Modal Energy Research Articles

High-Order Theory Approach for Debonded Sandwich Panels—Part I: Formulation and Displacement Fields

Abstract A high-order theory is developed to model asymmetric sandwich panels with face/core debonds and to provide a solution for the energy release rate and mode mixty. This new theory is a novel re-formulation of the extended high-order sandwich panel theory (EHSAPT), in which faces and core were originally considered to be perfectly bonded. In the new formulation, a sandwich panel with an interfacial debond can be divided into three parts, namely, the debonded part, the substrate part, and the base part. A new high-order displacement pattern is developed to describe the core’s deformation in the substrate part, and it is compatible with the displacement field of the core in the base part. In addition, capturing the high-order shear deformation of the core, this new theory is able to take the transverse compressibility and axial rigidity of the core into account. In this Part I of this two-part research, we focus on the formulation and the displacement field. In Part II, the fracture parameters, namely, the energy release rate and the mode mixity will be addressed. Accordingly, in this paper, results for the deformation of the debonded panel are produced and compared with the ones given by the finite element method with a very fine mesh. The accuracy is proven for a wide range of core materials and for a wide range of debond lengths.

High-Order Theory Approach for Debonded Sandwich Panels—Part II: Energy Release Rate and Mode Mixity

Abstract A novel re-formulation of the extended high-order sandwich panel theory (EHSAPT) for the case of a face/core debond was done in Part I of this two-part series of papers. This high-order theory is capable of including not only the transverse shear but also the transverse compressibility and axial rigidity of the core. In this Part II paper, a closed-form expression for the energy release rate is derived in terms of the equivalent resultant forces and displacements at the two edge sections. Together with the crack surface displacement method, the mode mixity is determined from the displacement field. Benefiting from the accurate displacement field given by the proposed theory, this paper presents a self-contained approach for the mode mixity that is free of parameters that need to be determined via additional numerical simulations (i.e., no extrapolation needed). Results are compared with the ones given by the classical theory in the literature and the ones given by the finite element method with a very fine mesh. The accuracy is proven for a wide range of core materials from the stiffer cores to the very compliant ones, and for a wide range of debond lengths.

Highly Efficient and Linearly Polarized Light Emission of Micro-LED Integrated with Double-Functional Meta-Grating.

Linearly polarized micro light-emitting diodes (LP-Micro-LEDs) exhibit exceptional potential across diverse fields. The existing methods to introduce polarization to initially unpolarized Micro-LEDs and to further enhance the degree of polarization are, however, at the expense of low luminous efficiency. We fabricated a GaN-based blue Micro-LED integrated with a Al nanograting and a specially designed Ag/GaN meta-grating, which overcomes the dilemma between the luminous efficiency and polarization degree by simultaneously introducing the effects of mode selection and energy recycling. The fabricated LP-Micro-LED achieves an average polarization extinction ratio (ER) of 21.92 dB within ±60°, showing a 2.04-fold increase in efficiency and a 1.32-fold increase in ER compared to the Ag reflector design. This approach opens the way toward the next generation of high-efficiency and low-cost optoelectronic devices in encryption, displays, optical communication, and medicine.

Shaping Quantum Noise through Cascaded Nonlinear Processes in a Dissipation-Engineered Multimode Cavity

Multimode quantum light is enticing for several applications, spanning imaging, spectroscopy, communication, and more. Parametric nonlinear processes have been vital in realizing squeezed and other quantum states of light. However, most work exploiting these processes has focused on generating multimode squeezed vacua and squeezing in mode superpositions (supermodes). Bright squeezing in multiple discrete frequency modes, if realized, could unlock novel applications in quantum-enhanced spectroscopy and optical quantum computing. Here, we show how dissipation engineering of a multimode nonlinear cavity with cascaded three-wave-mixing processes allows us to shape above-threshold frequency combs that feature strong single-mode output amplitude noise squeezing over 10 dB below the shot-noise limit, tunable across the comb. In addition, we demonstrate squeezing for multiple discrete frequency modes above threshold. This bright squeezing arises from enhancement of the (noiseless) nonlinear rate relative to decay rates in the system due to the cascaded generation of photons in a single idler “bath” mode. A natural consequence of the strong nonlinear coupling in our system is the creation of an effective cavity in the synthetic frequency dimension that sustains Bloch oscillations in the modal energy distribution. Bloch mode engineering could provide an opportunity to better control nonlinear energy flow in the synthetic frequency dimension, with exciting applications in quantum random walks and topological photonics. Lastly, we show evidence of long-range correlations in amplitude noise between discrete frequency modes, enabling long-range entanglement in a synthetic frequency dimension and providing a new resource for quantum communication. Published by the American Physical Society 2024

