in the proposed PC systems. This work provides presents a simple method to flexibly control the topological interface state, further facilitating the potential applications of elastic topological systems such as energy harvesters, wave filters and switches.

Analysis of flexural and torsional vibration band gaps in phononic crystal beam

Phononic crystals (PCs) play an important role in the reduction of vibration within a targeted frequency range. Most research of the one-dimensional PCs focuses on the properties or applications of the flexural band gaps; however, practically, the broadband environmental excitations also induce the torsional vibration. Hence, this paper studies a two-degrees-of-freedom local resonance (2DOF-LR) phononic crystal, which can both suppress the propagation of flexural and torsion waves in the same frequency range. To improve the computational efficiency, the Timoshenko theory with a modified transfer matrix (MTM) approach is used for flexural vibration band structure analysis. Through the finite element method (FEM), the vibration attenuation characteristics of the structure within the band gaps are verified. A comprehensive study is conducted to investigate the effects of geometric and material parameters on the attenuation characteristics of the phononic crystal. Finally, a prototype of the proposed phononic crystal is fabricated for the vibration experiment. It is worth noting that a novel experimental setup using the lever principle is designed in this paper to verify the torsional band gap. The frequency ranges of the experimental vibration attenuation match well with the numerical results.

Band structure analysis of Green-Naghdi thermoelastic wave propagation in a GPLs/CNTs-reinforced metamaterial with energy dissipation

In this paper, the band structure analysis of the thermoelastic wave propagation in a phononic crystal (PC), which it is reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs), is presented. The reinforced PC beam is made of periodic unit-cells including a metal section and a GPLs/CNTs-reinforced epoxy section. The Green-Naghdi theory of the generalized coupled thermoelasticity with energy dissipation and a new modified micromechanical model to predict the mechanical properties of the reinforced section are employed in the analysis. An analytical solution and the transfer matrix method are adopted to compute the band structures. The frequency band-gaps are obtained and the effects of the GPLs and CNTs volume fractions on the width and location of the band-gaps are analyzed and discussed in details. The results show that the GPLs influence the frequency band-gaps and the band structures of the thermoelastic wave propagation in the reinforced PC beam much more remarkably than the CNTs. The proposed analytical solution method, the modified micromechanical model and the presented results can be employed for designing the reinforced PC structures by the GPLs, CNTs or both of them and also for tuning the band-gaps in the future researches.

Automated design of phononic crystals under thermoelastic wave propagation through deep reinforcement learning

This article presents a novel concept of deep reinforcement learning (DRL) to facilitate the reverse design of layered phononic crystal (PC) beams with anticipated band structures focusing on the band structure analysis of thermoelastic waves propagating. To this end, we define the reverse design of phononic crystals (PCs) as a game for the DRL agent. To achieve the desired band structure, the DRL agent needs to obtain the topological system of PC. We trained a DRL agent called deep deterministic policy gradient (DDPG). An environment is developed and used to simulate the reverse design of layered PCs with the acquisition of a reward function. The presented reward function encourages the agent to achieve the desired bandgaps. The trained DDPG agent can maximize the game’s score by attaining the desired bandgap. The presented concept allows the user to instantly generate the design parameters through the trained DDPG agent without unnecessary search over the design space. We demonstrated that the DRL agent could perform very well for the automated design of PCs with hundred design cases.

Periodically alternated elastic support induced topological phase transition in phononic crystal beam systems

Determining strong robustness in flexural wave propagation in beam systems has always been a promising achievement with various real-life applications such as energy harvesting and waveguiding. In this manuscript, the bending characteristics of a phononic crystal beam on periodically alternated linear elastic support systems with topologically protected wave propagation are proposed. Based on the Timoshenko beam theory, general solutions of this periodic beam-foundation topological system are obtained. Subsequently, by applying the Bloch theory, the dispersion relation is obtained using the transfer matrix method. Comparing with finite element numerical solutions, excellent agreement is observed with only a minor difference due to the assumptions in the Timoshenko beam theory. Generally, any breaking of spatial symmetry in beam systems can be achieved by changing geometry of beam cross-sections or tuning the material properties of substructures. We herein propose a new approach to break the spatial symmetry, i.e., tuning the elastic stiffnesses of the periodically alternated elastic supports. It is found that beam bending on an infinite continuously distributed elastic foundation leads to a band-crossing point. After tuning the elastic support stiffness in a periodic manner, the band-crossing point is broken and a new bandgap appears due to the breaking of structural symmetry. Further, a mode shape inversion and Zak phase transition are captured. Based on a unit cell analysis, we examine the topologically protected interface modes in an array constructed with periodically arranged unit cells with two corresponding phase states. Furthermore, several numerical examples are used to demonstrate the defect- and disorder-immune properties in this one-dimensional topological system. This new proposed general mechanism can be extended to establish topological phase transitions in other mechanical and dynamic systems.

Flexural wave energy harvesting by the topological interface state of a phononic crystal beam

In this study, we design the 3D-printed phononic crystal (PnC) beam with the topological interface state for harvesting the mechanical energy of flexural waves. The PnC beam is formed by arranging periodic grooves on its surface. The PnC beam with either topologically trivial or non-trivial phase can be achieved via changing the distance between the grooves. The topological interface state is then generated by combining two PnCs with distinct topological phases. The existence of the interface state of the PnC beam is verified both numerically and experimentally. To convert the mechanical energy into the electricity, a piezoelectric disc is attached at the interface of the proposed PnC beam. Compared to the reference beam harvester, the measured output power is significantly amplified by the PnC harvester at the frequency corresponding to the interface state. Furthermore, the PnC beam energy harvester based on the topological state exhibits robustness against geometrical disorders.

A deep learning approach based on a data-driven tool for classification and prediction of thermoelastic wave’s band structures for phononic crystals

This article deals with the data-driven prediction of the band structures of thermoelastic waves in the nano-scale phononic crystal beams considering nano-size effects. The computational intelligence methods are developed using a data-driven tool to discover the design space of phononic crystals, which are subjected to thermal shock loading. For this purpose, a rich dataset is created utilizing an analytical solution, which was previously proposed for the nonlocal coupled thermoelasticity analysis in a nano-sized phononic crystal beam. The preprocessing methods, hyperparameters optimization, and shallow and deep neural networks are used to classify and predict the bandgaps. Also, according to the created dataset and the data-driven method, the phononic crystal feature importance and behavior based on the design parameters are assessed in detail. The detailed investigation reveals the importance of the design parameters according to the deep neural network’s results. It is demonstrated by numerical results that the proposed final data-driven model can predict the characteristics of the phononic crystals pretty well. Also, the results show that the deep neural network outperforms the shallow neural network for the classification and prediction of the band structures. The final results can be a helpful tool to have a fast numerical framework for the prediction of photonic crystals’ bandgaps before the application of time-consuming accurate frameworks.

Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties

Periodic structures can be designed to exhibit elastic wave propagation band gap behaviour by varying material or geometrical properties, i.e. phononic crystals, or by periodically distributed resonators or boundary conditions, i.e. acoustic metamaterials, with various applications in passive noise and vibration control. However, variability in the manufacturing process causes material and geometry uncertainties that affect their band gap robustness and consequently their dynamic attenuation performance. In this work, the effects of slowly varying spatial properties on the vibration suppression performance of metamaterials and phononic crystals are investigated. The spectral element and the wave and finite element approaches are used for modelling the unit cells such that a wave-like interpretation can be derived for nearly-periodic structures. A beam with evenly spaced attached resonators and an undulating beam are analysed. In both cases, the band gap formation is investigated considering both non-uniform deterministic and spatially stochastic material and geometric variability. The proposed approach provides a framework to represent variability and randomness with spatial correlation of the periodic unit cell and then to assess their effects on the vibration suppression performance. It is shown that even a slowly varying spatial profile, or the correlation length in the case of random fields, plays a role on the band gap performance and that the presence of a critical section, i.e. a transition region between propagating and non-propagating waves, can significantly affect the band gap width and the amplitude of vibration attenuation. Moreover, it is shown the slowly varying approach is suitable to represent the ensemble statistics of band gaps, even considering the occurrence of such critical sections.