Energy crisis of 2021–2022 as a harbinger of a change in the global energy system

The energy mode concept, has been characterized. Energy patterns types, history of their formation and development have been summarized. The prerequisites for forming a new energy mode based on the increasing share of renewable energy sources and hydrogen raw materials in the energy production structure have been highlighted. The change of the energy structure will take place in the coming decades. The following scientific methods of research were used in the paper: literature analysis and analysis of statistical data. Data for the period from 1965 to 2022 were used. The purpose of the study is to identify the role of the energy crisis of 2021–2022 as a factor contributing to a new energy structure formation that will be implemented in the coming decades. The subject of the study is to analyze and evaluate the change of the energy pattern in the international energy market, and the object of the study is the world energy market.

Particle flow simulation of fracture responses and anchoring mechanisms of cemented materials subjected to static-dynamic combined loads

This study aims to reveal the evolution of energy, cracks, force chain, and ultimate failure modes of cemented gangue backfill materials subjected to static-dynamic combined loads, as well as the reinforcement mechanisms of pre-tightening bolts on mechanical performance and progressive damage. The particle flow models with various fractal dimensions (D) of particle size distribution were established, and irreversible damage accumulation during dynamic loading was achieved through a nonlinear parallel-bonded stress corrosion model. The simulation results show that, compared to uniaxial compression, the energy release lag at peak strength is eliminated under static-dynamic combined loading, and the brittle failure feature becomes more pronounced. The filling effect of fine aggregates optimizes the uniformity of internal stress distribution, with the peak parallel bond strain energy increasing by 9.60%, 8.42%, and 14.81% as D increases from 2.1 to 2.85. At initial dynamic loading, the instantaneous increase in axial stress reaches the crack initiation stress, significantly increasing the number of tensile cracks. As pre-static load increases, the model sample is subjected to a higher internal stress environment during dynamic loading, leading to more remarkable force chain breakage observed at peak strength. Shear failure, including oblique shear failure and tensile-shear mixed failure, is the primary failure mode under static-dynamic combined loading. The additional constraints provided by bolts increase strain energy stored in particles and contacts and reduce the crack number at peak strength, with the constraining effect exhibiting more pronounced as preload increases. For anchored samples, the end of pallets is the initiation point for shear cracks, which extend along the edge of the preload concentration area, while tensile cracks initiating from the sample ends propagate toward the preload concentration area.

Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surfaces Empowered Cooperative Rate Splitting with User Relaying

In this work, we unveil the advantages of synergizing cooperative rate splitting (CRS) with user relaying and simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR RIS). Specifically, we propose a novel STAR RIS-assisted CRS transmission framework, featuring six unique transmission modes that leverage various combinations of the relaying protocols (including full duplex-FD and half duplex-HD) and the STAR RIS configuration protocols (including energy splitting-ES, mode switching-MS, and time splitting-TS). With the objective of maximizing the minimum user rate, we then propose a unified successive convex approximation (SCA)-based alternative optimization (AO) algorithm to jointly optimize the transmit active beamforming, common rate allocation, STAR RIS passive beamforming, as well as time allocation (for HD or TS protocols) subject to the transmit power constraint at the base station (BS) and the law of energy conservation at the STAR RIS. To alleviate the computational burden, we further propose a low-complexity algorithm that incorporates a closed-form passive beamforming design. Numerical results show that our proposed framework significantly enhances user fairness compared with conventional CRS schemes without STAR RIS or other STAR RIS-empowered multiple access schemes. Moreover, the proposed low-complexity algorithm dramatically reduces the computational complexity while achieving very close performance to the AO method.

Linear and energy stability analyses of onset of Darcy-Bénard convection due to combustion

Purpose This paper aims to perform a linear and nonlinear analysis of the stability of a chemically reacting Newtonian fluid in a Darcy porous medium. The purpose of selecting both analyses is to investigate the probability of subcritical instability resulting from combustion. Design/methodology/approach The chemical reaction problem in a Darcy porous medium with Arrhenius kinetics is considered. The effect of the Frank-Kamenetskii number on the linear and nonlinear stability is analysed. The critical eigenvalue is obtained numerically by the Chebyshev pseudospectral method for both analyses. Findings The inference from the two analyses is that in the presence of combustion, the situation in the Darcy−Bénard convection problem can lead to subcritical instability. It is found that the value of the critical Frank-Kamenetskii number keeps on changing as the lower boundary temperature changes, beyond the critical value of the Frank-Kamenetskii number where the system splits, going from a steady condition to an explosive state. Originality/value The Chebyshev pseudospectral approach has been applied to address the combustion problem in this research. The normal mode methodology and energy method are used for linear and nonlinear analyses, and the effects of nonlinear factors are examined by comparing the outcomes.

Test rig for validating the integrated motion measurement of flexible beams

AbstractThe fundamental principle of integrated motion measurement (IMM) is integrated navigation with inertial sensors combined with, for example, a satellite navigation receiver. Accordingly, IMM makes use of the specific advantages of complementary sensors and blends them in a filter algorithm. To meet requirements in advanced motion measurements, for instance, for structural health monitoring or for structural control purposes, the approach of a single rigid body like in classical navigation no longer holds for IMM. As a solution, additional degrees of freedom (DOFs) for the moving structure are introduced, which represent deformations and allow the navigated body to be treated as a flexible structure. To cover a variety of flexible deformation shapes, a sufficient number of distributed inertial sensors is required. To restrict accumulating errors of these sensors, additional structural measurements for aiding are necessary. The signals of the inertial sensors and the aiding measurements are fused by an extended Kalman filter (EKF) to obtain an optimal estimation of the usual navigation states, extended by the deformation variables. The contribution presents the preparation of the experimental validation of an IMM system for a flexible structure, which represents an idealization of a wing or rotor blade by a movable beam. The mechanical and electrical setup of a test rig is described. Furthermore, the simulation of the test configuration, that is the model of a test beam with a variety of distributed sensors for generating artificial measurements as a test reference, is discussed. Finally, for an optimal sensor placement, the two methods of effective independence and maximization of modal energy are compared and experimentally tested for different amounts of additional flexible DOFs.

Experimental study on the effect of wall proximity on the flow around a cylinder under an axial magnetic field

Investigations are conducted on the effect of wall proximity on the flow around a cylinder under an axial magnetic field, using the electrical potential probe technology to measure the velocity of liquid metal flow. The study focused on the impact of the inlet velocity of the fluid, the magnetic field and wall proximity on the characteristics of velocity fields, particularly on the vortex-shedding mode. Based on different magnitudes of the magnetic field and the distance from the cylinder to the duct wall, three types of vortex-shedding modes are identified, (I) shear layer oscillation state, (II) quasi-two-dimensional vortex-shedding states and (III) transition of the magnetohydrodynamic to hydrodynamic Kármán street. The transitions between these modes are analysed in detail. The experimental results show that the weak wall-proximity effect leads to the formation of the Kármán vortex street, while a reverse Kármán vortex street and secondary vortices emerge under a strong wall-proximity effect. It is noticed that the Kelvin–Helmholtz instability drives vortex shedding under regime I, leading to an increase in the Strouhal number (St) with stronger magnetic fields. Additionally, under a strong axial magnetic field, the wall-proximity effect (‘Shercliff layer effect’) promotes the instability of shear layers on both sides of the cylinder. These unique coupling effects are validated by variations in modal coefficients and energy proportions under different vortex-shedding regimes using the proper orthogonal decomposition method.

Performance enhancement of ammonium dinitramide (ADN)-based thruster using coaxial dielectric barrier discharge

To enhance the performance of conventional ADN-based catalytic ignition thrusters, a plasma-assisted thruster was developed employing coaxial cylinder electrodes within a 1N-class thruster configuration. Steady-state ignition tests conducted on the experimental bench, demonstrated high repeatability in an atmospheric environment. High-speed imaging and proper orthogonal decomposition (POD) analysis revealed that plasma reduced the pulsation energy of the first mode from 84.96% to 75.21%, improving flame stability and concentrating the flame in the upstream part of the combustion chamber, without propagating toward the nozzle. Experimental evolution spectra of H2O, NH3, and CO2 were obtained through near-infrared (NIR) and mid-infrared (MIR) spectrometers to probe chemical dynamics. The peak radiation intensity of H2O and NH3 in the 1.6-2.4 μm range was observed to precede by about one second with plasma compared to the catalyst-only case. An increased radiation intensity ratio of H2O/NH3 in the presence of plasma indicated plasma's promotion of H2O production and NH3 consumption. Furthermore, the radiation intensity of CO2 increased by approximately 100-fold in the plasma-assisted case, indicating accelerated chemical reactions and more complete combustion. These findings highlight the potential of plasma-assisted technologies to improve the efficiency of ionic liquid-based thrusters and provide a foundation for future advancements in plasma-assisted propulsion systems.

Energy cascade and Burgers turbulence in the Fermi-Pasta-Ulam-Tsingou chain.

The dynamics of initial long-wavelength excitations of the Fermi-Pasta-Ulam-Tsingou chain has been the subject of intense investigations since the pioneering work of Fermi and collaborators. We have recently found a regime where the spectrum of the Fourier modes decays with a power law and we have interpreted this regime as a transient turbulence associated with the Burgers equation. In this paper we present the full derivation of the latter equationfrom the lattice dynamics using an infinite-dimensional Hamiltonian perturbation theory. This theory allows us to relate the time evolution of the Fourier spectrum E_{k} of the Burgers equationto that of the Fermi-Pasta-Ulam-Tsingou (FPUT) chain. As a consequence, we derive analytically both the shock time and the power law -8/3 of the spectrum at this time. Using the shock time as a unit, we follow numerically the time evolution of the spectrum and observe the persistence of the power -2 over an extensive time window. The exponent -2 has been widely discussed in the literature on the Burgers equation. The analysis of the Burgers equationin Fourier space also gives information on the time evolution of the energy of each single mode which, at short time, is also a power law depending on the kth wavenumber E_{k}∼t^{2k-2}. This approach to the FPUT dynamics opens the way to a wider study of scaling regimes arising from more general initial conditions.

Office Furniture Partition Space Design Based on Intelligent Domain Perception and Digital Twins

With the increasing focus on sustainable development in society, intelligent domain perception and digital twin technology can be used to evaluate and optimize the design of office furniture. This study analyzed sensor data through machine-learning and data-mining techniques to identify patterns and trends in the office environment. Simultaneously, a digital twin model of office furniture partition space was established to simulate the usage of furniture partition space throughout its full lifecycle. When 50% of nodes fail, the minimum transmission energy mode was significantly better than the maximum greedy forwarding mode in terms of cumulative throughput. The distributed, event-based, unsupervised clustering algorithm successfully reduced communication energy consumption, and the lightweight gradient boosting machine algorithm achieved the best design optimization rate, with an improvement of 0.53%. The ratio of value-added time to non-value-added time increased by 56.3%. The study aimed to provide innovative ideas for the development of intelligent office environments, promote the design of office furniture toward intelligence and sustainability, and improve the adaptability and efficiency of the work environment.

Goffin's cockatoos use object mass but not balance cues when making object transport decisions.

Utilising weight cues can improve the efficiency of foraging behaviours by providing information on nutritional value, material strength, and tool functionality. Attending to weight cues may also facilitate the optimisation of object transport. Though some animals' ability to assess weight cues has been determined, research into whether they can apply weight assessment during practical decision making is limited. In this study, we investigate whether Goffin's cockatoos (Cacatua goffiniana) account for relative weight and unequal versus equal weight distribution when making object transport decisions, and whether sensitivity to these cues varies depending on transport mode. We conducted a series of binary choice experiments in which birds could choose to transport one of two identical, non-functional, equally rewarded objects differing only in overall weight (experiment 1) or weight balance (experiment 2) over a short distance. We found that in experiment 1, Goffin's cockatoos preferred to transport light objects over heavy objects and seemed to rely more on weight cues to inform decisions over time, whereas in experiment 2, weight balance cues were ignored. Contrary to our predictions, Goffin's cockatoos did not show increased preference for lighter or more balanced objects when employing higher energy transport modes (flight) compared to lower energy modes (walking). We suggest that this may be due to an insufficient difference in physical effort between transport modes due to the short distance travelled. These findings provide the first evidence of weight cues being considered to optimise object transport in birds.

Reference frequency variance-based rapid identification method for vortex flow rate under mixed vibration interference

Pipeline systems in industrial applications may encounter strong mixed vibration interference, resulting in measurement errors of vortex flowmeters. Current research primarily addresses single types of vibration interference. Various signals output by vortex flow sensors under diverse operating conditions were analyzed to tackle the issue of mixed vibration interference. The amplitude and frequency characteristics of transient impact-type interferences were studied. The differences in frequency fluctuations between periodic interferences and periodic signals were investigated. Then, a method based on reference frequency variance was proposed to resist mixed vibration interference. The primary calculation load of this method arises from the execution of Fast Fourier Transform (FFT). To meet the instrument requirements of low-power consumption and real-time performance, a multipoint FFT method based on a low-power accelerator built-in microcontroller was proposed, which remarkably improved the calculation speed of multipoint FFT and conserved storage space. The reference frequency variance-based antimixed vibration interference algorithm was implemented in real time using a low-power vortex flowmeter system developed by our team, and an antimixed vibration interference gas flow verification experiment was conducted. The method can accurately identify vortex flow signals when the interference energy of the periodic type and the main mode energy of the transient impact surpasses the energy of the flow signal.

Failure mechanisms of coarse-grained sandstone under pure mode I/II loading: insights from energy evolution and acoustic emission

ABSTRACT Tensile and shear failure are the main damage modes of rocks in geotechnical engineering. To investigate the energy evolution and failure characteristics of coarse-grained sandstone during pure mode I/II loading, loading-unloading tests were performed on cracked straight-through Brazilian discs (CSTBD) with different unloading levels (i), and its acoustic emission (AE) signals and microstructure were monitored. The results show that the AE signals of the CSTBD are negligible before the peak load (Mode I), or appear when the axial load exceeds a stress threshold and then increases significantly before the peak load (Mode II), and the Kaiser effect was observed in the second loading stage. The specimens’ input, elastic and dissipative energies varied quadratically with i. The elastic energy is always greater than the dissipative energy (Mode I), whereas the dissipative energy exceeds the elastic energy at i < 0.5 (Mode II). The crack propagation paths start from the crack tip and extend rapidly and straightly (Mode I) or slowly in the form of wing crack (Mode II) to the loading point. The microstructures of the specimens are mainly intergranular fracture (mode I) and transgranular fracture (mode II). The results provide references for studying energy evolution and failure mechanisms of rocks under mixed modes I+II/I+III loading.

Synthesis, Biological Evaluation, and Molecular Docking Studies of Indole-Based Heterocyclic Scaffolds as Potential Antibacterial Agents.

Indole-based heterocyclic scaffolds have become increasingly important in medicinal chemistry due to their notable pharmacological and biological properties. Their role in the discovery and development of innovative drugs for treating various diseases highlights their value. This study aimed to synthesize C3-indole derivatives linked to various heterocyclic scaffolds, including thiophenes, thiazolidine-4-ones, and 1,3,4-thiadiazoles, via the reaction of ethylthioacetanilide 2 with different α-haloketones.The structures of the target compounds were established using 1H and 13C nuclear magnetic resonance spectroscopy, mass spectrometry, infrared spectroscopy, and elemental analysis. The synthesized compounds were tested for antimicrobial activity against different microbes: S. aureus ATCC 6538 (Gram-positive bacteria), E. coli ATCC 25933 (Gram-negative bacteria), C. albicans ATCC 10231 (yeast), and fungi (A. niger NRRL-A326). Thiophene 6a, thiazolidine-4-one 8, and compound 10d exhibited the highest antimicrobial activities. The molecular docking study showed that compounds 2, 4, 6a, and 6c had good binding energy and favorable binding modes of interactions with the DNA gyrase B enzymes (PDB: 3 U2D) and (PDB: 1S14). The results showed that the NH group of the indole in compounds 2 and 4, together with the nitrile group (CN), played an important role in inhibiting DNA gyrase B of S. aureus, PDB: 3 U2D. Furthermore, the NH of the indole ring, together with the ethylamino group of compound 2, was crucial in inhibiting DNA gyrase B of E. coli, PDB: 1S14. These findings may encourage researchers to develop more effective C3-indole derivatives in their search for antimicrobial drugs.

Impact resistance performance of 3D woven TZ800H plates with different textile architecture

Two typical methods commonly used to improve the mechanical properties and impact resistance properties of 3D woven composites are studied, namely weave pattern and layered architectures. The mechanical property and impact resistance performance were studied by utilising the quasi-static compressive test, split Hopkinson pressure bar (SHPB) test and ballistic impact test. The compressive responses in warp and weft directions with different strain rates 0.001, 500 and 1300 s-1 were presented and analysed, providing strain rate influence on the material strength of different 3D woven composites. The impact resistance performance including damage mode, ballistic limit and specific energy absorption of three structures were discussed through impact tests. The results reveal that as the strain rate increases, the compressive strength and Young's modulus in both directions of 3D woven composites exhibit a significant increase. The compressive strength and modulus in the warp direction of the composites can be enhanced by using shallow interlocking of the warp tow or layered architectures. However, the two methods degrade the failure strain and weaken the strain rate strengthening effect of compressive strength in the weft direction, resulting in a significant decrease in the average strain energy density. For the ballistic impact case, the crimp of warp tows would decrease its load-bearing capacity, while resisting matrix crack growth under the ballistic impact. The significant reduction in the average strain energy density in the weft direction leads to a decrease in ballistic limit and specific energy absorption capacity under ballistic impact.

Discovery of novel fused-heterocycle-bearing diarypyrimidine derivatives as HIV-1 potent NNRTIs targeting tolerant region I for enhanced antiviral activity and resistance profile

As an important part of anti-AIDS therapy, HIV-1 non-nucleoside reverse transcriptase inhibitors are plagued by resistance and toxicity issues. Taking our reported XJ-18b1 as lead compound, we designed a series of novel diarypyrimidine derivatives by employing a scaffold hopping strategy to discover potent NNRTIs with improved anti-resistance properties and drug-like profiles. The most active compound 3k exhibited prominent inhibitory activity against wild-type HIV-1 (EC50 = 0.0019 μM) and common mutant strains including K103 N (EC50 = 0.0019 μM), L100I (EC50 = 0.0087 μM), E138K (EC50 = 0.011 μM), along with low cytotoxicity and high selectivity index (CC50 = 21.95 μM, SI = 11478). Additionally, compound 3k demonstrated antiviral activity against HIV-2 with EC50 value of 6.14 μM. The enzyme-linked immunosorbent assay validated that 3k could significantly inhibit the activity of HIV-1 reverse transcriptase (IC50 = 0.025 μM). Furthermore, molecular dynamics simulation studies were performed to illustrate the potential binding mode and binding free energy of the RT-3k complex, and in silico prediction revealed that 3k possessed favorable drug-like profiles. Collectively, 3k proved to be a promising lead compound for further optimization to obtain anti-HIV drug candidates.

Analysis of Influence of Excitation Source Direction on Sound Transmission Loss Simulation Based on Alloy Steel Phononic Crystal

As a type of locally resonant phononic crystal, alloy steel phononic crystals have achieved notable advancements in vibration and noise reduction, particularly in the realm of low-frequency noise. Their exceptional band gap characteristics enable the efficient reduction of vibration and noise at low frequencies. However, the conventional transmission loss (TL) simulation of finite structures remains the benchmark for plate structure TL experiments. In this context, the TL in the XY-direction of phononic crystal plate structures has been thoroughly investigated and analyzed. Given the complexity of sound wave incident directions in practical applications, the conventional TL simulation of finite structures often diverges from reality. Taking tungsten steel phononic crystals as an example, this paper introduces a novel finite element method (FEM) simulation approach for analyzing the TL of alloy steel phononic crystal plates. By setting the Z-direction as the excitation source, the tungsten steel phononic crystal plate exhibits distinct responses compared to excitation in the XY-direction. By combining energy band diagrams and modes, the impact of various excitation source directions on the TL simulations is analyzed. It is observed that the tungsten steel phononic crystal plate exhibits a more pronounced energy response under longitudinal excitation. The TL map excited in the Z-direction lacks the flat region present in the XY-direction TL map. Notably, the maximum TL in the Z-direction is 131.5 dB, which is significantly lower than the maximum TL of 298 dB in the XY-direction, with a more regular peak distribution. This indicates that the TL of alloy steel phononic crystals in the XY-direction is closely related to the acoustic wave propagation characteristics within the plate, whereas the TL in the Z-direction aligns more closely with practical sound insulation and noise reduction engineering applications. Therefore, future research on alloy steel phononic crystal plates should not be confined to the TL in the XY-direction. Further investigation and analysis of the TL in the Z-direction are necessary. This will provide a novel theoretical foundation and methodological guidance for future research on alloy steel phononic crystals, enhancing the completeness and systematicness of studies on alloy steel phononic crystal plates. Simultaneously, it will advance the engineering application of alloy steel phononic crystal plates.